<?xml version="1.0" encoding="UTF-8"?><rss version="2.0" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:wfw="http://wellformedweb.org/CommentAPI/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:sy="http://purl.org/rss/1.0/modules/syndication/" xmlns:slash="http://purl.org/rss/1.0/modules/slash/" > <channel> <title>math – GMAT</title> <atom:link href="https://www.manhattanprep.com/gmat/blog/tag/math/feed/" rel="self" type="application/rss+xml" /> <link>https://www.manhattanprep.com/gmat</link> <description>GMAT Prep Course, Best GMAT Class & Study Books | Manhattan Prep GMAT</description> <lastBuildDate>Thu, 05 Sep 2019 16:22:27 +0000</lastBuildDate> <language>en-US</language> <sy:updatePeriod> hourly </sy:updatePeriod> <sy:updateFrequency> 1 </sy:updateFrequency> <generator>https://wordpress.org/?v=6.3.2</generator> <item> <title>The 4 Math Strategies Everyone Must Master, part 2</title> <link>https://www.manhattanprep.com/gmat/blog/the-4-math-strategies-everyone-must-master-part-2/</link> <dc:creator><![CDATA[Stacey Koprince]]></dc:creator> <pubDate>Mon, 30 Dec 2013 17:33:45 +0000</pubDate> <category><![CDATA[How to Study]]></category> <category><![CDATA[Quant]]></category> <category><![CDATA[advanced quant]]></category> <category><![CDATA[GMAT]]></category> <category><![CDATA[gmat quant]]></category> <category><![CDATA[math]]></category> <category><![CDATA[math strategies]]></category> <category><![CDATA[math tip]]></category> <guid isPermaLink="false">http://www.manhattangmat.com/blog/?p=6880</guid> <description><![CDATA[<p>Last time, we talked about the first 2 of 4 quant strategies that everyone must master: Test Cases and Choose Smart Numbers. Today, we’re going to cover the 3rd and 4th strategies. First up, we have Work Backwards. Let’s try a problem first: open up your Official Guide, 13th edition (OG13), and try problem solving […]</p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/the-4-math-strategies-everyone-must-master-part-2/">The 4 Math Strategies Everyone Must Master, 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" fetchpriority="high" class="size-full wp-image-6890 alignleft" title="Math-strategies-gmat" alt="Math-strategies-gmat" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/math-strategies-gmat.png" width="403" height="403" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/math-strategies-gmat.png 403w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/math-strategies-gmat-150x150.png 150w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/math-strategies-gmat-300x300.png 300w" sizes="(max-width: 403px) 100vw, 403px" />Last time, <a href="https://www.manhattanprep.com/gmat/blog/2013/12/23/the-4-math-strategies-everyone-must-master-part-1/">we talked about the first 2 of 4 quant strategies</a> that everyone must master: Test Cases and Choose Smart Numbers.</p> <p>Today, we’re going to cover the 3<sup>rd</sup> and 4<sup>th</sup> strategies. First up, we have Work Backwards. Let’s try a problem first: open up your Official Guide, 13<sup>th</sup> edition (OG13), and try problem solving #15 on page 192. (Give yourself about 2 minutes.)</p> <p>I found this one by popping open my copy of OG13 and looking for a certain characteristic that meant I knew I could use the Work Backwards technique. Can you figure out how I knew, with just a quick glance, that this problem qualified for the Work Backwards strategy? (I’ll tell you at the end of the solution.)</p> <p>For copyright reasons, I can’t reproduce the entire problem, but here’s a summary: John spends 1/2 his money on fruits and vegetables, 1/3 on meat, and 1/10 on treats from the bakery. He also spends $6 on candy. By the time he’s done, he’s spent all his money. The problem asks how much money he started out with in the first place.</p> <p>Here are the answer choices:</p> <p>“(A) $60</p> <p>“(B) $80</p> <p>“(C) $90</p> <p>“(D) $120</p> <p>“(E) $180”</p> <p>Work Backwards literally means to start with the answers and do all of the math in the reverse order described in the problem. You’re essentially plugging the answers into the problem to see which one works. This strategy is very closely tied to the first two we discussed last time—except, in this instance, you’re not picking your own numbers. Instead, you’re using the numbers given in the answers.</p> <p>In general, when using this technique, start with answer (B) or (D), your choice. If one looks like an easier number, start there. If (C) looks a lot easier than (B) or (D), start with (C) instead.