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		<title>Trick-or-Treaters Are Using the Executive Mindset</title>
		<link>https://www.manhattanprep.com/gmat/blog/executive-mindset-gmat-halloween/</link>
		
		<dc:creator><![CDATA[Patrick Tyrrell]]></dc:creator>
		<pubDate>Mon, 08 Oct 2018 18:42:22 +0000</pubDate>
				<category><![CDATA[Business Mindset]]></category>
		<category><![CDATA[Challenge Problem]]></category>
		<category><![CDATA[Critical Reasoning]]></category>
		<category><![CDATA[Data Sufficiency]]></category>
		<category><![CDATA[For Current Studiers]]></category>
		<category><![CDATA[Geometry]]></category>
		<category><![CDATA[GMAT 101]]></category>
		<category><![CDATA[GMAT Prep]]></category>
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		<category><![CDATA[GMAT Strategies]]></category>
		<category><![CDATA[GMAT Study Guide]]></category>
		<category><![CDATA[How to Study]]></category>
		<category><![CDATA[Quant]]></category>
		<category><![CDATA[Reading Comprehension]]></category>
		<category><![CDATA[Sentence Correction]]></category>
		<category><![CDATA[Taking the GMAT]]></category>
		<category><![CDATA[Verbal]]></category>
		<category><![CDATA[Absolute Value]]></category>
		<category><![CDATA[combinatorics]]></category>
		<category><![CDATA[Executive Mindset]]></category>
		<category><![CDATA[Executive Reasoning]]></category>
		<category><![CDATA[Functions]]></category>
		<category><![CDATA[inequalities]]></category>
		<category><![CDATA[probability]]></category>
		<category><![CDATA[Quadratics]]></category>
		<category><![CDATA[Rate Problems]]></category>
		<category><![CDATA[Sequences]]></category>
		<category><![CDATA[Subscripts]]></category>
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					<description><![CDATA[<p>Haaaappy Halloweeeeen, dear reader. What’s that? You’re already annoyed by the trite conceit of this conveniently-timed piece about trick-or-treating? (INTERNET: “Did Patrick stumble upon this trick-or-treating metaphor organically, or did he just think about the post date of the blog and reverse-engineer something safe—and topical for fifth graders?!”) Easy there, Bub. We don’t need a [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/executive-mindset-gmat-halloween/">Trick-or-Treaters Are Using the Executive Mindset</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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										<content:encoded><![CDATA[<p><img decoding="async" fetchpriority="high" class="alignnone size-full wp-image-16419" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/10/trick-or-treaters-using-executive-mindset-patrick-tyrrell.png" alt="Manhattan Prep GMAT Blog - Trick-or-Treaters Are Using the Executive Mindset by Patrick Tyrrell" width="1200" height="628" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/10/trick-or-treaters-using-executive-mindset-patrick-tyrrell.png 1200w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/10/trick-or-treaters-using-executive-mindset-patrick-tyrrell-300x157.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/10/trick-or-treaters-using-executive-mindset-patrick-tyrrell-768x402.png 768w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/10/trick-or-treaters-using-executive-mindset-patrick-tyrrell-1024x536.png 1024w" sizes="(max-width: 1200px) 100vw, 1200px" /></p>
<p><span style="font-weight: 400;">Haaaappy Halloweeeeen, dear reader. What’s that? You’re already annoyed by the trite conceit of this conveniently-timed piece about trick-or-treating?</span><span id="more-16391"></span></p>
<p><span style="font-weight: 400;">(</span><i><span style="font-weight: 400;">INTERNET</span></i><span style="font-weight: 400;">: “Did Patrick stumble upon this trick-or-treating metaphor organically, or did he just think about the post date of the blog and reverse-engineer something safe—and topical for fifth graders?!”)</span></p>
<p><iframe src="https://giphy.com/embed/uhDDQ9UNoXISQ" width="480" height="352" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p>
<p><a href="https://giphy.com/gifs/halloween-horror-uhDDQ9UNoXISQ"></a></p>
<p><span style="font-weight: 400;">Easy there, Bub. We don’t need a heckler.</span></p>
<p><span style="font-weight: 400;">If Hallowed Eve’s sacred thirty-first night of Octobreth weren’t so nigh, I would have called this “Kids at Amusement Parks Are Using the </span><a id="bloglink" href="https://www.manhattanprep.com/gmat/blog/2016/05/26/develop-a-business-mindset-to-maximize-your-roi-on-the-gmat/" target="_blank" rel="noopener"><span style="font-weight: 400;">Executive Mindset</span></a><span style="font-weight: 400;">.” Ya happy? It’s </span><i><span style="font-weight: 400;">kind of </span></i><span style="font-weight: 400;">a</span> <span style="font-weight: 400;">well-thought-out metaphor. </span></p>
<p><span style="font-weight: 400;">The underlying dilemma of amusement parks, trick-or-treating, and GMAT is that you have a lit fuse: a finite, insufficient amount of time to cash in on all the available opportunities. So you have to strategize where to invest your time and where to just say “skip it.”</span></p>
<h4><b>Trick-or-Treating Executive Mindset Dilemma #1</b></h4>
<p><i><span style="font-weight: 400;">Do you go for the homes of wealthy people?</span></i></p>
<p><iframe src="https://giphy.com/embed/HChtj3gzcVsXK" width="480" height="480" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p>
<p><a href="https://giphy.com/gifs/rich-the-simpsons-laughing-HChtj3gzcVsXK"></a></p>
<p><span style="font-weight: 400;">Pro: the candy’s usually more luxe (rich people have never even heard of fun size).</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">Con: the yards are so large that the commute time to the next house is brutal.</span></p>
<p><span style="font-weight: 400;">The opposite pendulum is an apartment complex. Door density reaches peak levels, but so does the risk of receiving unfamiliar treats. (“Sorry, sir, you said this Blartz bar is from… </span><i><span style="font-weight: 400;">Latvia</span></i><span style="font-weight: 400;">?”)</span></p>
<p><span style="font-weight: 400;">If I may presumptuously speak for everyone (</span><i><span style="font-weight: 400;">INTERNET</span></i><span style="font-weight: 400;">: “You may not!”), I think we can all agree that the best value trick-or-treating neighborhood is middle-class.</span></p>
<p><span style="font-weight: 400;">Similarly, on GMAT (</span><i><span style="font-weight: 400;">INTERNET: </span></i><span style="font-weight: 400;">“Oh, how rewarding, the completely-expected GMAT segue…”),</span> <span style="font-weight: 400;">we get the best score our current ability level will allow when we invest our time in modest but rewarding challenges. Looking for solutions that are too quick will leave your score with the acrid taste of a Blartz bar in its mouth. Walking super-long driveways to hopefully get a premium reward will leave you huffing and puffing to the next house, forcing you to go home long before you get a chance to visit the whole neighborhood.</span></p>
<h4><b>Trick-or-Treating Executive Mindset Dilemma #2</b></h4>
<p><span style="font-weight: 400;">Now that we’ve established the right rhythm for trick-or-treating (moderate walks, not sprints or marathons), let’s talk house selection.</span></p>
<p><span style="font-weight: 400;">There are a few houses we’re probably going to want to avoid:</span></p>
<ul>
<li style="font-weight: 400;"><b>Ol’ Man Squirrel Whisperer</b></li>
<li style="font-weight: 400;"><b>The House Where the Teenage Boys and Maybe the Dad Never Have Their Shirts On</b></li>
<li style="font-weight: 400;"><b>The Dunphys (not literally from </b><b><i>Modern Family</i></b><b>, but your local overachievers)</b></li>
<li style="font-weight: 400;"><b>The Green Party Birkenstock’d Couple Who Consider Flax Wafers a Non-Insult</b></li>
<li style="font-weight: 400;"><b>The House That’s Probably a Cult Because Their Clothing is at Best Perplexing</b></li>
</ul>
<p><iframe loading="lazy" src="https://giphy.com/embed/5xtDarEXlXBmnOuTh0k" width="480" height="267" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p>
<p><a href="https://giphy.com/gifs/puppy-corgi-pumpkin-5xtDarEXlXBmnOuTh0k"></a></p>
<p><span style="font-weight: 400;">Similarly, there are a few </span><i><span style="font-weight: 400;">GMAT</span></i><span style="font-weight: 400;"> “houses” we’d like to avoid.</span></p>
<p><span style="font-weight: 400;">(</span><i><span style="font-weight: 400;">INTERNET</span></i><span style="font-weight: 400;">: [groan] “Stop this overwrought metaphor. I mean, I was about to say, ‘You’re better than this,’ but then I thought to myself, ‘</span><i><span style="font-weight: 400;">Is </span></i><span style="font-weight: 400;">he?’ and deleted my comment.”)</span></p>
<h4><strong> The House of Mirrors (Inequalities / Quadratics / Absolute Value)</strong></h4>
<p><iframe loading="lazy" src="https://giphy.com/embed/3ov9kaQ40mXaLb98dO" width="480" height="360" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p>
<p><a href="https://giphy.com/gifs/halloween-scared-scary-3ov9kaQ40mXaLb98dO"></a></p>
<p><span style="font-weight: 400;">It’s easy to get turned around in these worlds, because you see the image of a number, but you can’t tell whether it’s on the positive or negative side of the mirror.</span></p>
<p><span style="font-weight: 400;">When we see something like “xy > xz,” we do </span><b>not </b><span style="font-weight: 400;">divide by ‘x’ to get “y > z.”</span></p>
<p><span style="font-weight: 400;">When you multiply or divide an inequality by a negative number, you have to flip the sign. Is “x” negative or positive? We don’t know. It’s exactly like shooting a gun at something in a house of mirrors.</span></p>
<p><span style="font-weight: 400;">When Data Sufficiency asks us, “</span><b>What’s the value of x?</b><span style="font-weight: 400;">” and Statement 1 says </span><span style="font-weight: 400;">(1) x²</span><span style="font-weight: 400;"> = 25, it is insufficient, because we don’t know whether x is 5 or -5.</span></p>
<p><span style="font-weight: 400;">Incidentally, a lot of people don’t realize that when you square root that </span><b>quadratic</b><span style="font-weight: 400;">, √x²</span><span style="font-weight: 400;"> = √25, we get the </span><b>absolute value </b><span style="font-weight: 400;">of the square root when a variable is involved. |x| = 5</span></p>
<p><span style="font-weight: 400;">You know the magnitude, but you don’t know whether it’s positively or negatively charged.</span></p>
<p><span style="font-weight: 400;">When we get an absolute value equation or inequality, such as |x – 3| = 10 or |x – 3| > 10, we solve for the positive and the negative version of what’s in the absolute value: (x &#8211; 3) = 10 </span><b>and </b><span style="font-weight: 400;">-(x &#8211; 3) = 10 or (x &#8211; 3) > 10 </span><b>and </b><span style="font-weight: 400;">-(x &#8211; 3) > 10.</span></p>
<p><span style="font-weight: 400;">&#8230;Sort of like when you’re trying to shoot someone in a hall of mirrors: ideally, you have two guns that can be pointed in opposite directions, just to cover your bases. Well, </span><i><span style="font-weight: 400;">ideally</span></i><span style="font-weight: 400;">, and if money is no object, you’d have to say the Omni-Gun is the obvious choice for covering all polygonal permutations of halls of mirror.</span></p>
<p><span style="font-weight: 400;">(</span><i><span style="font-weight: 400;">INTERNET</span></i><span style="font-weight: 400;">: “Nice sensitivity, Patrick. What if someone gets triggered by your violent hall of mirrors metaphor?”)</span></p>
<p><span style="font-weight: 400;">That would make me very sad, Internet. I hope this is a farcical enough example that it only triggers Bruce Lee’s character in </span><i><span style="font-weight: 400;">Enter the Dragon</span></i><span style="font-weight: 400;">.</span></p>
<h4><strong>Gross-Looking Monsters (Sequences / Functions)</strong></h4>
<p><iframe loading="lazy" src="https://giphy.com/embed/ObBurbVUbOqMo" width="480" height="372" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p>
<p><a href="https://giphy.com/gifs/monster-art-ObBurbVUbOqMo"></a></p>
<p><span style="font-weight: 400;">You wanna tell whether someone’s mathphobic? Put a problem involving </span><b>subscripts</b><span style="font-weight: 400;"> or </span><b>functions </b><span style="font-weight: 400;">in front of them and monitor their swallowing for any hints of tiny, vomitous reactions when they first see the problem.</span></p>
<p><span style="font-weight: 400;">Doesn’t this look lucid and welcoming?</span></p>
<p><span style="font-weight: 400;">In the sequence a</span><span style="font-weight: 400;"><sub>1</sub></span><span style="font-weight: 400;">, a</span><span style="font-weight: 400;"><sub>2</sub></span><span style="font-weight: 400;">, a</span><span style="font-weight: 400;"><sub>3</sub></span><span style="font-weight: 400;">, … a</span><span style="font-weight: 400;"><sub>n</sub></span><span style="font-weight: 400;">, …., where n >2, a</span><span style="font-weight: 400;"><sub>n</sub></span><span style="font-weight: 400;"> = 3(a</span><span style="font-weight: 400;"><sub>n-1</sub></span><span style="font-weight: 400;">) – 4(a</span><span style="font-weight: 400;"><sub>n-2</sub></span><span style="font-weight: 400;">)</span></p>
