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	<title>GMAT Quant Strategies &#8211; GMAT</title>
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		<title>GMAT Quant Tips: Mental Math &#8211; Part 2</title>
		<link>https://www.manhattanprep.com/gmat/blog/gmat-quant-tips-mental-math-part-2/</link>
		
		<dc:creator><![CDATA[Ryan Jacobs]]></dc:creator>
		<pubDate>Wed, 12 Feb 2020 05:12:13 +0000</pubDate>
				<category><![CDATA[GMAT Strategies]]></category>
		<category><![CDATA[gmat quant]]></category>
		<category><![CDATA[GMAT Quant Strategies]]></category>
		<category><![CDATA[gmat quant tips]]></category>
		<guid isPermaLink="false">https://www.manhattanprep.com/gmat/?p=18623</guid>

					<description><![CDATA[<p>In my last blog post, I had a chat with my dad, a math teacher, about the importance of mental math. Today, I want to get more specific: I want to give you some things to memorize before you take the GMAT or GRE, along with a few tips about how to practice memorizing them. [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/gmat-quant-tips-mental-math-part-2/">GMAT Quant Tips: Mental Math &#8211; Part 2</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 wp-image-18625 size-full" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2020/02/mprep-blogimages-wave1-38-2-e1581483622329.png" alt="gmat quant tips" width="1200" height="628" /></p>
<p><span style="font-weight: 400;">In</span><a href="https://www.manhattanprep.com/gmat/blog/gmat-quant-tips-mental-math/"> <span style="font-weight: 400;">my last blog post,</span></a><span style="font-weight: 400;"> I had a chat with my dad, a math teacher, about the importance of mental math. Today, I want to get more specific: I want to give you some things to memorize before you take the GMAT or GRE, along with a few tips about how to practice memorizing them.</span></p>
<p><span id="more-18623"></span></p>
<h3><b>What to Memorize for GMAT Quant </b></h3>
<h4>GMAT Mental Math Tip 1:</h4>
<p><b>What:</b><span style="font-weight: 400;"> Times tables up to 12 (and practice your multiplication and division in general)</span></p>
<p><b>Why:</b><span style="font-weight: 400;"> You’ll be doing these calculations so often during the test that errors will destroy your score and cost you time. When my students complain that they make too many “silly mistakes,” one of the first things that I ask them is, “What’s 12 times 7?” If you can’t answer that quickly, then not only have you identified the problem, you’ve also learned that the solution to your problem is a relatively low-effort one.</span></p>
<p><b>How:</b><span style="font-weight: 400;"> (1) Make flashcards! And don’t use a flashcard app; there’s some evidence that writing the flashcard yourself will help you memorize it. (2) There are endless opportunities in everyday life to practice your times tables: my suggestion is to just stop using your calculator when your brain will do. Need to buy eight pizzas at $9 each for your little sister’s soccer team? Figure out the total in your head. Need to split that total among 6 team parents? Put that calculator app away, cheater – you can do that on your own now! Got an option to pay your car insurance in a lump sum vs. 12 monthly payments? Figure out how much more the monthly option is going to cost you. Bored at the gas tank? Check your odometer at two fill-ups in a row, and figure out what kind of mileage your car </span><i><span style="font-weight: 400;">actually</span></i><span style="font-weight: 400;"> gets (vs. what the slick car ad copy promised). There are endless opportunities out there as long as you stay curious.</span></p>
<h4>GMAT Mental Math Tip 2:</h4>
<p><b>What:</b><span style="font-weight: 400;"> Fraction-percent conversions for 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1/10, 1/20, and 1/100.</span></p>
<p><b>Why:</b><span style="font-weight: 400;"> Because these conversions lead to many other conversions (for example, 1/9 is 11.1%, so 7/9 is 77.7%). Also, a problem that is difficult in decimal/percent form can become infinitely easier in fraction form, and vice versa. Want proof? What’s 37.5 percent of 560? Easy: it’s 3/8 of 560. So divide by 8 to get 70, then multiply by 3 to get 210.</span></p>