</p> <p>This time, the numbers are all equally “hard,” so start with answer (B). Here’s what you’re going to do:</p> <p>(B) $80</p> <table border="1" cellspacing="0" cellpadding="0"> <tbody> <tr> <td valign="top" width="66"> <p align="center"><strong> </strong></p> </td> <td valign="top" width="79"> <p align="center"><strong>F + V (1/2)</strong></p> </td> <td valign="top" width="68"> <p align="center"><strong>M (1/3)</strong></p> </td> <td valign="top" width="72"> <p align="center"><strong>B (1/10)</strong></p> </td> <td valign="top" width="63"> <p align="center"><strong>C $6</strong></p> </td> <td valign="top" width="63"> <p align="center"><strong>Add?</strong></p> </td> </tr> <tr> <td valign="top" width="66">(B) $80</td> <td valign="top" width="79"> <p align="center">$40</p> </td> <td valign="top" width="68"> <p align="center">…?</p> </td> <td valign="top" width="72"></td> <td valign="top" width="63"> <p align="center">$6</p> </td> <td valign="top" width="63"></td> </tr> </tbody> </table> <p>Set up a table to calculate each piece. If John starts with $80, then he spends $40 on fruits and vegetables. He spends… wait a second! $80 doesn’t go into 1/3 in a way that would give a dollar-and-cents amount. It would be $26.66666 repeating forever. This can’t be the right answer!</p> <p>Interesting. Cross off answer (B), and glance at the other answers. They’re all divisible by 3, so we can’t cross off any others for this same reason.</p> <p>Try answer (D) next.</p> <table border="1" cellspacing="0" cellpadding="0"> <tbody> <tr> <td valign="top" width="66"> <p align="center"><strong> </strong></p> </td> <td valign="top" width="79"> <p align="center"><strong>F + V (1/2)</strong></p> </td> <td valign="top" width="68"> <p align="center"><strong>M (1/3)</strong></p> </td> <td valign="top" width="72"> <p align="center"><strong>B (1/10)</strong></p> </td> <td valign="top" width="63"> <p align="center"><strong>C $6</strong></p> </td> <td valign="top" width="63"> <p align="center"><strong>Add to?</strong></p> </td> </tr> <tr> <td valign="top" width="66">(B) $80</td> <td valign="top" width="79"> <p align="center">$40</p> </td> <td valign="top" width="68"> <p align="center">…?</p> </td> <td valign="top" width="72"></td> <td valign="top" width="63"> <p align="center">$6</p> </td> <td valign="top" width="63"> <p align="center">?</p> </td> </tr> <tr> <td valign="top" width="66"><strong>(D) $120</strong></td> <td valign="top" width="79"> <p align="center">$60</p> </td> <td valign="top" width="68"> <p align="center">$40</p> </td> <td valign="top" width="72"> <p align="center">$12</p> </td> <td valign="top" width="63"> <p align="center">$6</p> </td> <td valign="top" width="63"> <p align="center">$118</p> </td> </tr> </tbody> </table> <p> </p> <p>In order for (D) to be the correct answer, the individual calculations would have to add back up to $120, but they don’t. They add up to $118.</p> <p>Okay, so (D) isn’t the correct answer either. Now what? Think about what you know so far. Answer (D) didn’t work, but the calculations also fell short—$118 wasn’t large enough to reach the starting point. As a result, try a smaller starting point next.</p> <table border="1" cellspacing="0" cellpadding="0"> <tbody> <tr> <td valign="top" width="66"> <p align="center"><strong> </strong></p> </td> <td valign="top" width="79"> <p align="center"><strong>F + V (1/2)</strong></p> </td> <td valign="top" width="68"> <p align="center"><strong>M (1/3)</strong></p> </td> <td valign="top" width="72"> <p align="center"><strong>B (1/10)</strong></p> </td> <td valign="top" width="63"> <p align="center"><strong>C $6</strong></p> </td> <td valign="top" width="63"> <p align="center"><strong>Add?</strong></p> </td> </tr> <tr> <td valign="top" width="66">(B) $80</td> <td valign="top" width="79"> <p align="center">$40</p> </td> <td valign="top" width="68"> <p align="center">…?</p> </td> <td valign="top" width="72"></td> <td valign="top" width="63"> <p align="center">$6</p> </td> <td valign="top" width="63"> <p align="center">?</p> </td> </tr> <tr> <td valign="top" width="66">(D) $120</td> <td valign="top" width="79"> <p align="center">$60</p> </td> <td valign="top" width="68"> <p align="center">$40</p> </td> <td valign="top" width="72"> <p align="center">$12</p> </td> <td valign="top" width="63"> <p align="center">$6</p> </td> <td valign="top" width="63"> <p align="center">$118</p> </td> </tr> <tr> <td valign="top" width="66"><strong>(C) $90</strong></td> <td valign="top" width="79"> <p align="center">$45</p> </td> <td valign="top" width="68"> <p align="center">$30</p> </td> <td valign="top" width="72"> <p align="center">$9</p> </td> <td valign="top" width="63"> <p align="center">$6</p> </td> <td valign="top" width="63"> <p align="center">$90</p> </td> </tr> </tbody> </table> <p> </p> <p>It’s a match! The correct answer is (C).</p> <p>Now, why would you want to do the problem this way, instead of the “straightforward,” normal math way? The textbook math solution on this one involves finding common denominators for three fractions—somewhat annoying but not horribly so. If you dislike manipulating fractions, or know that you’re more likely to make mistakes with that kind of math, then you may prefer to work backwards.