<p><span style="font-weight: 400;">Those subscripts are risin’ from the GRAVE, I tellz ya!</span></p>
<p><span style="font-weight: 400;">In reality, sequence problems can be tamed, once we learn to read a sequence equation as a </span><i><span style="font-weight: 400;">process</span></i><span style="font-weight: 400;">: a set of instructions to follow for figuring out the next term in a sequence. All that gobbledygook was saying was, “This is a sequence problem. Here is your process: a</span><span style="font-weight: 400;"><sub>n</sub></span><span style="font-weight: 400;"> = 3(a</span><span style="font-weight: 400;"><sub>n-1</sub></span><span style="font-weight: 400;">) – 4(a</span><span style="font-weight: 400;"><sub>n-2</sub></span><span style="font-weight: 400;">). That means, “To find a term, multiply the previous term by 3 and the term before that by 4, and subtract one from the other.” Hey, Internet… I almost tried to make a goblin pun on “gobbledygook,” but I refrained. Proud much?</span></p>
<p><span style="font-weight: 400;">(</span><i><span style="font-weight: 400;">INTERNET</span></i><span style="font-weight: 400;">: “Sighhhh… I’ll tell you what&#8230; Good job. It’s a start.”)</span></p>
<p><b>Function </b><span style="font-weight: 400;">problems also present a process, but whereas sequences always have that same subscript look, functions get dressed up in a lot of different costumes.</span></p>
<p><iframe loading="lazy" src="https://giphy.com/embed/5vCWii3HEE75e" width="480" height="360" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p>
<p><a href="https://giphy.com/gifs/halloween-dance-5vCWii3HEE75e"></a></p>
<p><span style="font-weight: 400;">(</span><i><span style="font-weight: 400;">INTERNET</span></i><span style="font-weight: 400;">: “I can’t believe we started to believe in you.”)</span></p>
<p><span style="font-weight: 400;">Just because we haven’t seen a function before doesn’t mean we’re unprepared. They are novel tasks that we simply have to patiently read and follow.</span></p>
<p><span style="font-weight: 400;">For example: If </span><i><span style="font-weight: 400;">the nightmare on x street </span></i><span style="font-weight: 400;">means the smallest prime number greater than half of x, what is </span><i><span style="font-weight: 400;">the nightmare on 16 street +</span></i> <i><span style="font-weight: 400;">the nightmare on 30 street</span></i><span style="font-weight: 400;">?</span></p>
<p><i><span style="font-weight: 400;">The nightmare on 16 street </span></i><span style="font-weight: 400;">= the smallest prime that’s bigger than ½ of 16.</span><span style="font-weight: 400;"><br />
</span><i><span style="font-weight: 400;">The nightmare on 30 street </span></i><span style="font-weight: 400;">= the smallest prime that’s bigger than ½ of 30.</span></p>
<p><span style="font-weight: 400;">The smallest prime bigger than ½ of 16, or 8, is 11.</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">The smallest prime bigger than ½ of 30, or 15, is 17.</span></p>
<p><span style="font-weight: 400;">So </span><i><span style="font-weight: 400;">the nightmare on 16 street +</span></i> <i><span style="font-weight: 400;">the nightmare on 30 street</span></i><span style="font-weight: 400;"> = 11 + 17 = 28.</span></p>
<h4><strong>The Foggy Night (Rate Problems and Geometry Problems)</strong></h4>
<p><iframe loading="lazy" src="https://giphy.com/embed/l3q2EceFe6B0xomFG" width="480" height="270" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p>
<p><a href="https://giphy.com/gifs/fog-foggy-l3q2EceFe6B0xomFG"></a></p>
<p><span style="font-weight: 400;">These can take a while to wade through, and you often can’t envision how you’re getting to the finish line when you begin. It’s very important to take these one step at a time.</span></p>
<p><span style="font-weight: 400;">On Rate problems, ask yourself, “1 hour later, what has happened? 2 hours later, what has happened?” Once you paw at the air in the dark for a couple seconds, you ultimately find something to hold onto.</span></p>
<p><span style="font-weight: 400;">On Geometry problems, you keep yourself calm by forcing yourself to write out known formulas. Once you have a formula on your page, e.g. area = ½ (base)*(height), those three parts of the formula act like Ghostbuster containment units for the ideas in the problem. You can see which of those unknowns the problem gave you values for or algebra for and write them into their place in the formula.</span></p>
<p><span style="font-weight: 400;">(</span><i><span style="font-weight: 400;">INTERNET</span></i><span style="font-weight: 400;">: “Hey, old man, despite the recent all-female reboot, we don’t know what </span><i><span style="font-weight: 400;">Ghostbusters</span></i><span style="font-weight: 400;"> is.”)</span></p>
<p><span style="font-weight: 400;">You know what, Internet? I don’t think I’m welcome here anymore. While I’d love to keep expounding on these horror show topics, I would have to write so much that I’d be forcing Thanksgiving wordplay on you.</span></p>
<p><span style="font-weight: 400;">Let’s switch to the lightning round of Haunted Topics:</span></p>
<p><iframe loading="lazy" src="https://giphy.com/embed/jpbAaUG7cjkZy" width="480" height="351" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p>
<p><a href="https://giphy.com/gifs/halloween-skeleton-jpbAaUG7cjkZy"></a></p>
<h4><b>Combinatorics and Probability</b></h4>
<p><span style="font-weight: 400;">If it’s easy, do it. If you’re great at them, do it. Otherwise, skip it! You’ll probably only see one of these on your test and it will usually be a difficult-ranked problem that is harmlessly missed.</span></p>
<h4><b>YES / NO Data Sufficiency</b></h4>
<p><span style="font-weight: 400;">Make sure you have consistent habits on your paper of differentiating between a legal number that answers the question NO and an illegal number that violates a constraint and therefore cannot provide any possible answer to the question.</span></p>
<p><span style="font-weight: 400;">You might want to enact a habit of check-marking your numbers when you test cases (like verifying their Twitter accounts) to show that their creds have been vetted. They comply with the constraints. And when you accidentally consider an illegal number, scratch that work out.</span></p>
<p><span style="font-weight: 400;">A legal NO case should have a checkmark that shows the number fits the constraint and the answer NO circled proudly nearby. An illegal case should just be scratched out.</span></p>
<h4><b>Critical Reasoning</b></h4>
<p><i><span style="font-weight: 400;">Assumption</span></i><span style="font-weight: 400;"> – The task here is really “which answer, if negated, most weakens,” and because of that, people often struggle to apply the right mindset. (When in doubt, remember that about half of all correct answers contain the word ‘not.’)</span></p>
<p><i><span style="font-weight: 400;">Describe the Role of Bold</span></i><span style="font-weight: 400;"> – The answers are completely abstract, so students are often lost in the terminology. Remind yourself when you’re initially searching for the conclusion that it will usually appear </span><b>earlier </b><span style="font-weight: 400;">in the paragraph than its supporting ideas (on this question type only). Try to pre-phrase each bold as either Main Conclusion, Supporting, Opposing, or Neutral.</span></p>
<h4><b>Reading Comprehension</b></h4>
<p><i><span style="font-weight: 400;">Inference</span></i><span style="font-weight: 400;"> – The question stem may use “inferred”, “implies”, “suggests”, or “most likely to agree.” All of those formulations tend to sound ‘loose’ enough that students typically assume they have the freedom to speculate, and students too frequently assume that the correct answer should reinforce the main point of the passage.</span></p>
<p><span style="font-weight: 400;">In reality, we’re just looking for whichever answer is the most provable idea, given the text in the passage. The correct answer usually reinforces a single line reference, but sometimes it involves pulling together details from two different lines of the passage. The test writers go out of their way to find an unexpected way to rephrase something we were told.</span></p>
<p><span style="font-weight: 400;">Told that “George Washington was the first president of the U.S.”? This suggests that “Not all nations choose Banksy as their inaugural leader.”</span></p>
<p><span style="font-weight: 400;">Told that “Mailing my ex-girlfriend dead flowers gave her the creeps”? We can infer that “My ability to make people uncomfortable is not limited to my ability to invert my eyelids.”</span></p>
<h4><b>Sentence Correction</b></h4>
<p><i><span style="font-weight: 400;">Pronouns and Complex Tenses </span></i><span style="font-weight: 400;">– These are guilty until proven innocent. </span></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">When we see “it / its / that of,” we need to find if there’s a singular noun in the sentence to which this pronoun clearly refers.</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">When we see “they / them / their / those of,” we need to find if there’s a plural noun in the sentence to which this pronoun clearly refers.</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">When we see “has/have,” we need to ask whether we can justify using the complex present perfect tense (‘is it referring to an </span><i><span style="font-weight: 400;">ongoing time period </span></i><span style="font-weight: 400;">or an </span><i><span style="font-weight: 400;">unspecified time period</span></i><span style="font-weight: 400;">?’).</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">When we see “had,” we need to ask whether we can justify using past perfect (‘is this referring to something that’s </span><i><span style="font-weight: 400;">deeper in the past</span></i><span style="font-weight: 400;"> than some other part of the sentence that’s in the past?’)</span></li>
</ul>
<p><i><span style="font-weight: 400;">Being</span></i><span style="font-weight: 400;"> – 97% of the time we see this word in an answer choice, the choice is wrong. It’s very frequently inserted into an answer choice to give it that “wordy, awkward, un-idiomatic” complaint that GMAT often uses in its explanations. It </span><i><span style="font-weight: 400;">can </span></i><span style="font-weight: 400;">be right, but seeing ‘being’ should lead to fleeing</span></p>
<p><span style="font-weight: 400;">(</span><i><span style="font-weight: 400;">INTERNET</span></i><span style="font-weight: 400;">:</span> <span style="font-weight: 400;">“I think that was clever? I don’t even know what I like anymore.”)</span></p>
<p><span style="font-weight: 400;">In summary, if you’re hoping to apply the wisdom of efficient trick-or-treating to your next GMAT:</span></p>
<p>1. Overall, plan to work moderately hard for your answers. If you’re guessing too quickly or taking too long, you’re browsing in the wrong neighborhood.</p>
<p><span style="font-weight: 400;">2. Keep an eye out for a handful of haunted topics that generally aren’t a great value. Consider hitting them up briskly or not at all.</span></p>
<p><span style="font-weight: 400;">I hope you’ll join me next month for what will surely be an overwrought attempt to relate the GMAT to the midterm elections.</span></p>
<p><span style="font-weight: 400;">(</span><i><span style="font-weight: 400;">INTERNET</span></i><span style="font-weight: 400;">: “Can this ‘Internet’ character come back too, or is Jim Gaffigan going to come after you for stealing his ‘Audience Guy’ character?”)</span></p>
<p><span style="font-weight: 400;">Probably the latter. G’night, sweet prince. ?</span></p>
<p><iframe loading="lazy" src="https://giphy.com/embed/3mJSsgvBGp1tNbpskE" width="480" height="360" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p>
<p><a href="https://giphy.com/gifs/alice-cooper-welcome-to-my-nightmare-3mJSsgvBGp1tNbpskE"></a></p>
<hr />
<p><b><i>Want some more GMAT tips from Patrick? Attend the first session of one of his </i></b><b><i><a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/#instructor/270" target="_blank" rel="noopener">upcoming GMAT courses</a> </i></b><b><i>absolutely free, no strings attached. Seriously.</i></b></p>
<hr />
<p><em><strong><img decoding="async" loading="lazy" class="alignleft wp-image-15335 size-thumbnail" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/03/patrick-tyrell-150x150.png" alt="patrick-tyrrell" width="150" height="150" /><a id="bloglink" href="https://www.manhattanprep.com/instructors/patrick-tyrrell/" target="_blank" rel="noopener">Patrick Tyrrell</a> is a Manhattan Prep instructor based in Los Angeles, California.</strong> He has a B.A. in philosophy, a 780 on the GMAT, and relentless enthusiasm for his work. In addition to teaching test prep since 2006, he’s also an avid songwriter/musician. <a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/#instructor/270" target="_blank" rel="noopener">Check out Patrick’s upcoming GMAT courses here!</a></em></p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/executive-mindset-gmat-halloween/">Trick-or-Treaters Are Using the Executive Mindset</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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		<title>A Memorizable List of GMAT Quant Content (Quantent)</title>
		<link>https://www.manhattanprep.com/gmat/blog/list-gmat-quant-content/</link>
		