<p><b>How:</b><span style="font-weight: 400;"> Remember that pizza for your little sis? What’s the delivery charge going to be if you want to give the delivery person a 15% tip? (Just take 1/10 of the total, then half of that, and add those two numbers together). Want to buy that flat screen TV at Costco, but worried about the 9% sales tax? Just divide the price by 11 and tack it on. Here’s one of my personal favorites: every time you see some item on sale for some percentage off, figure out what it actually costs, and then immediately find something else that you wanted recently that you could buy at full price for roughly that same amount of money. Then you’ll know whether you’re really getting a deal. Oh, also: tip charts are the new answer keys. Figure out the tip yourself first, then check to make sure you’re right!</span></p>
<h4>GMAT Mental Math Tip 3:</h4>
<p><b>What:</b><span style="font-weight: 400;"> Prime numbers up to 100</span></p>
<p><b>Why:</b><span style="font-weight: 400;"> Because most big numbers are just a bunch of smaller prime numbers multiplied together. I saw a GMAT problem where a crucial final step was to add 1/15 + 1/18. Far too many of my students thought that they needed to convert the denominator to 270. But the ones who found prime factors of 15 (3 × 5) and 18 (2 × 3 × 3) noticed that both 15 and 18 contain a 3, so 90 is actually the common denominator; those students, on average, solved the problem about a full minute faster. Also, some GMAT problems ask you quite directly whether a number is prime. Why not just memorize some primes in advance?</span></p>
<p><b>How:</b><span style="font-weight: 400;"> For all positive integers from 2 to 100, a number is prime if it’s not divisible by 2, 3, 5, or 7. So just start learning primes in the shower; see if you can get to 100 without missing any. Conveniently, this will also teach you shortcuts for how to check whether a number is divisible by 2, 3, or 5 (there’s no great shortcut for 7, so see “times tables,” above!).</span></p>
<h4>GMAT Mental Math Tip 4:</h4>
<p><b>What:</b><span style="font-weight: 400;"> Powers of 2 (2, 4, 8, 16, 32, 64, 128, 256, 512)</span></p>
<p><b>Why:</b><span style="font-weight: 400;"> Because you’ll need to be able to recognize them on sight, not to mention that it’s important if you want to keep the respect of your IT team. The GMAT and GRE will ask you to simplify expressions like 32^5 · 64^3. This is impossible without knowing that 32 is 2^5, and 64 is 2^6.</span></p>
<p><b>How:</b><span style="font-weight: 400;"> Do a web search for “2048” – it’s a surprisingly addictive web-based game; if your boss catches you playing at work, don’t say I didn’t warn you.</span></p>
<h4>Honorable Mention Tips:</h4>
<p><span style="font-weight: 400;">Learn the two most common Pythagorean Triples (3-4-5 and 5-12-13), the ratio of sides in a 45-45-90 triangle and a 30-60-90 triangle, the decimal approximations (to a tenth) of √2, √3, and π, powers of 3 (notice I said “powers,” not “multiples”), factorials from 2! to 6!, and how to factor the difference of squares. If you show up to the first day of my GMAT class with everything in this post down cold, I promise it will not only enrich your experience in class, it will also help you achieve the best score possible!</span></p>
<p><b>RELATED: </b><a href="https://www.manhattanprep.com/gmat/blog/common-math-errors-on-the-gmat/"><span style="font-weight: 400;">Common Math Errors on the GMAT</span></a></p>
<p><b><i>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 href="https://www.manhattanprep.com/gmat/classes/"><b><i>Check out our upcoming courses here</i></b></a><b><i>.</i></b></p>
<hr />
<p><em><strong><img decoding="async" class="alignleft wp-image-15202 size-thumbnail" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/02/ryan-jacobs-e1501597417957-150x150.png" alt="ryan-jacobs" width="150" height="150" /><a id="bloglink" href="https://www.manhattanprep.com/instructors/ryan-jacobs/" target="_blank" rel="noopener">Ryan Jacobs</a> is a Manhattan Prep instructor based in San Francisco, California.</strong> He has an MBA from UC San Diego, a 780 on the GMAT, and years of GMAT teaching experience. His other interests include music, photography, and hockey. <a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/#instructor/288" target="_blank" rel="noopener">Check out Ryan’s upcoming GMAT prep offerings here</a>.</em></p>