</p> <p>Note, though, that the above problem is a lower-numbered problem. On harder problems, this Work Backwards technique can become far easier than the textbook math. Try PS #203 in OG13. I would <span style="text-decoration: underline">far</span> rather Work Backwards on this problem than do the textbook math!</p> <p>So, have you figured out how to tell, at a glance, that a problem might qualify for this strategy?</p> <p>It has to do with the form of the answer choices. First, they need to be numeric. Second, the numbers should be what we consider “easy” numbers. These could be integers similar to the ones we saw in the above two problems. They could also be smaller “easy” fractions, such as 1/2, 1/3, 3/2, and so on.</p> <p>Further, the question should ask about a single variable or unknown. If it asks for <em>x</em>, or for the amount of money that John had to start, then Work Backwards may be a great solution technique. If, on the other hand, the problem asks for <em>x</em> – <em>y</em>, or some other combination of unknowns, then the technique may not work as well.</p> <p>(Drumroll, please) We’re now up to our fourth, and final, Quant Strategy that Everyone Must Master. Any guesses as to what it is? Try this GMATPrep© problem.</p> <p> </p> <p><img decoding="async" class="alignnone size-full wp-image-6899" title="geometry" alt="geometry" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/geometry.png" width="170" height="142" /></p> <p>“In the figure above, the radius of the circle with center <em>O</em> is 1 and <em>BC</em> = 1. What is the area of triangular region <em>ABC</em>?</p> <p><img decoding="async" class="alignnone size-full wp-image-6886" title="Screen Shot 2013-12-29 at 3.26.36 PM" alt="Screen Shot 2013-12-29 at 3.26.36 PM" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/screen-shot-2013-12-29-at-3.26.36-pm.png" width="88" height="166" /></p> <p>If the radius is 1, then the bottom line (the hypotenuse) of the triangle is 2. If you drop a line from point <em>B</em> to that bottom line, or base, you’ll have a height and can calculate the area of the triangle, since <em>A</em> = (1/2)<em>bh</em>.</p> <p>You don’t know what that height is, yet, but you do know that it’s smaller than the length of <em>BC</em>. If <em>BC</em> were the height of the triangle, then the area would be<em> A</em> = (1/2)(2)(1) = 1. Because the height is smaller than <em>BC</em>, the area has to be smaller than 1. Eliminate answers (C), (D), and (E).</p> <p>Now, decide whether you want to go through the effort of figuring out that height, so that you can calculate the precise area, or whether you’re fine with guessing between 2 answer choices. (Remember, unless you’re going for a top score on quant, you only have to answer about 60% of the questions correctly, so a 50/50 guess with about 30 seconds’ worth of work may be your best strategic move at this point on the test!)</p> <p>The technique we just used to narrow down the answers is one I’m sure you’ve used before: Estimation. Everybody already knows to estimate when the problem asks you for an approximate answer. When else can (and should) you estimate?</p> <p>Glance at the answers. Notice anything? They can be divided into 3 “categories” of numbers: less than 1, 1, and greater than 1.</p> <p>Whenever you have a division like this (greater or less than 1, positive or negative, really big vs. really small), then you can estimate to get rid of some answers. In many cases, you can get rid of 3 and sometimes even all 4 wrong answers. Given the annoyingly complicated math that sometimes needs to take place in order to get to the final answer, your best decision just might be to narrow down to 2 answers quickly and then guess.</p> <p>Want to know how to get to the actual answer for this problem, which is (B)? <a href="https://www.manhattanprep.com/gmat/blog/2013/12/17/tackling-multi-shape-geometry-on-the-gmat/">Take a look at the full solution here</a>.</p> <p><strong>The 4 Quant Strategies Everyone Must Master</strong></p> <p>Here’s a summary of our four strategies.</p> <p>(1) Test Cases.</p> <p>– Especially useful on Data Sufficiency with variables / unknowns. Pick numbers that fit the constraints given and test the statement. That will give you a particular answer, either a value (on Value DS) or a yes or no (on Yes/No DS). Then test another case, choosing numbers that differ from the first set in a mathematically appropriate way (e.g., positive vs. negative, odd vs. even, integer vs. fraction). If you get an “always” answer (you keep getting the same value or you get always yes or always no), then the statement is sufficient. If you find a different answer (a different value, or a yes plus a no), then that statement is not sufficient.