		<dc:creator><![CDATA[Patrick Tyrrell]]></dc:creator>
		<pubDate>Mon, 13 Aug 2018 17:11:15 +0000</pubDate>
				<category><![CDATA[Algebra]]></category>
		<category><![CDATA[Challenge Problem]]></category>
		<category><![CDATA[For Current Studiers]]></category>
		<category><![CDATA[Fractions, Decimals, Percents]]></category>
		<category><![CDATA[GMAT 101]]></category>
		<category><![CDATA[GMAT Prep]]></category>
		<category><![CDATA[GMAT Resources]]></category>
		<category><![CDATA[GMAT Strategies]]></category>
		<category><![CDATA[GMAT Study Guide]]></category>
		<category><![CDATA[How to Study]]></category>
		<category><![CDATA[Quant]]></category>
		<category><![CDATA[Taking the GMAT]]></category>
		<category><![CDATA[Algebraic Story Problems]]></category>
		<category><![CDATA[Decimals]]></category>
		<category><![CDATA[divisibility]]></category>
		<category><![CDATA[Exponents]]></category>
		<category><![CDATA[inequalities]]></category>
		<category><![CDATA[Linear Algebra]]></category>
		<category><![CDATA[Odds and Evens]]></category>
		<category><![CDATA[Positives and Negatives]]></category>
		<category><![CDATA[Quantent]]></category>
		<category><![CDATA[Roots]]></category>
		<category><![CDATA[statistics]]></category>
		<category><![CDATA[Units Digits]]></category>
		<guid isPermaLink="false">https://www.manhattanprep.com/gmat/?p=16100</guid>