<p> </p>
<p> </p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/gmat-quant-tips-mental-math-part-2/">GMAT Quant Tips: Mental Math &#8211; Part 2</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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		<title>Want to do better on GMAT Quant? Put your pen down!</title>
		<link>https://www.manhattanprep.com/gmat/blog/want-to-do-better-on-gmat-quant-put-your-pen-down/</link>
		
		<dc:creator><![CDATA[Céilidh Erickson]]></dc:creator>
		<pubDate>Thu, 10 Mar 2016 22:47:31 +0000</pubDate>
				<category><![CDATA[GMAT Prep]]></category>
		<category><![CDATA[How to Study]]></category>
		<category><![CDATA[Problem Solving]]></category>
		<category><![CDATA[Quant]]></category>
		<category><![CDATA[Taking the GMAT]]></category>
		<category><![CDATA[GMAT Quant Strategies]]></category>
		<guid isPermaLink="false">http://www.manhattanprep.com/gmat/?p=11134</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. Let&#8217;s do an experiment. This is one I do with all of my GMAT classes and tutoring students. Grab a piece of paper, a pen, [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/want-to-do-better-on-gmat-quant-put-your-pen-down/">Want to do better on GMAT Quant? Put your pen down!</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><img decoding="async" class="alignleft size-full wp-image-11135" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/03/blog-quantpen.png" alt="Manhattan Prep GMAT Blog - Want to Do Better on GMAT Quant? Put the Pen Down by Ceilidh Erickson" width="676" height="264" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/03/blog-quantpen.png 676w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2016/03/blog-quantpen-300x117.png 300w" sizes="(max-width: 676px) 100vw, 676px" /><strong><em>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! <a href="https://www.manhattanprep.com/gmat/classes/?utm_source=manhattanprep.com%2Fgmat%2Fblog&#038;utm_medium=blog&#038;utm_content=GMAT%20Complete%20Courses%20Plug&#038;utm_campaign=GMAT%20Blog">Check out our upcoming courses here</a>.</em></strong></p>
<hr />
<p>Let&#8217;s do an experiment. This is one I do with all of my GMAT classes and tutoring students. Grab a piece of paper, a pen, and a stopwatch (or use the stopwatch function on your mobile device).<span id="more-11134"></span></p>
<p>When you’re ready, click “start” on the stopwatch and begin the following Problem Solving problem…</p>
<p>Solution A contains 20% alcohol by volume, and Solution B contains 50% alcohol by volume. If the two solutions are combined, the resulting mixture of A and B contains 32% alcohol by volume. What percent of the total volume of the mixture is Solution A?</p>
<p>(A) 35%</p>
<p>(B) 40%</p>
<p>(C) 50%</p>
<p>(D) 60%</p>
<p>(E) 70%</p>
<p>Ok, write down the answer you got, and how much time it took you.</p>
<p>Right now, though, I’m not interested in what answer you got. I just want to know 2 things:</p>
<ol>
<li>At what point did you start writing on your paper? 5 seconds into the problem? 10? 30?</li>
<li>How long did you take on the problem overall?</li>
</ol>
<p>Believe it or not, there is probably an <em>inverse correlation</em> between those two answers. Students who dive in and start writing equations right away will often spend 2:30 to 3:30 on a question like this – generally much longer than students who take their time before writing things down. They’re also much more likely to get the question wrong!</p>
<p>Savvy test takers don’t dive in and start solving right away. They know that slowing down at first (even though it seems counter-intuitive) can improve both timing and accuracy.</p>
<p>The <em>savvy</em> way to approach Problem Solving questions is this:</p>
<ol>
<li><strong> Read the entire problem, pen down.</strong></li>
</ol>