</p> <p>– Also useful on “theory” Problem Solving questions, particularly ones that ask what must be true or could be true. Test the answers using your own real numbers and cross off any answers that don’t work with the given constraints. Keep testing, using different sets of numbers, till you have only one answer left (or you think you’ve spent too much time).</p> <p>(2) Choose Smart Numbers.</p> <p>– Used on Problem Solving questions that don’t require you to find something that must or could be true. In this case, you need to select just one set of numbers to work through the math in the problem, then pick the one answer that works.</p> <p>– Look for variable expressions (no equals or inequalities signs) in the answer choices. Will also work with fraction or percent answers.</p> <p>(3) Work Backwards.</p> <p>– Used on Problem Solving questions with numerical answers. Most useful when the answers are “easy”—small integers, easy fractions, and so on—and the problem asks for a single variable. Instead of selecting your own numbers to try in the problem, use the given answer choices.</p> <p>– Start with answer (B) or (D). If a choice doesn’t work, cross it off but examine the math to see whether you should try a larger or smaller choice next.</p> <p>(4) Estimate.</p> <p>– You’re likely already doing this whenever the problem actually asks you to find an approximate answer, but look for more opportunities to save yourself time and mental energy. When the answers are numerical and either very far apart or split across a “divide” (e.g., greater or less than 0, greater or less than 1), you can often estimate to get rid of 2 or 3 answers, sometimes even all 4 wrong answers.</p> <p>The biggest takeaway here is very simple: these strategies are just as valid as any textbook math strategies you know, and they also require just as much practice as those textbook strategies. Make these techniques a part of your practice: master how and when to use them, and you will be well on your way to mastering the Quant portion of the GMAT!</p> <p>Read <a href="//www.manhattanprep.com/gmat/blog/2013/12/23/the-4-math-strategies-everyone-must-master-part-1/">The 4 Math Strategies Everyone Must Master, Part 1.</a></p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/the-4-math-strategies-everyone-must-master-part-2/">The 4 Math Strategies Everyone Must Master, part 2</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p> ]]></content:encoded> </item> <item> <title>Tackling Multi-Shape Geometry on the GMAT</title> <link>https://www.manhattanprep.com/gmat/blog/tackling-multi-shape-geometry-on-the-gmat/</link> <dc:creator><![CDATA[Stacey Koprince]]></dc:creator> <pubDate>Tue, 17 Dec 2013 14:30:24 +0000</pubDate> <category><![CDATA[Geometry]]></category> <category><![CDATA[Quant]]></category> <category><![CDATA[GMAT]]></category> <category><![CDATA[gmat math]]></category> <category><![CDATA[math]]></category> <category><![CDATA[quant]]></category> <guid isPermaLink="false">http://www.manhattangmat.com/blog/?p=6795</guid> <description><![CDATA[<p>What do you do when you realize a geometry problem has just popped up on the screen? Try this GMATPrep© problem from the free practice test and then we’ll talk about what to do! In the figure above, the radius of the circle with center O is 1 and BC = 1. What is the […]</p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/tackling-multi-shape-geometry-on-the-gmat/">Tackling Multi-Shape Geometry on the GMAT</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p> ]]></description> <content:encoded><![CDATA[<p>What do you do when you realize a geometry problem has just popped up on the screen? Try this GMATPrep© problem from the free practice test and then we’ll talk about what to do!</p> <p><img decoding="async" loading="lazy" class="aligncenter size-full wp-image-6796" title="gmat12" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/gmat12.png" alt="gmat12" width="201" height="215" /></p> <p>In the figure above, the radius of the circle with center <em>O</em> is 1 and <em>BC</em> = 1. What is the area of triangular region <em>ABC</em>?</p> <p style="text-align: center"><img decoding="async" loading="lazy" class="wp-image-6801 aligncenter" title="gmat12" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/gmat121.png" alt="gmat12" width="61" height="195" /></p> <p>What’s your first step? Let’s use this problem as an opportunity to practice the Quant Process.