					<description><![CDATA[<p>Even though there’s no “new math” on GMAT Quant, there is still a ton of content to keep on our radar. And just like the tragic studying for a vocab test, we’ll have to learn 200 different things, even though the test is going to only ask us 31 of those things (because we don’t [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/list-gmat-quant-content/">A Memorizable List of GMAT Quant Content (Quantent)</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-16135" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/07/memorizable-list-gmat-quant-content-quantent-patrick-tyrrell.png" alt="Manhattan Prep GMAT Blog - A Memorizable List of GMAT Quant Content (Quantent) by Patrick Tyrrell" width="1200" height="628" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/07/memorizable-list-gmat-quant-content-quantent-patrick-tyrrell.png 1200w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/07/memorizable-list-gmat-quant-content-quantent-patrick-tyrrell-300x157.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/07/memorizable-list-gmat-quant-content-quantent-patrick-tyrrell-768x402.png 768w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/07/memorizable-list-gmat-quant-content-quantent-patrick-tyrrell-1024x536.png 1024w" sizes="(max-width: 1200px) 100vw, 1200px" /></p>
<p><span style="font-weight: 400;">Even though there’s no “new math” on GMAT Quant, there is still a </span><i><span style="font-weight: 400;">ton </span></i><span style="font-weight: 400;">of content to keep on our radar. And just like the tragic studying for a vocab test, we’ll have to learn 200 different things, even though the test is going to only ask us 31 of those things (because we don’t know which 31 things we’ll get asked on our test day).</span><span id="more-16100"></span></p>
<p><span style="font-weight: 400;">How are we going to keep all that stuff in our brain at once? It takes most students at least a couple weeks to cycle through 200 different GMAT Quant problems, so by the time you’re doing the 200</span><span style="font-weight: 400;">th</span><span style="font-weight: 400;"> problem, it’s usually been a few weeks since you’ve seen the content on the first 10 problems. </span></p>
<p><span style="font-weight: 400;">In order to take quicker laps around the GMAT Quant universe, you want to make some of your practice feel like you’re studying for a vocab test. We can take a lap through 200 vocab flashcards much more quickly than we can through 200 GMAT Quant problems.</span></p>
<p><span style="font-weight: 400;">Instead of having vocab flashcards with Word on one side and Definition on the other, we’ll have GMAT Quant flashcards that have Topic/Stimulus on one side, and First Move/First Thought on the other.</span></p>
<p><span style="font-weight: 400;">If Pavlov can get dogs to salivate in response to a bell, we can get ourselves to break a number down to primes in response to ‘divisibility language.’ But we’ll have to outdo Pavlov, or at least outdo his dogs, by learning way more than just one stimulus/response pairing. Are you all ready to outdo Pavlov’s certain-to-be-dead-by-now dogs?!</span></p>
<p><span style="font-weight: 400;">(Moment of silence: I hope in doggy heaven, every time the bell rings, you really </span><i><span style="font-weight: 400;">do </span></i><span style="font-weight: 400;">get a treat.)</span></p>
<p><span style="font-weight: 400;">In the rest of Part 1 (of this 2-part post), I’ll get you started with a baker’s dozen topics. Next month, we’ll finish off the list.</span></p>
<p><span style="font-weight: 400;">Your job: if you see anything you don’t already know with the ease/certainty of a famous actor’s name/face, then commit that fact to flashcard. Quiz yourself on those flashcards at least three times a week. Add your own flashcards as you review problems you’ve tried and see moves you wish you had made, or number properties you wish you would have inferred.</span></p>
<p><span style="font-weight: 400;">Let us know if you have any questions.</span></p>
<h4><strong>DIVISIBILITY on GMAT Quant</strong></h4>
<p><span style="font-weight: 400;">#1 Move: If we see </span><i><span style="font-weight: 400;">x is </span></i><b><i>divisible</i></b><i><span style="font-weight: 400;"> by y, x is a </span></i><b><i>multiple</i></b><i><span style="font-weight: 400;"> of y, y is a </span></i><b><i>factor</i></b><i><span style="font-weight: 400;"> of x, x/y </span></i><b><i>is an integer</i></b><i><span style="font-weight: 400;">, </span></i><span style="font-weight: 400;">then we </span><b>break these numbers down to primes.</b></p>
<p><b>Divisibility </b><span style="font-weight: 400;">means “the numerator has </span><i><span style="font-weight: 400;">at least </span></i><span style="font-weight: 400;">the primes in the denominator.”</span></p>
<p><span style="font-weight: 400;">“x is divisible by 45” = x has at least 3 * 3 * 5 in it.</span></p>
<p><span style="font-weight: 400;">“x is not a multiple of 12” = x either has fewer than two 2’s or doesn’t have a 3, or both.</span></p>
<p><span style="font-weight: 400;">“36 is a factor of 8x” = <sup>2*2*2*x</sup><sub>2*2*3*3</sub> = <sup><del>2*2</del>*2*x</sup><sub><del>2*2</del>*3*3</sub> = <sup>2x</sup><sub>3*3 </sub></span>= x has at least 3*3 in it.</p>
<p><span style="font-weight: 400;">#2 Move: If we see a </span><i><span style="font-weight: 400;">multiplication cluster + integer</span></i><span style="font-weight: 400;">, then we think about </span><b>the logic of multiples</b><span style="font-weight: 400;"> and ask, “What are both quantities divisible by?”</span></p>
<p><span style="font-weight: 400;">If we see 14x + 35, we think “both 14x and 35 are divisible by 7,” so 14x +35 is divisible by 7.</span><span style="font-weight: 400;"><br />
</span><i><span style="font-weight: 400;">a multiple of 7 + a multiple of 7 = a multiple of 7</span></i></p>
<p><span style="font-weight: 400;">If we see 7! + 15, we think “both 7! and 15 are divisible by 5,” so 7! + 15 is divisible by 5.</span></p>
<h4><strong>STATISTICS on GMAT Quant</strong></h4>
<p><span style="font-weight: 400;">If we’re talking </span><b>median,</b></p>
<ul>
<li><span style="font-weight: 400;">arrange everything in ascending order</span></li>
<li>odd number of data points → median is the middle data point</li>
<li>even number of data points → median is the average of the two middle data points</li>
</ul>
<p>If we’re talking <b>average,</b></p>
<ul>
<li><b>calculate sum</b><span style="font-weight: 400;"> (remember&#8230; Sum = Avg * # of things)</span></li>
</ul>
<p><span style="font-weight: 400;">If we’re talking </span><b>standard deviation,</b></p>
<ul>
<li><span style="font-weight: 400;">we need to know </span><b>how far each data point</b><span style="font-weight: 400;"> is from the average and </span><b>how many data points</b><span style="font-weight: 400;"> there are</span></li>
<li>adding outlier data points (towards or beyond the current extremes) will increase SD</li>
<li>adding center data points (on or near the average) will decrease SD</li>
</ul>
<h4><strong>ODDS/EVENS on GMAT Quant</strong></h4>
<p><span style="font-weight: 400;">#1 Thought: </span><b>even * anything = even</b></p>
<p><span style="font-weight: 400;">#2 Thought: Remember or derive the E/O rules for addition/subtraction/multiplication</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">E +/- E = E       E * E = E </span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">E +/- O = O     E * O = E </span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">O +/- O = E     O * O = O </span></p>
<p><span style="font-weight: 400;">Usual #1 Move: Take anything with an even coefficient and translate that quantity into E.</span></p>
<p><span style="font-weight: 400;"> 3x + </span><b>4y</b><span style="font-weight: 400;"> is odd → 3x + </span><b>E</b><span style="font-weight: 400;"> = O → 3x = O – E → 3x = O → x = O </span></p>
<p><span style="font-weight: 400;">Dealing with division facts: If we see “x/y is even,” we write, <sup>x</sup><sub>y </sub></span><span style="font-weight: 400;">= Even, and then multiply y to the other side to get  x = Even (y). </span><span style="font-weight: 400;">This tells us that x is even (we know nothing about y).</span></p>
<p><b>Useful Shortcut:</b><span style="font-weight: 400;"> If something has an even coefficient, we won’t learn whether that variable is even or odd. The even coefficient will “hide” which type it is.</span></p>
<h4><strong>POSITIVE/NEGATIVE on GMAT Quant</strong></h4>
<p><span style="font-weight: 400;">#1 Thought: </span><b>Keep track</b><span style="font-weight: 400;"> of possible words with </span><b>“pos, neg” or “+, -”</b></p>
<p><span style="font-weight: 400;">#1 Move: Use the pos/neg properties of addition, subtraction, multiplication, and division to eliminate possible words.</span></p>
<p><span style="font-weight: 400;">x+y > 0 (at least one positive … eliminate neg/neg)     </span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">x+y < 0 (at least one negative … eliminate pos/pos)</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">x-y > 0 (x > y  … eliminate neg/pos)</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">x-y < 0 (x < y  … eliminate pos/neg)</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">xy > 0 or x/y > 0 (same sign … must be pos/pos or neg/neg)</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;"> xy < 0 or x/y < 0 (opposite signs … must be pos/neg or neg/pos)</span></p>
<p><b>Useful Shortcut:</b><span style="font-weight: 400;"> If something has an even exponent, we won’t learn whether that variable is positive or negative. The even exponent will “hide” which type it is.</span></p>
<h4><strong>DECIMALS on GMAT Quant</strong></h4>
<p><span style="font-weight: 400;">#1 Move: Clean it up by</span><b> multiplying by a power of 10.</b></p>
<p><span style="font-weight: 400;">If we see 0.0045, we write  45 * 10<sup>-4</sup></span></p>
<p><span style="font-weight: 400;">#2 Move: Line up the decimals, add zeros where necessary, then remove the decimal.</span></p>
<p><span style="font-weight: 400;">If we see 1.2/.03, we write 1.2</span><b>0</b><span style="font-weight: 400;">/</span><b>0</b><span style="font-weight: 400;">.03 = 120/3 = 40.</span></p>
<h4><strong>UNITS DIGITS on GMAT Quant</strong></h4>
<p><span style="font-weight: 400;">#1 Move: </span><b>Write out the pattern</b><span style="font-weight: 400;"> for that units digit.</span><b> Example: </b><span style="font-weight: 400;">What’s the units digit of 63<sup>45</sup></span><span style="font-weight: 400;">?</span></p>
<p><span style="font-weight: 400;">Write out the pattern for powers of 3 (the patterns are either a constant digit, a cycle of 2, or a cycle of 4).</span></p>
<p><span style="font-weight: 400;">3¹</span><span style="font-weight: 400;"> ends in 3<br />
</span><span style="font-weight: 400;">3²</span><span style="font-weight: 400;"> ends in 9<br />
</span><span style="font-weight: 400;">3³</span><span style="font-weight: 400;"> ends in 7</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">3<sup>4</sup></span><span style="font-weight: 400;"> ends in 1</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">&#8212;&#8212;&#8212;&#8212;&#8212;- </span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">3<sup>5</sup></span><span style="font-weight: 400;"> ends in 3<br />
</span><span style="font-weight: 400;">3<sup>6</sup></span><span style="font-weight: 400;"> ends in 9<br />
</span><span style="font-weight: 400;">3<sup>7</sup></span><span style="font-weight: 400;"> ends in 7</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">3<sup>8</sup></span><span style="font-weight: 400;"> ends in 1</span></p>
<p><span style="font-weight: 400;">Since every power that’s a multiple of 4 will end in 1, 3<sup>44</sup></span><span style="font-weight: 400;"> = ends in a 1.</span></p>
<p><span style="font-weight: 400;">So 3<sup>45</sup></span><span style="font-weight: 400;"> = ends in a 3, so the units digit of 63<sup>45</sup></span><span style="font-weight: 400;"> </span><span style="font-weight: 400;">is 3.</span></p>
<h4><strong>EXPONENTS/ROOTS on GMAT Quant</strong></h4>
<p><span style="font-weight: 400;">#1 Move: If any of the bases aren’t currently prime, </span><b>break the bases down to primes.</b><b></b></p>
<p><span style="font-weight: 400;">If we see 14<sup>x</sup></span><span style="font-weight: 400;"> * 10<sup>y</sup></span><span style="font-weight: 400;"> * 8<sup>5</sup></span><span style="font-weight: 400;"> = 2³²</span><span style="font-weight: 400;"> * 5<sup>z+1</sup></span><span style="font-weight: 400;"> * 7<sup>4</sup></span></p>
<p><span style="font-weight: 400;">Then our next move is: 2<sup>x </sup></span><span style="font-weight: 400;">7<sup>x</sup></span><span style="font-weight: 400;"> * 2<sup>y</sup></span><span style="font-weight: 400;"> 5<sup>y</sup></span><span style="font-weight: 400;"> * (2³</span><span style="font-weight: 400;">)<sup>5</sup></span><span style="font-weight: 400;"> = 2³²</span><span style="font-weight: 400;"> * 5<sup>z+1</sup></span><span style="font-weight: 400;"> * 7<sup>4</sup></span></p>
<p><span style="font-weight: 400;">#2 Move: If the problem involves addition or subtraction, we need to </span><b>factor something out.</b></p>
<p><span style="font-weight: 400;">If we see 2³²</span><span style="font-weight: 400;"> – 2<sup>30</sup></span></p>
<p><span style="font-weight: 400;">Then our next move is: 2<sup>30</sup></span><span style="font-weight: 400;"> (2²</span><span style="font-weight: 400;"> – 1) =  2<sup>30</sup></span><span style="font-weight: 400;"> (3).</span></p>
<h4><strong>INEQUALITIES on GMAT Quant</strong></h4>
<p><span style="font-weight: 400;">#1 Thought: </span><b>Watch out for negatives! </b><span style="font-weight: 400;">(When we multiply or divide by a negative, we have to flip the sign. We shouldn’t multiply or divide by variables unless we know their sign.)</span></p>
<p><span style="font-weight: 400;">#2 Thought: If it deals with exponents and inequalities, </span><b>try fractions </b><span style="font-weight: 400;">between 0 and 1, and maybe also fractions between -1 and 0 (numbers between 0 and 1 are the only numbers in the universe where x²</span><span style="font-weight: 400;"> < x).</span></p>
<p><span style="font-weight: 400;">#3 Thought: If we have </span><b>two inequalities</b><span style="font-weight: 400;">, line up the inequality sign and </span><b>add them</b><span style="font-weight: 400;"> to each other.</span></p>
<h4><strong>ALGEBRAIC STORY PROBLEMS on GMAT Quant</strong></h4>
<p><span style="font-weight: 400;">#1 Thought: </span><b>Should I just backsolve</b><span style="font-weight: 400;">, rather than translating the story into variables/equations and trying to solve that way?</span></p>
<p><span style="font-weight: 400;">#2 Thought: If I’m going to translate, let me do so carefully.</span></p>
<p><span style="font-weight: 400;">is (or any other verb) </span><span style="font-weight: 400;">→</span><span style="font-weight: 400;"> “=”<br />
</span><span style="font-weight: 400;">of </span><span style="font-weight: 400;">→</span><span style="font-weight: 400;"> “multiply”<br />
</span><span style="font-weight: 400;">percent </span><span style="font-weight: 400;">→</span><span style="font-weight: 400;">  /100<br />
</span><span style="font-weight: 400;">“There are” </span><span style="font-weight: 400;">→</span><span style="font-weight: 400;"> the coefficient goes on the 2</span><span style="font-weight: 400;">nd</span><span style="font-weight: 400;"> thing<br />
</span><span style="font-weight: 400;">(“There are 2/3 as many boys as girls” </span><span style="font-weight: 400;">→</span><span style="font-weight: 400;">  B = 2/3 G)</span></p>
<h4><strong>LINEAR ALGEBRA on GMAT Quant</strong></h4>
<p><span style="font-weight: 400;">#1 Thought: </span><b>Am I solving for one variable or two</b><span style="font-weight: 400;"> (a “Combo”)?</span></p>
<p><span style="font-weight: 400;">We can solve systems of equations by substitution (</span><b>isolate</b><span style="font-weight: 400;"> some variable or expression in one equation and then </span><b>substitute</b><span style="font-weight: 400;"> the other side of the equation into the second equation).</span></p>
<p><span style="font-weight: 400;">Or we can solve systems of equations by elimination (</span><b>stack</b><span style="font-weight: 400;"> the equations on top of each other, </span><b>scale one or both of them up</b><span style="font-weight: 400;"> so that the coefficient of one of the variables is the same number, then </span><b>add or subtract the two equations</b><span style="font-weight: 400;"> in order to eliminate the same-numbered variable).</span></p>
<p><span style="font-weight: 400;">Solving for a Combo, like “What is 3x + 2y?” means that instead of trying to get x = ___ , y = ____  and then plugging those values in for x and y, we should be trying to get 3x + 2y = _____.</span></p>
<h4><b>TRAP AWARENESS on GMAT Quant</b></h4>
<p><b></b><span style="font-weight: 400;">When the two DS statements show you a pair of equations with the same two variables, the answer is almost never C (we refer to that as “the C trap”).</span></p>
<p><span style="font-weight: 400;">Sometimes, it’s NOT solvable (the answer is E) because the two equations are actually the same equation, if we simplified or scaled them up/down.</span></p>
<p><i><span style="font-weight: 400;">What’s the value of x?</span></i><i><span style="font-weight: 400;"><br />
</span></i><span style="font-weight: 400;">1) 3x + 2y = 40</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">2) 9x – 120 = -6y<br />
</span><span style="font-weight: 400;">(Answer: E)</span></p>
<p><span style="font-weight: 400;">Other times, it’s solvable with only one statement (the answer is A or B) because one of the statements gives us an equation that we could manipulate into showing us the value of the Combo we’re looking for.</span></p>
<p><i><span style="font-weight: 400;">What’s the value of 3x + 2y?</span></i><i><span style="font-weight: 400;"><br />
</span></i><span style="font-weight: 400;">1) 9x – 120 = -6y</span><span style="font-weight: 400;"><br />
</span><span style="font-weight: 400;">2) 5x + 4y = 12<br />
</span><span style="font-weight: 400;">(Answer: A)</span></p>
<p><span style="font-weight: 400;">More to come next month! ?</span></p>
<hr />
<p><b><i>Want some more GMAT tips from Patrick? Attend the first session of one of his </i></b><b><i><a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/#instructor/270" target="_blank" rel="noopener">upcoming GMAT courses</a> </i></b><b><i>absolutely free, no strings attached. Seriously.</i></b></p>
<hr />
<p><em><strong><img decoding="async" loading="lazy" class="alignleft wp-image-15335 size-thumbnail" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/03/patrick-tyrell-150x150.png" alt="patrick-tyrrell" width="150" height="150" /><a id="bloglink" href="https://www.manhattanprep.com/instructors/patrick-tyrrell/" target="_blank" rel="noopener">Patrick Tyrrell</a> is a Manhattan Prep instructor based in Los Angeles, California.</strong> He has a B.A. in philosophy, a 780 on the GMAT, and relentless enthusiasm for his work. In addition to teaching test prep since 2006, he’s also an avid songwriter/musician. <a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/#instructor/270" target="_blank" rel="noopener">Check out Patrick’s upcoming GMAT courses here!</a></em></p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/list-gmat-quant-content/">A Memorizable List of GMAT Quant Content (Quantent)</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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		<title>Help! I Can&#8217;t Handle GMAT Probability and Combinatorics (Part 3)</title>
		<link>https://www.manhattanprep.com/gmat/blog/help-i-cant-handle-gmat-probability-and-combinatorics-part-3/</link>
		