<p>It’s not Reading Comprehension, so you don’t need to take notes! If you’re writing while you’re reading, you’re much more likely to miss key pieces of information. Think about the concept that’s being tested and what information the problem is giving you.</p>
<p>Here’s what I’d be thinking while reading the problem above: “Okay, this is a weighted average problem – we’re mixing 2 things together. They’re each different amounts of alcohol, and then we’re given a total.”</p>
<ol start="2">
<li><strong> Define what the question is asking for.</strong></li>
</ol>
<p>Again, before writing equations down, just define the question. Is it asking us for a value, a sum, a difference, a proportion, a variable “in terms of” another variable, etc.?</p>
<p>This is the best way to ensure that you don’t accidentally solve for the wrong thing! The GMAT loves to trick us into doing that. How many times have you looked back to realize that your algebra was correct, but you just answered the wrong question?</p>
<p>My thoughts: “The question is asking me about A as a percentage of the <em>total </em>of A and B. I bet they’ll include a trap if I accidentally solve for B!”</p>
<ol start="3">
<li><strong> Scan the answers &#038; try to eliminate.</strong></li>
</ol>
<p>Before picking up the pen, <em>do a common sense test </em>first! This isn’t high school, where you have to show all of your work before picking an answer. Think of the answers as part of the problem itself!</p>
<p>Scanning the answers first can give you powerful clues for how to solve a PS problem. For example, if a geometry problem featured √3 in some of the answer choices, that’s your clue to think about 30:60:90 right triangles. If a ratio problem featured some ratios that were greater than 1 (e.g. 3:2) and some that were less than 1 (2:3), that’s your clue to assess which portion should be greater.</p>
<p>My thoughts on the problem above: “I notice that some of the answer choices are less than 50%, one is 50%, and the others are greater than 50%. If I can just figure out whether I have more A or more B in the mixture, I can narrow it down.”</p>
<p>“Since the 32% in the overall mixture is closer to A’s 20% than B’s 50%, that means that A must make up more of the overall mixture – in other words, more than 50%. I can eliminate (A), (B), and (C).”</p>
<ol start="4">
<li><strong> Look out for Traps</strong></li>
</ol>
<p>As I mentioned before, the GMAT loves to set traps for us. If you become aware of those traps, you can narrow down answer choices easily. Here are some common traps to watch out for:</p>
<ul>
<li><strong>Numbers in the Problem</strong> – these are rarely right answers. The GMAT imagines that if a student didn’t know what to do, she would just say, “um, that number looks familiar. I guess I’ll pick it.” Don’t do that! We could eliminate (A) and (C) (if we hadn’t already) since they’re in the problem.</li>
</ul>
<ul>
<li><strong>One-Move Answers</strong> – similar to the above. If you can get to one of the answers just by performing one operation (addition, subtraction, multiplication, division) to 2 of the numbers in the problem, that’s almost certainly a trap. 50 + 20 = 70, so (E) is almost certainly a trap answer.</li>
</ul>
<ul>
<li><strong>“Evil Twins” </strong>– if we expect that the GMAT is trying to trick us into answering the wrong question (for example, solving for B instead of A here), we should look for answers that form a pair. We know that the percentage of A + the percentage of B will add to 100%. So, look for 2 answers that add to 100: only (B) and (D) in this case. Since we know A has to be more than half of the total, that means that (B) is probably an “evil twin” trap!</li>
</ul>
<p>If we eliminate all of the likely trap answers, that just leaves us with (D).</p>
<ol start="5">
<li><strong> Be Strategic</strong></li>
</ol>
<p>In a situation like this, the best strategic move would be to pick (D) and move on. It’s a bad idea to get bogged down in a lot of algebra just to prove what you probably already know to be true. The savvy test-taker would say “90% sure of my answer in 40 seconds is better than 100% sure of my answer in 3 minutes.”</p>