</p> <p> </p> <p><img decoding="async" loading="lazy" class="aligncenter size-full wp-image-6805" title="gmat12" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/gmat122.png" alt="gmat12" width="239" height="182" /></p> <p>At a glance, you can see that the problem provides a diagram. Draw! Make it big enough that you can add labels as you calculate new pieces of information (and, of course, jot down any information given in the problem).</p> <p>Finally, write down any formulas you’ll need, as well as whatever the problem asks you to find. Your scrap paper might look something like this:<br /> <span id="more-6795"></span><br /> <img decoding="async" loading="lazy" class="aligncenter size-full wp-image-6814" title="Screen Shot 2013-12-10 at 4.21.55 PM" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/screen-shot-2013-12-10-at-4.21.55-pm.png" alt="Screen Shot 2013-12-10 at 4.21.55 PM" width="587" height="223" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/screen-shot-2013-12-10-at-4.21.55-pm.png 587w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/screen-shot-2013-12-10-at-4.21.55-pm-300x113.png 300w" sizes="(max-width: 587px) 100vw, 587px" /></p> <p> </p> <p>Before you dive in and try to find this height, though, Reflect! Ask yourself whether there are other possible ways to move forward. Sometimes, the “obvious” way turns out not to be the easiest way to proceed.</p> <p>In particular, this is a “multi-shape” problem: you were given both a triangle and a circle. Why did they include the circle? Pay particular attention to where the two shapes overlap.</p> <p>Hmm. The hypotenuse of the triangle is also a diameter of the circle. How can you use that to solve?</p> <p>It turns out that when a triangle is inscribed in a circle (the 3 vertices of the triangle all sit on the circle), and the hypotenuse of that triangle is also a diameter of the circle, then the triangle in question is a right triangle. (This is one of the rules we’re supposed to memorize for the test.)</p> <p>In this case, the right angle is labeled <em>B</em>. Is that information useful at all? Well, if you’re trying to find the area of a right triangle, then you just need to know the lengths of the two legs: <em>AB</em> and <em>BC</em>. The problem says that <em>BC</em> = 1, so the only unknown is <em>AB</em>.</p> <p>Now you have a choice: do you think it’ll be easier to find the length of <em>AB </em>or to find the length of the vertical line that you drew in below point <em>B</em>?</p> <p>Because <em>ABC</em> is a right triangle, it’s easier to find <em>AB</em>. The short leg is 1 and the hypotenuse is 2. Do those numbers match any of the “smart” triangles that you’ve studied? (If not, use the Pythagorean Theorem.)</p> <p>Yes! These match the 30-60-90 triangle parameters.</p> <p><img decoding="async" loading="lazy" class="aligncenter size-full wp-image-6819" title="gmat12" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/gmat127.png" alt="gmat12" width="418" height="127" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/gmat127.png 418w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/gmat127-300x91.png 300w" sizes="(max-width: 418px) 100vw, 418px" /></p> <p>The length of <em>AB </em>is <img decoding="async" loading="lazy" class="alignnone wp-image-6820" title="gmat12" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/gmat128.png" alt="gmat12" width="22" height="23" />. Plug this into the area formula:</p> <p><img decoding="async" loading="lazy" class="alignleft wp-image-6821" title="gmat12" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/gmat129.png" alt="gmat12" width="76" height="86" /></p> <p> </p> <p> </p> <p> </p> <p> </p> <p><strong>The correct answer is (B). </strong></p> <p><strong>Key Takeaways for Multi-Shape Geometry.</strong></p> <p>(1) Examine the “overlap” between the shapes. Most likely, some rule about that connection exists and this rule will help make the problem easier to solve.</p> <p>(2) Draw! This is key for any geometry problem, but especially so for multi-shape problems. There are too many moving parts; you need to keep track of everything in a clear way.</p> <p>(3) Remember our Quant Process: Reflect before you Work! In this case, the first, more obvious path would have been a lot more difficult to execute. Reflecting for a moment allowed you to notice the connection between the circle and the triangle. The subsequent solution path turned out to be much more straightforward.