		<dc:creator><![CDATA[Chelsey Cooley]]></dc:creator>
		<pubDate>Thu, 13 Apr 2017 16:30:30 +0000</pubDate>
				<category><![CDATA[Challenge Problem]]></category>
		<category><![CDATA[For Current Studiers]]></category>
		<category><![CDATA[GMAT Prep]]></category>
		<category><![CDATA[GMAT Strategies]]></category>
		<category><![CDATA[GMAT Study Guide]]></category>
		<category><![CDATA[Quant]]></category>
		<category><![CDATA[GMAT Probability and Combinatorics]]></category>
		<category><![CDATA[Probability and Combinatorics]]></category>
		<guid isPermaLink="false">http://www.manhattanprep.com/gmat/?p=13515</guid>

					<description><![CDATA[<p>Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here. In the previous articles in this series, we developed a critical skill for GMAT probability and combinatorics problems: listing out cases. Let’s start by taking [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/help-i-cant-handle-gmat-probability-and-combinatorics-part-3/">Help! I Can&#8217;t Handle GMAT Probability and Combinatorics (Part 3)</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13589" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/4-13-17-social-1.png" alt="Manhattan Prep GMAT Blog - Help! I Can't Handle GMAT Probability and Combinatorics (Part 3) by Chelsey Cooley" width="1200" height="628" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/4-13-17-social-1.png 1200w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/4-13-17-social-1-300x157.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/4-13-17-social-1-768x402.png 768w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/4-13-17-social-1-1024x536.png 1024w" sizes="(max-width: 1200px) 100vw, 1200px" /></p>
<p><b><i>Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! </i></b><a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/" target="_blank"><b><i>Check out our upcoming courses here</i></b></a><b><i>.</i></b></p>
<hr />
<p><b><i></i></b><span style="font-weight: 400;">In the </span><a id="bloglink" href="https://www.manhattanprep.com/gmat/blog/2017/03/30/help-i-cant-handle-gmat-probability-and-combinatorics-part-2/" target="_blank"><span style="font-weight: 400;">previous articles in this series</span></a><span style="font-weight: 400;">, we developed a critical skill for GMAT probability and combinatorics problems: </span><i><span style="font-weight: 400;">listing out cases</span></i><span style="font-weight: 400;">. Let’s start by taking another look at the practice problem from the end of the last article.</span><span id="more-13515"></span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">Six coworkers (Anil, Boris, Charlie, Dana, Emmaline, and Frank) are having dinner at a restaurant. They’ll sit in chairs that are evenly spaced around a circular table. Boris, Charlie, and Dana refuse to sit directly across from Anil, because he chews with his mouth open. Frank and Emmaline won’t sit next to each other. Finally, Emmaline and Dana insist on sitting next to each other. How many different arrangements will work? (Ignore the arrangements that come from ‘rotating’ the whole table – only focus on the relative positions of the diners.)</span></i></p>
<p><span style="font-weight: 400;">You know by now that you should solve problems like this by </span><b>finding an organized way to list the possibilities</b><span style="font-weight: 400;">. The key is to divide the problem into smaller, simpler problems, to make it easier to write that list. </span></p>
<p><span style="font-weight: 400;">In this problem, there are only two people who can sit across from Anil. Only Emmaline and Frank will put up with him! We’ll start by looking at</span><b> cases where Emmaline sits across from Anil</b><span style="font-weight: 400;">, and then we’ll look at</span><b> cases where Frank sits across from Anil</b><span style="font-weight: 400;">. Here’s what my scratch work looked like as I started this problem.</span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13516" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/gmat-blog-pc-part-3-img-1.png" alt="Manhattan Prep GMAT Blog - Help! I Can't Handle GMAT Probability and Combinatorics (Part 3) by Chelsey Cooley" width="447" height="274" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/gmat-blog-pc-part-3-img-1.png 447w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/gmat-blog-pc-part-3-img-1-300x184.png 300w" sizes="(max-width: 447px) 100vw, 447px" /></p>
<p><span style="font-weight: 400;">Next, I focused in on the table on the left. I know that </span><b>Frank won’t sit next to Emmaline.</b><span style="font-weight: 400;"> So, Frank is either to the left of Anil, or to the right of Anil.</span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13517" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/gmat-blog-pc-part-3-img-2.png" alt="Manhattan Prep GMAT Blog - Help! I Can't Handle GMAT Probability and Combinatorics (Part 3) by Chelsey Cooley" width="273" height="159" /></p>
<p><span style="font-weight: 400;">Also, </span><b>Dana has to sit next to Emmaline</b><span style="font-weight: 400;">. Combining those two facts together, there are four possible ways to set everything up. Here they are:</span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13518" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/gmat-blog-pc-part-3-img-3.png" alt="Manhattan Prep GMAT Blog - Help! I Can't Handle GMAT Probability and Combinatorics (Part 3) by Chelsey Cooley" width="533" height="138" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/gmat-blog-pc-part-3-img-3.png 533w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/gmat-blog-pc-part-3-img-3-300x78.png 300w" sizes="(max-width: 533px) 100vw, 533px" /></p>
<p><span style="font-weight: 400;">Finally, Boris and Charlie can sit wherever they’d like. That doubles the number of possibilities, giving us a total of </span><b>8</b><span style="font-weight: 400;">. </span></p>
<p><span style="font-weight: 400;">Next, look at the scenarios where Frank sits across from Anil. Try it on your own: can you identify the </span><b>4 possible scenarios</b><span style="font-weight: 400;"> that work? Combining those with the 8 scenarios we found already gives a total of </span><b>12 ways to arrange the diners</b><span style="font-weight: 400;">. </span></p>
<p><span style="font-weight: 400;">Now, that practice problem is more time-consuming than anything you’re likely to see on the GMAT. However, you can use the basic ideas from that problem on a wide range of GMAT probability and combinatorics problems! </span></p>
<p><span style="font-weight: 400;">On the GMAT, you may have heard about “order matters” and “order doesn’t matter” combinatorics problems—let’s talk a bit about those. Personally, I find the “order matters” terminology to be confusing, so I’m not going to use those words in this article. Instead, here’s a method that will use the skill of “splitting up the problem” that you’ve already been developing. Here’s an example problem.</span></p>
<p style="padding-left: 30px;"><em><span style="font-weight: 400;">In how many ways can a committee of 5 members be chosen from a class of 10 people? </span></em></p>
<p style="padding-left: 30px;"><span style="font-weight: 400;">(A) 40<br />
</span><span style="font-weight: 400;">(B) 126<br />
</span><span style="font-weight: 400;">(C) 252<br />
</span><span style="font-weight: 400;">(D) 6048<br />
</span><span style="font-weight: 400;">(E) 30240</span></p>
<p><span style="font-weight: 400;">Yikes—those numbers are too big to </span><i><span style="font-weight: 400;">just</span></i><span style="font-weight: 400;"> list out the possibilities, like we have been. How do we start? Just like we have been, start by making the problem simpler. Don’t try to do the whole thing at once. Instead of asking yourself how to choose the committee, ask yourself: </span><b>in how many ways can I choose the first member of the committee?</b><span style="font-weight: 400;"> Well, there are 10 people in the class, so there are 10 ways to do it. </span></p>
<p><span style="font-weight: 400;">Now, zoom in. If you’ve already chosen the first member, how many ways are there to choose the second member? There are 9 people left, so there are 9 ways to choose. For each of 10 first members, there are 9 second members. Keep doing this until you’ve chosen the entire committee: (10)(9)(8)(7)(6).</span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13519" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/cc-42.png" alt="Manhattan Prep GMAT Blog - Help! I Can't Handle GMAT Probability and Combinatorics (Part 3) by Chelsey Cooley" width="650" height="37" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/cc-42.png 650w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/cc-42-300x17.png 300w" sizes="(max-width: 650px) 100vw, 650px" /></p>
<p>One of my high school math teachers loved to tell this joke:</p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">How many legs does a cow have?</span></i></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">Eight: two front legs, two back legs, two left legs, and two right legs. </span></i></p>
<p><span style="font-weight: 400;">When we found the solution above, we made the exact same mistake. We counted each committee more than once, just like my math teacher counted each leg more than once. Let’s see how it happened. </span></p>
<p><span style="font-weight: 400;">We started by picking the first committee member. Let’s say that was Anil. Then, we picked a second committee member: that was Boris. Then, we picked Charlie, then Dana, then Emmaline. However, we </span><i><span style="font-weight: 400;">separately </span></i><span style="font-weight: 400;">counted the scenario where we started by picking Dana, then picked Anil, then Charlie, then Emmaline, then Boris. And we </span><i><span style="font-weight: 400;">also</span></i><span style="font-weight: 400;"> separately counted the case where we picked Anil, then Charlie, then Boris, then Dana, then Emmaline. Those committees should </span><i><span style="font-weight: 400;">actually</span></i><span style="font-weight: 400;"> all be the </span><i><span style="font-weight: 400;">same </span></i><span style="font-weight: 400;">committee, because they have the same people on them! We should have only counted it once. But we messed up—we counted it a bunch of different times, just like we counted each of the cow’s legs too many times. </span></p>
<p><span style="font-weight: 400;">However, you can fix this problem easily. You just have to </span><b>divide by the number of times you counted each committee.</b><span style="font-weight: 400;"> (Notice that in my math teacher’s joke, we counted each leg twice—so, to get the right answer, you’d just have to divide by 2). How many times did we count the committee consisting of Anil, Boris, Charlie, Dana, and Emmaline? We counted it once for each possible order we could have picked them in. There are (5)(4)(3)(2)(1) different orders to put them in, which means we counted each committee 120 times. Our answer is 120 times too big. </span></p>
<p><span style="font-weight: 400;">Just divide by 120, and you have the right answer! Here’s what your scratch work would look like:</span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13520" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/04/cc-42-2.png" alt="Manhattan Prep GMAT Blog - Help! I Can't Handle GMAT Probability and Combinatorics (Part 3) by Chelsey Cooley" width="136" height="44" /></p>
<p><span style="font-weight: 400;">Okay, try it again, but more quickly: </span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">How many different poker hands of 5 cards can be drawn from a 52-card deck?</span></i></p>
<p><span style="font-weight: 400;">There are 52 ways to draw the first card, 51 ways to draw the second card, and so on. That makes (52)(51)(50)(49)(48) different hands. </span><b>Did we overcount?</b><span style="font-weight: 400;"> Yes! We counted each hand (5)(4)(3)(2)(1) = 120 times, just like we counted each committee 120 times. Divide by 120 to get your answer. </span></p>
<p><span style="font-weight: 400;">How about this one? </span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">A teacher asks 3 students from a class of 7 to stand in a straight line from left to right. In how many different ways can this be done? </span></i></p>
<p><span style="font-weight: 400;">Okay, there are 7 ways to choose the student on the left, then 6 students who could be in the middle, then 5 students on the right. (7)(6)(5) possibilities. </span><b>Did we overcount? </b><span style="font-weight: 400;">Actually, we didn’t. We don’t have to divide. That’s because the line consisting of Anil, Boris, and Charlie </span><i><span style="font-weight: 400;">should</span></i><span style="font-weight: 400;"> be counted separately from the line consisting of Charlie, Boris, and Anil. Those are two different lines, so you need to count them both individually. The right answer is (7)(6)(5) = 210—no division necessary. </span></p>
<p><span style="font-weight: 400;">Now you have a basic strategy for combinatorics problems with </span><b>bigger numbers</b><span style="font-weight: 400;">: count the possibilities as simply as possible. Then, </span><b>divide if necessary</b><span style="font-weight: 400;"> to fix the “cow has eight legs” mistake. This strategy achieves the same thing as thinking about “order matters,” but it keeps you from having to worry about which type of problem you’re dealing with! Instead, you can just use math and common sense to figure it out. ?</span></p>
<hr />
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<p><b><i><em><strong><a id="bloglink" href="https://www.manhattanprep.com/instructors/chelsey-cooley/" target="_blank">Chelsey Cooley</a><a href="https://www.manhattanprep.com/instructors/chelsey-cooley/?utm_source=manhattanprep.com%2Fgre%2Fblog&#038;utm_medium=blog&#038;utm_content=CooleyBioGREBlog&#038;utm_campaign=GRE%20Blog" target="_blank"><img decoding="async" loading="lazy" class="alignleft" title="Chelsey Cooley Manhattan Prep GRE Instructor" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2015/11/chelsey-cooley-150x150.jpg" alt="Chelsey Cooley Manhattan Prep GRE Instructor" width="150" height="150" /></a> is a Manhattan Prep instructor based in Seattle, Washington.</strong> </em></i></b><i><em>Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170/170 on the GRE. </em></i><i><em><a id="bloglink" href="https://www.manhattanprep.com/gre/classes/#instructor/48" target="_blank">Check out Chelsey’s upcoming GRE prep offerings here</a>.</em></i></p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/help-i-cant-handle-gmat-probability-and-combinatorics-part-3/">Help! I Can&#8217;t Handle GMAT Probability and Combinatorics (Part 3)</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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		<title>Help! I Can&#8217;t Handle GMAT Probability and Combinatorics (Part 2)</title>
		<link>https://www.manhattanprep.com/gmat/blog/help-i-cant-handle-gmat-probability-and-combinatorics-part-2/</link>
		
		<dc:creator><![CDATA[Chelsey Cooley]]></dc:creator>
		<pubDate>Thu, 30 Mar 2017 15:42:48 +0000</pubDate>
				<category><![CDATA[Challenge Problem]]></category>
		<category><![CDATA[For Current Studiers]]></category>
		<category><![CDATA[GMAT Prep]]></category>
		<category><![CDATA[GMAT Strategies]]></category>
		<category><![CDATA[GMAT Study Guide]]></category>
		<category><![CDATA[How to Study]]></category>
		<category><![CDATA[Quant]]></category>
		<category><![CDATA[GMAT Probability]]></category>
		<category><![CDATA[GMAT Probability and Combinatorics]]></category>
		<guid isPermaLink="false">http://www.manhattanprep.com/gmat/?p=13430</guid>