<p>It’s an uncomfortable feeling not to know for sure, but the GMAT is a time-constrained game! You don’t have time to be 100% sure of every answer.</p>
<p>If this question were different, and you weren’t able to eliminate all of the other answer choices, you would want to make a <em>strategic</em> decision about which approach would work best. Don’t just dive into doing algebra! Remember that there are other strategies that can often be faster: picking smart numbers, working backwards from answer choices, estimating, etc.</p>
<p>On this problem, <em>if </em>we wanted to solve, we could do a combination of strategies. Since we don’t have any concrete amounts given, we can pick our own numbers. Let’s say that the total mixture is 100 liters.</p>
<p>We could also work backwards from the answer choices, based on that 100L total. Since we suspect that the answer is (D), let’s then say A = 60 liters. The amount of alcohol in A would be 20% of 60, so 12L. If A is 60L, then B must be 40L. 50% of 40L would be 20L of alcohol. Thus the total amount of alcohol is 12 + 20 = 32 liters of alcohol out of 100 à 32%.</p>
<p>That works! So (D) must be the right answer.</p>
<p><strong>Saving time on PS.</strong></p>
<p>If you did long or complicated algebra on this question, you probably took well over 2 minutes to solve. It’s also <em>far</em> more likely that you got the answer wrong! Putting the pen down and thinking through the problem in the way we outlined above will improve both your timing and your accuracy.</p>
<p>The next time you’re doing a set of PS problems, write this on a post-it note and keep it next to you as you’re working:</p>
<ol>
<li>Read the entire problem, pen down</li>
<li>Define what the question is asking for</li>
<li>Scan answers &#038; try to eliminate</li>
<li>Look out for traps</li>
<li>Be strategic (either in solving, or in guessing &#038; moving on)</li>
</ol>
<p>Good luck!</p>
<hr />
<p><strong>Want full access to Céilidh’s trove of GMAT knowledge? Try the first class of one of <a href="https://www.manhattanprep.com/gmat/classes/?utm_source=manhattanprep.com%2Fgmat%2Fblog&#038;utm_medium=blog&#038;utm_content=Ceilidh%20Erickson%20InstruCeilidh%20Erickson%20Upcoming%20GMAT%20Courses%20Plug&#038;utm_campaign=GMAT%20Blog#instructor/276">her upcoming GMAT courses</a> absolutely free, no strings attached. </strong></p>
<hr />
<p><a href="https://www.manhattanprep.com/instructors/ceilidh-erickson/?utm_source=manhattanprep.com%2Fgmat%2Fblog&#038;utm_medium=blog&#038;utm_content=Ceilidh%20Erickson%20Instructor%20Bio&#038;utm_campaign=GMAT%20Blog" target="_blank"><img decoding="async" loading="lazy" class="alignleft wp-image-10992 size-thumbnail" title="Ceilidh Erickson Manhattan Prep GMAT Instructor" src="//d27gmszdzgfpo3.cloudfront.net/gmat/wp-content/uploads/sites/18/2016/02/ceilidh-erickson-150x150.png" alt="ceilidh-erickson-Manhattan-Prep-GMAT-Instructor" width="150" height="150" /></a><em><strong><a href="https://www.manhattanprep.com/instructors/ceilidh-erickson/?utm_source=manhattanprep.com%2Fgmat%2Fblog&#038;utm_medium=blog&#038;utm_content=Ceilidh%20Erickson%20Instructor%20Bio&#038;utm_campaign=GMAT%20Blog" target="_blank">Céilidh Erickson</a> is a Manhattan Prep instructor based on New York City.</strong> When she tells people that her name is pronounced “kay-lee,” she often gets puzzled looks. Céilidh is a graduate of Princeton University, where she majored in comparative literature. After graduation, tutoring was always the job that bought her the greatest joy and challenge, so she decided to make it her full-time job. Check out <a href="https://www.manhattanprep.com/gmat/classes/?utm_source=manhattanprep.com%2Fgmat%2Fblog&#038;utm_medium=blog&#038;utm_content=Ceilidh%20Erickson%20InstruCeilidh%20Erickson%20Upcoming%20GMAT%20Courses%20Plug&#038;utm_campaign=GMAT%20Blog#instructor/276" target="_blank">Céilidh’s upcoming GMAT courses</a> (she scored a 760, so you’re in great hands).</em></p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/want-to-do-better-on-gmat-quant-put-your-pen-down/">Want to do better on GMAT Quant? Put your pen down!</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p>
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