</p> <p><img decoding="async" loading="lazy" class="aligncenter size-full wp-image-6823" title="gmat12" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/12/gmat1210.png" alt="gmat12" width="237" height="186" /></p> <p>* GMATPrep© questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC</p> <p> </p> <p> </p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/tackling-multi-shape-geometry-on-the-gmat/">Tackling Multi-Shape Geometry on the GMAT</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p> ]]></content:encoded> </item> <item> <title>Reorient your View on Math Problems, Part 1</title> <link>https://www.manhattanprep.com/gmat/blog/reorient-your-view-on-math-problems-part-1/</link> <dc:creator><![CDATA[Stacey Koprince]]></dc:creator> <pubDate>Thu, 24 Oct 2013 20:00:12 +0000</pubDate> <category><![CDATA[Problem Solving]]></category> <category><![CDATA[Quant]]></category> <category><![CDATA[math]]></category> <category><![CDATA[problem solving]]></category> <category><![CDATA[quant]]></category> <guid isPermaLink="false">http://www.manhattangmat.com/blog/?p=6486</guid> <description><![CDATA[<p>The Quant section of the GMAT is not a math test. Really, it isn’t! It just looks like one on the surface. In reality, they’re testing us on how we think. As such, they write many math problems in a way that hides what’s really going on or even implies a solution method that is […]</p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/reorient-your-view-on-math-problems-part-1/">Reorient your View on Math Problems, 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" style="margin: 5px; padding: 0; border: 0;" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/10/istock-000005509580xsmall.jpg" alt="gmat investment" align="right" />The Quant section of the GMAT is not a math test. Really, it isn’t! It just looks like one on the surface. In reality, they’re testing us on how we <em>think</em>.</p> <p>As such, they write many math problems in a way that hides what’s really going on or even implies a solution method that is not the best solution method. Assume nothing and do <span style="text-decoration: underline;">not</span> accept that what they give you is your best starting point!</p> <p>In short, learn to reorient your view on math problems. When I look at a new problem, one of my first thoughts is, “What did they give me and how could it be made easier?” In particular, I look for things that I find annoying, as in, “Ugh, why did they give it to me in <em>that</em> form?” or “Ugh, I really don’t want to do that calculation.” My next question is how I can get rid of or get around that annoying part.</p> <p>What do I mean? Here’s an example from the free set of questions that comes with the GMATPrep software. Try it!</p> <blockquote><p>* ” If ½ of the money in a certain trust fund was invested in stocks, ¼ in bonds, <sup>1</sup>/<sub>5</sub> in a mutual fund, and the remaining $10,000 in a government certificate, what was the total amount of the trust fund?</p> <p>“(A) $100,000</p> <p>“(B) $150,000</p> <p>“(C) $200,000</p> <p>“(D) $500,000</p> <p>“(E) $2,000,000”</p></blockquote> <p>What did you get?</p> <p>Here’s my thought process:</p> <p style="padding-left: 30px;">(1) <strong>Glance</strong> (before I start reading). It’s a PS word problem. The answers are round / whole numbers, and they’re mostly spread pretty far apart. I might be able to estimate to get the answer and I should at least be able to tell whether it’s closer to (A) or (E).</p> <p style="padding-left: 30px;">(2) <strong>Read and Jot</strong>. As I read, I jot down numbers (and label them!):</p> <p style="padding-left: 30px;"><em>S</em> = <sup>1</sup>/<sub>2</sub></p> <p style="padding-left: 30px;"><em>B</em> = <sup>1</sup>/<sub>4</sub></p> <p style="padding-left: 30px;"><em>F</em> = <sup>1</sup>/<sub>5</sub></p> <p style="padding-left: 30px;"><em>C</em> = 10,000</p> <p style="padding-left: 30px;">(3) <strong>Reflect and Organize</strong>. Let’s see. The four things should add up to the total amount. Three of those are fractions. Oh, I see—if I had four fractions, they should all add up to 1. So if I take those three and add them, and then subtract that from 1, that’ll give me the fractional amount for the C. Since I know the real value for C, I can then figure out the total.</p> <p style="padding-left: 30px;">But, ugh, adding fractions is annoying! You need common denominators. I’m capable of doing this, of course, but I really don’t want to! Isn’t there an easier way?</p> <p style="padding-left: 30px;">In this case, yes! Adding decimals or percents is really easy. Adding fractions is annoying. Plus, check it out, the fractions given are all common ones that we (should) have memorized. So change those fractions to percents (or decimals)!</p> <p style="padding-left: 30px;">(4) <strong>Work</strong>. Let’s do it!</p> <p style="padding-left: 30px;"><em>S</em> = <sup>1</sup>/<sub>2</sub> = 50%</p> <p style="padding-left: 30px;"><em>B</em> = <sup>1</sup>/<sub>4</sub> = 25%</p> <p style="padding-left: 30px;"><em>F</em> = <sup>1</sup>/<sub>5</sub> = 20%</p> <p style="padding-left: 30px;">C = 10,000</p> <p style="padding-left: 30px;">Wow, this is a lot easier. I know that 50 + 25 + 25 would equal 100, but I’ve only got 50 + 25 + 20, so the total is 5 short of 100. The final value, C, then must be 5% of the total.