					<description><![CDATA[<p>Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here. In the previous article in this series, we introduced two big ideas about GMAT probability and combinatorics: Most people find them counterintuitive. The best way [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/help-i-cant-handle-gmat-probability-and-combinatorics-part-2/">Help! I Can&#8217;t Handle GMAT Probability and Combinatorics (Part 2)</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13509" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-30-17-social-1.png" alt="Manhattan Prep GMAT Blog - Help! I Can't Handle GMAT Probability and Combinatorics (Part 2) by Chelsey Cooley" width="1200" height="628" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-30-17-social-1.png 1200w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-30-17-social-1-300x157.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-30-17-social-1-768x402.png 768w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-30-17-social-1-1024x536.png 1024w" sizes="(max-width: 1200px) 100vw, 1200px" /></p>
<p><b><i>Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! </i></b><a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/" target="_blank"><b><i>Check out our upcoming courses here</i></b></a><b><i>.</i></b></p>
<hr />
<p><b><i></i></b><span style="font-weight: 400;">In the </span><a id="bloglink" href="https://www.manhattanprep.com/gmat/blog/2017/03/16/help-i-cant-handle-gmat-probability-and-combinatorics-part-1/" target="_blank"><span style="font-weight: 400;">previous article in this series</span></a><span style="font-weight: 400;">, we introduced two big ideas about GMAT probability and combinatorics:</span></p>
<ol>
<li style="font-weight: 400;"><span style="font-weight: 400;">Most people find them counterintuitive.</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">The best way to get past that is to </span><i><span style="font-weight: 400;">list the possibilities.</span></i></li>
</ol>
<p><span style="font-weight: 400;">In this article, we’ll focus more on #2. How do you list out the possibilities in a GMAT probability or combinatorics problem? Let’s try it on a simple probability problem.</span><span id="more-13430"></span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">If you flip three fair coins, what is the probability of getting exactly two heads? </span></i></p>
<p><span style="font-weight: 400;">Student A reasons as follows: “There are four different scenarios. You could get no heads, one head, two heads, or three heads. Therefore, the probability of getting two heads is one out of four, or ¼.”</span></p>
<p><span style="font-weight: 400;">Unfortunately, Student A is incorrect. That’s because </span><i><span style="font-weight: 400;">Student A’s four scenarios aren’t equally likely</span></i><span style="font-weight: 400;">. It’s actually more likely that you’ll get two heads than three heads. To see why (and to solve this problem), break down the possibilities more finely. Actually write out which coins will land heads up, and which ones will land tails up.</span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13431" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41.png" alt="" width="654" height="189" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41.png 654w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-300x87.png 300w" sizes="(max-width: 654px) 100vw, 654px" /></p>
<p><span style="font-weight: 400;">In </span><b>three out of the eight cases</b><span style="font-weight: 400;">, there are exactly two heads. The probability is 3/8.</span></p>
<p><span style="font-weight: 400;">How can you be sure that you’ve considered every case? The trick is to stay organized. To create the table above, I thought like this: </span></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">Let’s start with three heads. There’s only one way for that to happen. List it out.</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">Now, two heads. In that case, there’s one tail. The one tail could be the first coin, the second coin, or the third coin. List out those cases.</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">Next, one head. That single head could be the first coin, the second coin, or the third coin. That’s three more cases. List them out.</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">Finally, there could be zero heads. That’s the last case.</span></li>
</ul>
<p><span style="font-weight: 400;">I’m sure that I listed every case, because I considered all of the possibilities, from ‘all heads’ down to ‘no heads.’ But actually, that’s not the only way to list your cases! Here’s a second way to get the same result. </span></p>
<p><span style="font-weight: 400;">This time, start by listing out the cases that start with two heads. </span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13432" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-2.png" alt="" width="655" height="49" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-2.png 655w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-2-300x22.png 300w" sizes="(max-width: 655px) 100vw, 655px" /></p>
<p>Then, consider the cases that start with two tails:</p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13433" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-3.png" alt="" width="655" height="49" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-3.png 655w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-3-300x22.png 300w" sizes="(max-width: 655px) 100vw, 655px" /></p>
<p>Then, consider the cases that start with a head and a tail:</p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13434" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-4.png" alt="" width="659" height="48" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-4.png 659w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-4-300x22.png 300w" sizes="(max-width: 659px) 100vw, 659px" /></p>
<p>Finally, the cases that start with a tail and a head:</p>
<p><span style="font-weight: 400;"><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13435" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-5.png" alt="" width="654" height="45" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-5.png 654w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-5-300x21.png 300w" sizes="(max-width: 654px) 100vw, 654px" /></span></p>
<p><span style="font-weight: 400;">There are still eight cases, and three of them still have exactly two heads. </span><b>Once again, we can conclude that the probability is 3/8.</b></p>
<p><span style="font-weight: 400;">Before you keep reading, try listing out all of the scenarios that fit the following description. Stay organized, and use visuals if they help you!</span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;"> A family of five is going on a road trip. Their car has five seats: a driver’s seat and one passenger seat in the front, and two window seats and a middle seat in the back. The family consists of Mom, Dad, and three kids: Alice, Bob, and Claire. Only Mom and Dad are able to drive. Mom can’t sit in the back, because she gets carsick, and Alice and Claire can’t sit next to each other, or else they’ll fight. In how many different ways can the family sit in the car? </span></i></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13436" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-6.png" alt="" width="661" height="37" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-6.png 661w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-6-300x17.png 300w" sizes="(max-width: 661px) 100vw, 661px" /></p>
<p>Got your list? Okay, I’ll share how I thought about this one.</p>
<p><span style="font-weight: 400;">Let’s start with the driver, since that position has the fewest possibilities. Either Mom or Dad is driving. So, the first thing I jotted down on my paper was a two-column chart:</span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13437" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-7.png" alt="" width="658" height="52" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-7.png 658w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-7-300x24.png 300w" sizes="(max-width: 658px) 100vw, 658px" /></p>
<p>If Dad is driving, then Mom must be in the front passenger seat. She can’t be in the back, and that’s the only seat left. That leaves the three kids in the back.</p>
<p><span style="font-weight: 400;">If we put the three kids in the back, how many ways can we arrange them? Well, Bob has to be in the middle – otherwise, Alice and Claire would be next to each other, and we can’t have that. So there are really only two ways to do it. Either Alice is on the left and Claire is on the right, or it’s the other way around. </span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13438" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-8.png" alt="" width="656" height="70" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-8.png 656w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-8-300x32.png 300w" sizes="(max-width: 656px) 100vw, 656px" /></p>
<p>There are two possibilities, and they look like this:</p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13439" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/gmat-blog-pc-part-2-img-1.png" alt="" width="630" height="255" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/gmat-blog-pc-part-2-img-1.png 630w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/gmat-blog-pc-part-2-img-1-300x121.png 300w" sizes="(max-width: 630px) 100vw, 630px" /></p>
<p><b>What have we just learned? </b><span style="font-weight: 400;">First, if Dad is driving, there are only two different ways to seat everyone else. Second, despite my GMAT score, I’m not so great at drawing cars.  </span></p>
<p><span style="font-weight: 400;"> Okay, let’s turn our attention to the second scenario. What if Mom is driving?</span></p>
<p><span style="font-weight: 400;">Anybody could be in the front seat, so let’s split it up again to make things simpler. Let’s suppose that Dad is in the front seat. How many ways could we arrange everybody else? </span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13440" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-10.png" alt="" width="653" height="71" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-10.png 653w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-10-300x33.png 300w" sizes="(max-width: 653px) 100vw, 653px" /></p>
<p>If Dad is in the front with Mom, we have the same two cases we already looked at. Alice and Claire can’t be next to each other, so Bob is in the middle and his sisters are on either side.</p>
<p><span style="font-weight: 400;">What if Dad </span><i><span style="font-weight: 400;">isn’t</span></i><span style="font-weight: 400;"> in the front? Let’s try putting poor Bob in the front, instead of sticking him in the middle seat. </span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13441" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-11.png" alt="" width="655" height="127" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-11.png 655w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-11-300x58.png 300w" sizes="(max-width: 655px) 100vw, 655px" /></p>
<p>Dad would have to be in the middle, to separate Alice and Claire. That gives us two more possibilities.</p>
<p><span style="font-weight: 400;">What if Alice is in the front? Well, it doesn’t matter how we arrange the back seat, since there’s no risk of Alice and Claire fighting. There are 6 ways to arrange it, and they all work fine. </span><b>The same thing happens if we put Claire in front</b><span style="font-weight: 400;">: since one of the sisters is in the front, it doesn’t matter what order the back seat is in. </span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13442" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-12.png" alt="" width="663" height="247" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-12.png 663w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/cc-41-12-300x112.png 300w" sizes="(max-width: 663px) 100vw, 663px" /></p>
<p>If Mom is driving, there are 2 + 2 + 6 + 6 = 16 different ways for the family to sit. Add the two cases where Dad is driving, and that makes a total of 18 possibilities.</p>
<p><span style="font-weight: 400;">Here’s what I really want you to notice. </span><b>This process isn’t magic, and it isn’t math. </b><span style="font-weight: 400;">It’s just about organization. </span></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">First, we </span><b>split up the problem</b><span style="font-weight: 400;"> to make it easier. This is one of the basic principles of counting cases. </span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">We split it up that way for a good reason. </span><b>There were only two different people who could drive</b><span style="font-weight: 400;">, so splitting up the problem like that made it easy to stay organized. If we’d split up the problem based on who was in the passenger seat (for example), we still would’ve gotten the right answer, but it would have been much messier. </span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">When we realized that Mom driving still gave us a lot of different cases, we </span><b>split up the problem a second time</b><span style="font-weight: 400;">. </span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">We stayed organized by </span><b>drawing a chart on our paper and filling it in</b><span style="font-weight: 400;">. </span></li>
</ul>
<p><span style="font-weight: 400;">This problem only had a small number of scenarios. There’s one big question remaining: can we use the same technique to handle much larger problems? We can. In two weeks, <a id="bloglink" href="https://www.manhattanprep.com/gmat/blog/2017/04/13/help-i-cant-handle-gmat-probability-and-combinatorics-part-3/" target="_blank">check out the final article in this series</a> to learn how. And while you’re waiting, try this practice problem:  </span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">Six coworkers (Anil, Boris, Charlie, Dana, Emmaline, and Frank) are having dinner at a restaurant. They’ll sit in chairs that are evenly spaced around a circular table. Boris, Charlie, and Dana refuse to sit directly across from Anil, because he chews with his mouth open. Frank and Emmaline won’t sit next to each other. Finally, Emmaline and Dana insist on sitting next to each other. How many different arrangements will work? (Ignore the arrangements that come from ‘rotating’ the whole table – only focus on the relative positions of the diners.) </span></i><span style="font-weight: 400;">?</span></p>
<hr />
<p><b><i>Want more guidance from our GMAT gurus? You can attend the first session of any of our online or in-person GMAT courses absolutely free! We’re not kidding. </i></b><a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/" target="_blank"><b><i>Check out our upcoming courses here</i></b></a><b><i>.</i></b><span style="font-weight: 400;"></span></p>
<hr />
<p><b><i><em><strong><a id="bloglink" href="https://www.manhattanprep.com/instructors/chelsey-cooley/" target="_blank">Chelsey Cooley</a><a href="https://www.manhattanprep.com/instructors/chelsey-cooley/?utm_source=manhattanprep.com%2Fgre%2Fblog&#038;utm_medium=blog&#038;utm_content=CooleyBioGREBlog&#038;utm_campaign=GRE%20Blog" target="_blank"><img decoding="async" loading="lazy" class="alignleft" title="Chelsey Cooley Manhattan Prep GRE Instructor" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2015/11/chelsey-cooley-150x150.jpg" alt="Chelsey Cooley Manhattan Prep GRE Instructor" width="150" height="150" /></a> is a Manhattan Prep instructor based in Seattle, Washington.</strong> </em></i></b><i><em>Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170/170 on the GRE. </em></i><i><em><a id="bloglink" href="https://www.manhattanprep.com/gre/classes/#instructor/48" target="_blank">Check out Chelsey’s upcoming GRE prep offerings here</a>.</em></i></p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/help-i-cant-handle-gmat-probability-and-combinatorics-part-2/">Help! I Can&#8217;t Handle GMAT Probability and Combinatorics (Part 2)</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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		<title>Help! I Can&#8217;t Handle GMAT Probability and Combinatorics (Part 1)</title>
		<link>https://www.manhattanprep.com/gmat/blog/help-i-cant-handle-gmat-probability-and-combinatorics-part-1/</link>
		
		<dc:creator><![CDATA[Chelsey Cooley]]></dc:creator>
		<pubDate>Thu, 16 Mar 2017 15:57:23 +0000</pubDate>
				<category><![CDATA[Challenge Problem]]></category>
		<category><![CDATA[For Current Studiers]]></category>
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		<category><![CDATA[GMAT Probability and Combinatorics]]></category>
		<category><![CDATA[Probability and Combinatorics]]></category>
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					<description><![CDATA[<p>Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here. There’s a classic brain teaser called the Monty Hall problem. It’s named after the host of an old-timey TV game show, who used it to [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/help-i-cant-handle-gmat-probability-and-combinatorics-part-1/">Help! I Can&#8217;t Handle GMAT Probability and Combinatorics (Part 1)</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13415" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-16-17-social-1.png" alt="Manhattan Prep GMAT Blog - Help! I Can't Handle GMAT Probability and Combinatorics (Part 1) by Chelsey Cooley" width="1200" height="628" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-16-17-social-1.png 1200w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-16-17-social-1-300x157.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-16-17-social-1-768x402.png 768w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-16-17-social-1-1024x536.png 1024w" sizes="(max-width: 1200px) 100vw, 1200px" /></p>
<p><b><i>Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! </i></b><a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/" target="_blank"><b><i>Check out our upcoming courses here</i></b></a><b><i>.</i></b></p>
<hr />
<p><b><i></i></b><span style="font-weight: 400;">There’s a classic brain teaser called the Monty Hall problem. It’s named after the host of an old-timey TV game show, who used it to confound contestants. He’d present each contestant with three closed doors. Behind one door was a new car, and behind the other two doors were goats. </span></p>
<p><span style="font-weight: 400;">Monty invited the player to pick one of the three doors. Whichever door the player chose, Monty would then open a </span><i><span style="font-weight: 400;">different</span></i><span style="font-weight: 400;"> one, revealing a goat, not the car. Then, he would offer the player a choice. If the player wanted, he could </span><i><span style="font-weight: 400;">switch</span></i><span style="font-weight: 400;"> doors, picking the other unopened door. Or, he could stick with the door he picked in the first place. Whichever decision he made, he would win the prize behind the door he chose. </span><span id="more-13314"></span></p>
<p><span style="font-weight: 400;">The question is, </span><i><span style="font-weight: 400;">does switching doors give the contestant a higher probability of picking the car</span></i><span style="font-weight: 400;">? It should seem obvious that it doesn’t. The car is equally likely to be behind any of the doors. So, it seems like once one of the three doors is open, you have 50/50 odds of picking the car, regardless of whether you switch or stay. </span></p>
<p><span style="font-weight: 400;">However, </span><i><span style="font-weight: 400;">that isn’t true</span></i><span style="font-weight: 400;">. Believe it or not, switching actually increases the probability of picking the car to 2/3, while staying on the same door means that you only have a 1 in 3 chance of picking it. If you didn’t figure that out on your own, you’re in the company of many very smart people, including a number of famous mathematicians.</span></p>
<p><span style="font-weight: 400;">From a GMAT perspective, here’s what to take away from this little anecdote. GMAT probability and combinatorics are counterintuitive for </span><i><span style="font-weight: 400;">everyone</span></i><span style="font-weight: 400;">. I majored in math in college – I even took a couple of courses on probability – and I still can’t solve these problems by intuiting which formulas to use. It seems crazy to me that switching doors after the fact would make you more likely to pick the car. So, what do I do – and what should you do? I think about almost all GMAT probability and combinatorics problems in terms of </span><i><span style="font-weight: 400;">counting out possibilities</span></i><span style="font-weight: 400;">. </span></p>
<p><span style="font-weight: 400;">Let’s give it a try with the Monty Hall problem. Imagine that you play three games with Monty. Additionally, imagine we’re in probability land, where everything happens exactly according to its probability. Since there are three possible scenarios, and they’re all equally likely, here’s what your three games will look like. </span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13316" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/1-cc.png" alt="Manhattan Prep GMAT Blog - Help! I Can't Handle GMAT Probability and Combinatorics (Part 1) by Chelsey Cooley" width="673" height="108" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/1-cc.png 673w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/1-cc-300x48.png 300w" sizes="(max-width: 673px) 100vw, 673px" /></p>
<p><span style="font-weight: 400;">Now, Monty opens one of the two doors you didn’t pick. Remember that Monty always opens a door with a goat behind it. So, in two out of the three games, Monty is stuck: there’s only one door he can choose. </span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13317" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/2-cc.png" alt="Manhattan Prep GMAT Blog - Help! I Can't Handle GMAT Probability and Combinatorics (Part 1) by Chelsey Cooley" width="668" height="99" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/2-cc.png 668w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/2-cc-300x44.png 300w" sizes="(max-width: 668px) 100vw, 668px" /></p>
<p><span style="font-weight: 400;">In both of these games, you started with a goat. If you switch, you’ll win! </span></p>
<p><span style="font-weight: 400;">In game 3, Monty could pick either door, since they both have goats. Let’s say he flips a coin to decide which one to pick. If he gets heads, he’ll open the first mystery door. If he gets tails, he’ll open the second one. This scenario only comes up when you picked the car in the first place – so, Monty only needs to worry about it 1/3 of the time.</span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-13318" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-cc.png" alt="Manhattan Prep GMAT Blog - Help! I Can't Handle GMAT Probability and Combinatorics (Part 1) by Chelsey Cooley" width="664" height="98" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-cc.png 664w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2017/03/3-cc-300x44.png 300w" sizes="(max-width: 664px) 100vw, 664px" /></p>
<p><span style="font-weight: 400;">Interestingly, it doesn’t matter what Monty flips. No matter what, if Monty flips a coin at all, and you switch, you’ll lose. If you always switch, you’ll win 2 out of your 3 games, and lose 1 of them. That means that switching gives you a 2/3 probability of winning. </span></p>
<p><span style="font-weight: 400;">The reason the Monty Hall problem is so counterintuitive, is that people don’t remember that you’re more likely to start with a goat than with a car. Since there are two possibilities – goat or car – your brain wants to think that they’re equally likely. They aren’t. If you start with a goat, switching is always good, and if you start with a car, switching is always bad. You’re more likely to start with a goat than with a car, so without any more information, you should assume that switching is good. </span></p>
<p><span style="font-weight: 400;">How do you apply this to the GMAT? There are a few ways. First, recognize that probability is counterintuitive. Not just for you – for many people who are far better at math than you and I, as well. If you see a super tough GMAT probability and combinatorics problem, feel free to guess, since everyone else is probably getting it wrong too. And </span><i><span style="font-weight: 400;">don’t</span></i><span style="font-weight: 400;"> make the “obvious” guess, since it’s probably a trap. Second, the best way to work through counterintuitive GMAT probability and combinatorics problems is to write out, or think out, the different possibilities in an organized way. This is even possible when you’re doing problems with very large numbers, as you’ll learn from <a id="bloglink" href="https://www.manhattanprep.com/gmat/blog/2017/03/30/help-i-cant-handle-gmat-probability-and-combinatorics-part-2/" target="_blank">the next article in this series</a>. ?</span></p>
<hr />
<p><b><i>Want more guidance from our GRE gurus? You can attend the first session of any of our online or in-person GRE courses absolutely free! We’re not kidding. </i></b><a id="bloglink" href="https://www.manhattanprep.com/gre/classes/" target="_blank"><b><i>Check out our upcoming courses here</i></b></a><b><i>.</i></b></p>
<hr />
<p><b><i><em><strong><a id="bloglink" href="https://www.manhattanprep.com/instructors/chelsey-cooley/" target="_blank">Chelsey Cooley</a><a href="https://www.manhattanprep.com/instructors/chelsey-cooley/?utm_source=manhattanprep.com%2Fgre%2Fblog&#038;utm_medium=blog&#038;utm_content=CooleyBioGREBlog&#038;utm_campaign=GRE%20Blog" target="_blank"><img decoding="async" loading="lazy" class="alignleft" title="Chelsey Cooley Manhattan Prep GRE Instructor" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2015/11/chelsey-cooley-150x150.jpg" alt="Chelsey Cooley Manhattan Prep GRE Instructor" width="150" height="150" /></a> is a Manhattan Prep instructor based in Seattle, Washington.</strong> </em></i></b><i><em>Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170/170 on the GRE. </em></i><i><em><a id="bloglink" href="https://www.manhattanprep.com/gre/classes/#instructor/48" target="_blank">Check out Chelsey’s upcoming GRE prep offerings here</a>.</em></i></p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/help-i-cant-handle-gmat-probability-and-combinatorics-part-1/">Help! I Can&#8217;t Handle GMAT Probability and Combinatorics (Part 1)</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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		<title>Here&#8217;s How to do GMAT Unit Conversions Like a Pro</title>
		<link>https://www.manhattanprep.com/gmat/blog/heres-how-to-do-gmat-unit-conversions-like-a-pro/</link>
		