</p> <p style="padding-left: 30px;">So let’s see… if C = 10,000 = 5%, then 10% would be twice as much, or 20,000. And I just need to add a zero to get to 100%, or 200,000. Done!<span id="more-6486"></span></p> <p>The correct answer is (C).</p> <h3>What did we just learn?</h3> <p>There are two crucially important things to notice here.</p> <p>First, I did NOT just start calculating immediately. I had 3 whole steps before I really starting doing any work! Don’t just dive in and start doing stuff. Figure out where you want to go first.</p> <p>Second, don’t just accept what they give you. They gave the problem to us in fraction form precisely because fractions are so very annoying to add! They’re trying to see whether you notice that and can think flexibly enough to change your orientation on the problem and use percentages (or decimals) instead.</p> <p>So, how are you going to remember that next time?</p> <p style="padding-left: 60px;"><em>When I see:</em> A problem with multiple fractions, decimals, or percents</p> <p style="padding-left: 60px;"><em>Think:</em> Is the form given <em>really</em> the easiest way to do the math? If not, and if the numbers given are easy to convert, then convert to one of the other forms!</p> <p>And:</p> <p style="padding-left: 60px;"><em>When I see: </em>A problem requiring me to add fractions</p> <p style="padding-left: 60px;"><em>Think: </em>Can I convert easily to percentages or decimals? Would that make sense for this problem?</p> <p> </p> <p>As you study, make sure that you are actually using all four of the broad steps that I outlined above:</p> <p style="padding-left: 60px;">(1) Glance</p> <p style="padding-left: 60px;">(2) Read and Jot</p> <p style="padding-left: 60px;">(3) Reflect and Organize</p> <p style="padding-left: 60px;">(4) Work</p> <p>As you do the problem, keep an eye out for anything that you consider “annoying”—as in, they could have given this to me in an easier form, or I really wish I didn’t have to do this math that I’m doing right now! When this happens, take a step back to see whether you can spot a different, better approach.</p> <p>While the clock is ticking, you might not figure it out. In the moment, either do the math the “annoying” way or just pick an answer and move on. Pretend it’s the test and make the call.</p> <p>Afterwards, go back and figure it out. You can spend all the time you want playing with the problem, searching for alternative approaches. You can look up alternative solutions in our GMAT Navigator program or on the forums.</p> <p>Your very last step is to ask yourself how you’re going to notice a similar situation the next time you see it. Here, your takeaway should be written in the “When I see ABC; Think XYZ” form I used above. For the first part, make sure that you write down what <em>any</em> problem would need to include <em>in general</em>. Do NOT write out the actual problem itself—you aren’t going to see that problem on the test!</p> <p>Ready to test this out? This article is a 2-parter, so I’ll give you a homework assignment. (This problem is again from the free set that comes with GMATPrep.)</p> <blockquote><p>* ” If <img decoding="async" style="margin: 5px; padding: 0; border: 0;" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/10/untitled.jpg" alt="stacey diagram 1" />, then <img decoding="async" style="margin: 5px; padding: 0; border: 0;" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2013/10/stacey1023-2.jpg" alt="stacey diagram 2" /> =</p> <p>“(A) –<sup>1</sup>/<sub>2</sub></p> <p>“(B) –<sup>1</sup>/<sub>3</sub></p> <p>“(C) <sup>1</sup>/<sub>3</sub></p> <p>“(D) <sup>1</sup>/<sub>2</sub></p> <p>“(E) <sup>5</sup>/<sub>2</sub> ”</p></blockquote> <p> </p> <p><a href="//www.manhattanprep.com/gmat/blog/2013/10/29/reorient-your-view-on-math-problems-part-2/" target="_blank">Click here for the second half of this article</a>, where we discuss the solution to the above problem and also discuss a third problem. Further, make sure you practice using all 4 steps in the overall process so that you build the habit to reflect / organize your thinking before you dive into the work. This will help you learn to reorient your view and make GMAT math problems easier to tackle!</p> <p>* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.