		<dc:creator><![CDATA[Chelsey Cooley]]></dc:creator>
		<pubDate>Wed, 20 Jan 2016 17:45:36 +0000</pubDate>
				<category><![CDATA[Algebra]]></category>
		<category><![CDATA[Challenge Problem]]></category>
		<category><![CDATA[Data Sufficiency]]></category>
		<category><![CDATA[For Current Studiers]]></category>
		<category><![CDATA[Fractions, Decimals, Percents]]></category>
		<category><![CDATA[GMAT Prep]]></category>
		<category><![CDATA[How to Study]]></category>
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		<category><![CDATA[b-school]]></category>
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		<category><![CDATA[unit conversions]]></category>
		<guid isPermaLink="false">http://www.manhattanprep.com/gmat/?p=10904</guid>

					<description><![CDATA[<p>Sometimes the whole point of a specific GMAT problem is to convert between miles and kilometers, or meters and centimeters. In other problems, you&#8217;ll need to do a unit conversion as part of a longer solution. It&#8217;s easy to mess up unit conversions, and the GMAT writers know this &#8212; they include them on the [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/heres-how-to-do-gmat-unit-conversions-like-a-pro/">Here&#8217;s How to do GMAT Unit Conversions Like a Pro</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><img decoding="async" loading="lazy" class="alignleft size-full wp-image-10909" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/blog-metrics.png" alt="blog-metrics" width="676" height="264" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/blog-metrics.png 676w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/blog-metrics-300x117.png 300w" sizes="(max-width: 676px) 100vw, 676px" />Sometimes the whole point of a specific GMAT problem is to convert between miles and kilometers, or meters and centimeters. In other problems, you&#8217;ll need to do a unit conversion as part of a longer solution. It&#8217;s easy to mess up unit conversions, and the GMAT writers know this &#8212; they include them on the test in order to test your level of organization and your ability to double-check your work. Here&#8217;s how to add fast unit conversions to your repertoire of skills.  <span id="more-10904"></span></p>
<ol>
<li><strong> Write the units down</strong></li>
</ol>
<p>The easiest mistake to make is simply forgetting what units you&#8217;re working with. If the problem asks for a number of cents, but you calculate a number of dollars, you&#8217;ll be off by a factor of 100 even if you do all of the math correctly. If there&#8217;s any chance that units will come into play in a problem, write them out at every step.</p>
<ol start="2">
<li><strong> Treat units like variables</strong></li>
</ol>
<p>Units can be multiplied, divided, and canceled out, exactly like variables. (Remember that &#8216;per&#8217; always translates to division.) Suppose you&#8217;re converting 1400 crowns to rupees, and you know that the exchange rate is 0.4 crowns per rupee. Do you multiply 1400 by 0.4, or do you divide? Check by trying to cancel out the units:</p>
<p><strong>Wrong:</strong></p>
<p><strong><img decoding="async" loading="lazy" class="alignleft  wp-image-10905" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/unit-conversions-1.png" alt="Unit_Conversions_1" width="500" height="239" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/unit-conversions-1.png 364w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/unit-conversions-1-300x143.png 300w" sizes="(max-width: 500px) 100vw, 500px" /></strong></p>
<p> </p>
<p><strong><br />
</strong></p>
<p> </p>
<p> </p>
<p> </p>
<p><strong>Right:</strong></p>
<p><strong><img decoding="async" loading="lazy" class="alignleft  wp-image-10906" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/unit-conversions-2.png" alt="Unit_Conversions_2" width="731" height="303" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/unit-conversions-2.png 531w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/unit-conversions-2-300x124.png 300w" sizes="(max-width: 731px) 100vw, 731px" /></strong></p>
<p><strong><br />
</strong></p>
<p>Since division causes the units to correctly simplify to rupees, division is correct. Think about which units will need to cancel, and arrange them so that they do.</p>
<ol start="3">
<li><strong> One step at a time</strong></li>
</ol>
<p>With complex unit conversions, don&#8217;t skip steps. Convert a single unit at a time. In this example, we&#8217;ll convert 15 meters per second to kilometers per hour, by first converting seconds to minutes.</p>
<p><img decoding="async" loading="lazy" class="alignleft size-full wp-image-10907" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/unit-conversions-3.png" alt="Unit_Conversions_3" width="917" height="389" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/unit-conversions-3.png 917w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/01/unit-conversions-3-300x127.png 300w" sizes="(max-width: 917px) 100vw, 917px" /></p>
<p>All that&#8217;s left is to do the arithmetic, by calculating (15 x 60 x 60)/1000. The result is 54 kilometers per hour.</p>
<ol start="4">
<li><strong> Sanity check</strong></li>
</ol>
<p>Do a basic sanity check each time you finish a unit conversion using familiar units. If you&#8217;re converting two hundred dollars to cents, should the result be <em>greater than 200</em> or <em>less than 200</em>? If you&#8217;re converting 45 seconds to hours, should the result be <em>greater than 45</em> or <em>less than 45</em>? It&#8217;s easy to mix up multiplication and division, and quickly checking to make sure your result is sensible can help you avoid this.</p>
<ol start="5">
<li><strong> Practice with Google</strong></li>
</ol>
<p>Type &#8220;15 meters per second in kilometers per hour&#8221; into a Google search box. Google Calculator automatically handles many unit conversions, including complex ones. That means that you can use it to drill this skill after reading this article! Make up a few complex unit conversions and simplify them on paper, exactly as you would if you saw them on the GMAT. Then, use Google to check your answers.</p>
<p>Half an hour of work, right now, will make you much quicker and more confident at unit conversions. While they don&#8217;t appear in every Quant problem, the GMAT test writers love to throw them in at the end of a tricky problem, in the hopes that unprepared test takers will make an easy mistake. Make them part of your GMAT toolkit, and outsmart the test! <img src="https://s.w.org/images/core/emoji/14.0.0/72x72/1f4dd.png" alt="📝" class="wp-smiley" style="height: 1em; max-height: 1em;" /></p>
<hr />
<p><em><strong><a href="https://www.manhattanprep.com/instructors/chelsey-cooley/#" target="_blank"><img decoding="async" loading="lazy" class="alignleft wp-image-8513 size-thumbnail" src="//cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2015/11/chelsey-cooley-150x150.jpg" alt="Chelsey-Cooley" width="150" height="150" /></a></strong></em><em><strong><a href="https://www.manhattanprep.com/instructors/chelsey-cooley/?utm_source=manhattanprep.com%2Fgre%2Fblog&#038;utm_medium=blog&#038;utm_content=CooleyBioGREBlog&#038;utm_campaign=GRE%20Blog">Chelsey Cooley</a> is a Manhattan Prep instructor based in Seattle, Washington.</strong> Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170/170 on the GRE. Check out Chelsey’s upcoming GMAT prep offerings <a href="https://www.manhattanprep.com/gmat/classes/?utm_source=manhattanprep.com%2Fgmat%2Fblog&#038;utm_medium=blog&#038;utm_content=CooleyCoursesLinkGMATBlog&#038;utm_campaign=GMAT%20Blog#instructor/336">here</a>.</em></p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/heres-how-to-do-gmat-unit-conversions-like-a-pro/">Here&#8217;s How to do GMAT Unit Conversions Like a Pro</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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		<title>Manhattan Prep&#8217;s GMAT® study app is now available!</title>
		<link>https://www.manhattanprep.com/gmat/blog/manhattan-preps-gmat-study-app-is-now-available/</link>
		
		<dc:creator><![CDATA[Stacey Koprince]]></dc:creator>
		<pubDate>Tue, 17 Nov 2015 00:40:56 +0000</pubDate>
				<category><![CDATA[Algebra]]></category>
		<category><![CDATA[Apps and Admissions]]></category>
		<category><![CDATA[Challenge Problem]]></category>
		<category><![CDATA[Critical Reasoning]]></category>
		<category><![CDATA[Data Sufficiency]]></category>
		<category><![CDATA[Essay]]></category>
		<category><![CDATA[For Current Studiers]]></category>
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		<category><![CDATA[Geometry]]></category>
		<category><![CDATA[GMAT 101]]></category>
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		<category><![CDATA[GMAT Resources]]></category>
		<category><![CDATA[GMAT Study Guide]]></category>
		<category><![CDATA[MBA]]></category>
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		<category><![CDATA[Quant]]></category>
		<category><![CDATA[Reading Comprehension]]></category>
		<category><![CDATA[Sentence Correction]]></category>
		<category><![CDATA[Taking the GMAT]]></category>
		<category><![CDATA[Verbal]]></category>
		<category><![CDATA[b-school]]></category>
		<category><![CDATA[business school]]></category>
		<category><![CDATA[GMAT]]></category>
		<category><![CDATA[gmat app]]></category>
		<category><![CDATA[GMAT prep app]]></category>
		<category><![CDATA[gmat strategy]]></category>
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		<category><![CDATA[how to study]]></category>
		<category><![CDATA[Manhattan GMAT]]></category>
		<category><![CDATA[Manhattan Prep GMAT App]]></category>
		<guid isPermaLink="false">http://www.manhattanprep.com/gmat/?p=10630</guid>

					<description><![CDATA[<p>I am very excited to announce that our new GMAT® study app is available on both iOS and Android! Download now! iOS Android Do you need to drill foundational skills? Practice your process for any of the question types found in the Quant (DS, PS) or Verbal (CR, RC, SC) sections of the GMAT? Challenge yourself with some [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/manhattan-preps-gmat-study-app-is-now-available/">Manhattan Prep&#8217;s GMAT® study app is now available!</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><img decoding="async" loading="lazy" class="alignleft wp-image-10660 size-full" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/11/gmat-app-blog-header.png" alt="" width="676" height="264" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/11/gmat-app-blog-header.png 676w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/11/gmat-app-blog-header-300x117.png 300w" sizes="(max-width: 676px) 100vw, 676px" />I am very excited to announce that our new <a href="//www.manhattanprep.com/gmat/app/">GMAT® study app</a> is available on both <a href="https://itunes.apple.com/us/app/manhattan-prep-gmat/id1030031321?mt=8">iOS</a> and <a href="https://play.google.com/store/apps/details?id=com.hltcorp.gmat">Android</a>!</p>
<hr />
<h2 style="text-align: center;"><strong>Download now!</strong></h2>
<h3 style="text-align: center;"><span style="text-decoration: underline;"><span style="color: #ff0000; text-decoration: underline;"><strong><a style="color: #ff0000; text-decoration: underline;" href="https://itunes.apple.com/us/app/manhattan-prep-gmat/id1030031321?mt=8">iOS</a></strong></span></span></h3>
<h3 style="text-align: center;"><span style="text-decoration: underline;"><span style="color: #ff0000; text-decoration: underline;"><strong><a style="color: #ff0000; text-decoration: underline;" href="https://play.google.com/store/apps/details?id=com.hltcorp.gmat">Android</a></strong></span></span></h3>
<hr />
<h3 style="text-align: center;"></h3>
<p><span id="more-10630"></span></p>
<p>Do you need to drill foundational skills? Practice your process for any of the question types found in the Quant (DS, PS) or Verbal (CR, RC, SC) sections of the GMAT? Challenge yourself with some very advanced Quant problems?</p>
<p>We’ve got you covered. The full version of the app contains more than 2,000 practice problems along with comprehensive explanations—and even the free version will keep you busy for quite a while. Some problems are skill drills: you’ll make sure that you have all of the foundational knowledge you need in order to tackle the test. Others are full-on GMAT-format problems, so that you can practice exactly what you’ll need to do on test day.</p>
<p><img decoding="async" loading="lazy" class="wp-image-10653 aligncenter" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/11/advanced-quant-practice.jpg" alt="" width="325" height="577" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/11/advanced-quant-practice.jpg 640w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/11/advanced-quant-practice-169x300.jpg 169w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/11/advanced-quant-practice-577x1024.jpg 577w" sizes="(max-width: 325px) 100vw, 325px" /></p>
<p> </p>
<p>The app contains several glossaries, including grammar terms, math terms, and idioms. We also provide a whole host of study and time management strategies, and our friends over at <a href="//www.mbamission.com/" target="_blank">MBA Mission</a> have contributed great admissions tips.</p>
<div id="attachment_10635" style="width: 335px" class="wp-caption aligncenter"><img aria-describedby="caption-attachment-10635" decoding="async" loading="lazy" class="wp-image-10635" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/11/strategies.jpg" alt="Strategies" width="325" height="577" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/11/strategies.jpg 640w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/11/strategies-169x300.jpg 169w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/11/strategies-577x1024.jpg 577w" sizes="(max-width: 325px) 100vw, 325px" /><p id="caption-attachment-10635" class="wp-caption-text">Strategies to optimize your GMAT performance.</p></div>
<p>You can use the app in conjunction with one of our courses, but you don’t need to take a course to benefit from the app; it works just as well for stand-alone practice. You will want to identify other resources that, for example, lay out all of the grammar rules or formulas that you would need to know for the test. (Our strategy guides cover those areas.) The app is focused on practicing your skills on problems.</p>
<p>If you are taking one of our <a href="https://www.manhattanprep.com/gmat/classes/" target="_blank">courses</a> or <a href="https://www.manhattanprep.com/gmat/prep/on-demand/" target="_blank">guided self-study programs</a>, the full app won’t cost you anything; it’s included as part of your program. Now, you don’t have to have your books with you whenever you want to study. You can sneak in 5 or 10 minutes of practice while you’re waiting for that meeting to start.</p>
<p>The material is organized in the same way that our strategy guides are organized: quant by major content area and verbal by question type. Essentially, you can do any of your strategy guide end-of-chapter problem sets or online practice problems via the app rather than in your books or your Manhattan Prep student center.</p>
<p>I hope you’re as excited about the app as I am. Now, go get started and happy studying!</p>
<p>GMAT® is a registered trademark of the Graduate Management Admission Council.</p>
<hr />
<h2 style="text-align: center;"><strong>Download now!</strong></h2>
<h3 style="text-align: center;"><span style="text-decoration: underline;"><span style="color: #ff0000; text-decoration: underline;"><strong><a style="color: #ff0000; text-decoration: underline;" href="https://itunes.apple.com/us/app/manhattan-prep-gmat/id1030031321?mt=8">iOS</a></strong></span></span></h3>
<h3 style="text-align: center;"><span style="text-decoration: underline;"><span style="color: #ff0000; text-decoration: underline;"><strong><a style="color: #ff0000; text-decoration: underline;" href="https://play.google.com/store/apps/details?id=com.hltcorp.gmat">Android</a></strong></span></span></h3>
<hr />
<p><em><strong><img decoding="async" loading="lazy" class="alignleft size-thumbnail wp-image-9719" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/06/stacey-koprince-150x150.png" alt="stacey-koprince" width="150" height="150" />Stacey Koprince is a Manhattan Prep instructor based in Montreal, Canada and Los Angeles, California.</strong> Stacey has been teaching the GMAT, GRE, and LSAT  for more than 15 years and is one of the most well-known instructors in the industry. Stacey loves to teach and is absolutely fascinated by standardized tests. <a href="//www.manhattanprep.com/gmat/classes/#instructor/86">Check out Stacey’s upcoming GMAT courses here</a></em></p>
<p> </p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/manhattan-preps-gmat-study-app-is-now-available/">Manhattan Prep&#8217;s GMAT® study app is now available!</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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		<title>Monthly GMAT Challenge Problem Showdown: January 13, 2013</title>
		<link>https://www.manhattanprep.com/gmat/blog/monthly-gmat-challenge-problem-showdown-january-13-2013/</link>
		
		<dc:creator><![CDATA[Manhattan Prep]]></dc:creator>
		<pubDate>Mon, 13 Jan 2014 14:00:04 +0000</pubDate>
				<category><![CDATA[Challenge Problem]]></category>
		<category><![CDATA[challenge probelm]]></category>
		<category><![CDATA[GMAT]]></category>
		<category><![CDATA[quant]]></category>
		<guid isPermaLink="false">http://www.manhattangmat.com/blog/?p=6911</guid>

					<description><![CDATA[<p>We invite you to test your GMAT knowledge for a chance to win! The second week of every month, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that month&#8217;s drawing for free Manhattan GMAT prep materials. Tell your friends to get [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/monthly-gmat-challenge-problem-showdown-january-13-2013/">Monthly GMAT Challenge Problem Showdown: January 13, 2013</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><img decoding="async" loading="lazy" src="//cdn.manhattanprep.com/images/gmat/challengeproblemred_scribble.jpg" alt="challenge problem" width="506" height="102" /><br />
We invite you to test your GMAT knowledge for a chance to win! The second week of every month, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that month&#8217;s drawing for free Manhattan GMAT prep materials. Tell your friends to get out their scrap paper and start solving!</p>
<p>Here is this month&#8217;s problem:</p>
<blockquote><p>If <em>p</em>, <em>q</em>, and <em>r</em> are different positive integers such that <em>p</em> + <em>q</em> + <em>r</em> = 6, what is the value of <em>x</em> ?</p>
<p>(1) The average of <em>x<sup>p</sup></em> and <em>x<sup>q</sup></em> is <em>x<sup>r</sup></em>.</p>
<p>(2) The average of <em>x<sup>p</sup></em> and <em>x<sup>r</sup></em> is not <em>x<sup>q</sup></em>.</p></blockquote>
<p><span id="more-6911"></span></p>
<p><img decoding="async" style="margin: 5px;padding: 0;border: 0" src="//s17.postimage.org/bc3d39x5b/challengeproblem_RED_scribble_ICON.jpg" alt="GMAT Challenge Problem" align="right" />To see the answer choices, and to submit your answer, visit our <a href="/gmat/challenge-problems/" target="_blank">Challenge Problem Showdown</a> page on our site.</p>
<p>Discuss this month&#8217;s problem with like-minded GMAT takers on <a href="//www.facebook.com/pages/Manhattan-GMAT/39761815456" target="_blank">our Facebook page</a>.</p>
<p>The monthly winner, drawn from among all the correct submissions, will receive One Year of Access to our <a href="/storeitemshow.cfm?ItemID=61&#038;catid=4" target="_blank">Challenge Problem Archive</a>, AND the <a href="/storeitemshow.cfm?ItemID=336&#038;catid=4" target="_blank">GMAT Navigator</a>, AND Our <a href="/storeitemshow.cfm?ItemID=81&#038;catid=4" target="_blank">Six Computer Adaptive Tests</a> ($92 value).</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/monthly-gmat-challenge-problem-showdown-january-13-2013/">Monthly GMAT Challenge Problem Showdown: January 13, 2013</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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		<title>GMAT Challenge Problem Showdown: December 23, 2013</title>
		<link>https://www.manhattanprep.com/gmat/blog/gmat-challenge-problem-showdown-december-23-2013/</link>
		
		<dc:creator><![CDATA[Manhattan Prep]]></dc:creator>
		<pubDate>Mon, 23 Dec 2013 19:10:13 +0000</pubDate>
				<category><![CDATA[Challenge Problem]]></category>
		<guid isPermaLink="false">http://www.manhattangmat.com/blog/?p=6871</guid>

					<description><![CDATA[<p>We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week&#8217;s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/gmat-challenge-problem-showdown-december-23-2013/">GMAT Challenge Problem Showdown: December 23, 2013</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><img decoding="async" loading="lazy" src="//cdn.manhattanprep.com/images/gmat/challengeproblemred_scribble.jpg" alt="challenge problem" width="506" height="102" /><br />
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week&#8217;s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!</p>
<p>Here is this week&#8217;s problem:</p>
<blockquote><p>A pharmacy must purchase a set of <em>n</em> metal weights, each weighing an integer number of grams, such that all integer weights from 1 to 300 grams (inclusive) can be made with a combination of one or more of the weights. What is the minimum number of metal weights that the pharmacy must purchase?</p></blockquote>
<p><span id="more-6871"></span></p>
<p><img decoding="async" style="margin: 5px;padding: 0;border: 0" src="//s17.postimage.org/bc3d39x5b/challengeproblem_RED_scribble_ICON.jpg" alt="GMAT Challenge Problem" align="right" />To see the answer choices, and to submit your answer, visit our <a href="/challenge_thisweek.cfm" target="_blank">Challenge Problem Showdown</a> page on our site.</p>
<p>Discuss this week&#8217;s problem with like-minded GMAT takers on <a href="//www.facebook.com/pages/Manhattan-GMAT/39761815456" target="_blank">our Facebook page</a>.</p>
<p>The weekly winner, drawn from among all the correct submissions, will receive One Year of Access to our <a href="/storeitemshow.cfm?ItemID=61&#038;catid=4" target="_blank">Challenge Problem Archive</a>, AND the <a href="/storeitemshow.cfm?ItemID=336&#038;catid=4" target="_blank">GMAT Navigator</a>, AND Our <a href="/storeitemshow.cfm?ItemID=81&#038;catid=4" target="_blank">Six Computer Adaptive Tests</a> ($92 value).</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/gmat-challenge-problem-showdown-december-23-2013/">GMAT Challenge Problem Showdown: December 23, 2013</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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		<title>GMAT Challenge Problem Showdown: December 16, 2013</title>
		<link>https://www.manhattanprep.com/gmat/blog/gmat-challenge-problem-showdown-december-16-2013/</link>
		
		<dc:creator><![CDATA[Manhattan Prep]]></dc:creator>
		<pubDate>Mon, 16 Dec 2013 17:49:44 +0000</pubDate>
				<category><![CDATA[Challenge Problem]]></category>
		<category><![CDATA[Geometry]]></category>
		<category><![CDATA[Quant]]></category>
		<category><![CDATA[challenge problem]]></category>
		<category><![CDATA[GMAT]]></category>
		<category><![CDATA[gmat math]]></category>
		<category><![CDATA[quant]]></category>
		<guid isPermaLink="false">http://www.manhattangmat.com/blog/?p=6853</guid>

					<description><![CDATA[<p>We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week&#8217;s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/gmat-challenge-problem-showdown-december-16-2013/">GMAT Challenge Problem Showdown: December 16, 2013</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><img decoding="async" loading="lazy" src="//cdn.manhattanprep.com/images/gmat/challengeproblemred_scribble.jpg" alt="challenge problem" width="506" height="102" /><br />
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week&#8217;s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!</p>
<p>Here is this week&#8217;s problem:</p>
<blockquote><p><img decoding="async" src="https://cdn.manhattanprep.com/images/gmat/challenge/20131216/art1new.gif" alt="" /></p>
<p>A set of <em>n</em> identical triangles with angle <em>x</em>° and two sides of length 1 is assembled to make a parallelogram (if <em>n</em> is even) or a trapezoid (if <em>n</em> is odd), as shown. Is the perimeter of the parallelogram or trapezoid less than 10?</p></blockquote>
<p><span id="more-6853"></span></p>
<p><img decoding="async" style="margin: 5px;padding: 0;border: 0" src="//s17.postimage.org/bc3d39x5b/challengeproblem_RED_scribble_ICON.jpg" alt="GMAT Challenge Problem" align="right" />To see the answer choices, and to submit your answer, visit our <a href="/challenge_thisweek.cfm" target="_blank">Challenge Problem Showdown</a> page on our site.</p>
<p>Discuss this week&#8217;s problem with like-minded GMAT takers on <a href="//www.facebook.com/pages/Manhattan-GMAT/39761815456" target="_blank">our Facebook page</a>.</p>
<p>The weekly winner, drawn from among all the correct submissions, will receive One Year of Access to our <a href="/storeitemshow.cfm?ItemID=61&#038;catid=4" target="_blank">Challenge Problem Archive</a>, AND the <a href="/storeitemshow.cfm?ItemID=336&#038;catid=4" target="_blank">GMAT Navigator</a>, AND Our <a href="/storeitemshow.cfm?ItemID=81&#038;catid=4" target="_blank">Six Computer Adaptive Tests</a> ($92 value).</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/gmat-challenge-problem-showdown-december-16-2013/">GMAT Challenge Problem Showdown: December 16, 2013</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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