</p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/reorient-your-view-on-math-problems-part-1/">Reorient your View on Math Problems, Part 1</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p> ]]></content:encoded> </item> <item> <title>GMAT Challenge Problem Showdown: October 7, 2013</title> <link>https://www.manhattanprep.com/gmat/blog/gmat-challenge-problem-showdown-october-7-2013/</link> <dc:creator><![CDATA[Manhattan Prep]]></dc:creator> <pubDate>Mon, 07 Oct 2013 13:00:49 +0000</pubDate> <category><![CDATA[Challenge Problem]]></category> <category><![CDATA[challenge problem]]></category> <category><![CDATA[GMAT]]></category> <category><![CDATA[math]]></category> <category><![CDATA[quant]]></category> <guid isPermaLink="false">http://www.manhattangmat.com/blog/?p=6232</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’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap […]</p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/gmat-challenge-problem-showdown-october-7-2013/">GMAT Challenge Problem Showdown: October 7, 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’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’s problem:</p> <blockquote><p>The positive number <em>a</em> is <em>q</em> percent greater than the positive number <em>b</em>, which is <em>p</em> percent less than <em>a</em> itself. If <em>a</em> is increased by <em>p</em> percent, and the result is then decreased by <em>q</em> percent to produce a positive number <em>c</em>, which of the following could be true?</p> <p>I. <em>c</em> > <em>a</em><br /> II.<em> c</em> = <em>a</em><br /> III.<em> c</em> < <em>a</em></p></blockquote> <p><span id="more-6232"></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’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&catid=4" target="_blank">Challenge Problem Archive</a>, AND the <a href="/storeitemshow.cfm?ItemID=336&catid=4" target="_blank">GMAT Navigator</a>, AND Our <a href="/storeitemshow.cfm?ItemID=81&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-october-7-2013/">GMAT Challenge Problem Showdown: October 7, 2013</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p> ]]></content:encoded> </item> <item> <title>Announcing the New Advanced GMAT Quant Strategy Guide</title> <link>https://www.manhattanprep.com/gmat/blog/announcing-the-new-advanced-gmat-quant-strategy-guide/</link> <dc:creator><![CDATA[Stacey Koprince]]></dc:creator> <pubDate>Wed, 01 Jun 2011 18:27:01 +0000</pubDate> <category><![CDATA[MGMAT News]]></category> <category><![CDATA[advanced quant]]></category> <category><![CDATA[gmat math]]></category> <category><![CDATA[manhattan gmat news]]></category> <category><![CDATA[math]]></category> <category><![CDATA[new book]]></category> <category><![CDATA[quant]]></category> <guid isPermaLink="false">http://www.manhattangmat.com/blog/?p=1395</guid> <description><![CDATA[<p>Exciting news “ our Advanced Quant Strategy Guide is finally ready for prime time! We’re also launching a Foundations of Verbal book; click on the link to read about that one. Who should use this book? Great question. Are you already at the 70th-plus percentile (minimum) on quant and you’re looking to push yourself well […]</p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/announcing-the-new-advanced-gmat-quant-strategy-guide/">Announcing the New Advanced GMAT Quant Strategy Guide</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p> ]]></description> <content:encoded><![CDATA[<p><a href="/storeitemshow.cfm?ItemID=380&catid=10"><img decoding="async" style="float: left;margin: 0px 10px 0px 0px" src="//cdn.manhattanprep.com/images/gmat/advancedquantcover-small.jpg" alt="Advanced GMAT Quant Cover" /></a>Exciting news “ our <a href="/storeitemshow.cfm?ItemID=380&catid=10"> Advanced Quant Strategy Guide</a> is finally ready for prime time! We’re also launching a <a href="/storeitemshow.cfm?ItemID=379&catid=10" target="_blank">Foundations of Verbal</a> book;<a href="/gmat/blog/2011/06/01/announcing-the-new-foundations-of-verbal-strategy-guide/"> click on the link</a> to read about that one.</p> <p>Who should use this book? Great question. Are you already at the 70<sup>th</sup>-plus percentile (minimum) on quant and you’re looking to push yourself well into the 90s? This book is for you. In addition, please note that this book assumes that you have already worked through our five regular Strategy Guides (or the equivalent material from another company).</p> <p>To give you an idea of what to expect, excerpts from the new Advanced Quant guide are below. The main point I want to make is that this book covers both advanced <em>concepts</em> / mathematical material, and advanced problem solving <em>processes</em>. Both are critical for a 90th-plus percentile test-taker.</p> <p>Okay, without further ado, here’s excerpt #1, an introduction to a methodical solving style inspired by mathematician George Polya.<span id="more-1395"></span></p> <p><em>From <span style="text-decoration: underline">Advanced GMAT Quant</span>, copyright 2011 Manhattan GMAT; duplication or further distribution requires permission</em><br /> <img decoding="async" src="//cdn.manhattanprep.com/images/gmat/aq-1-2.jpg" alt="Advanced GMAT Quant excerpt 1" /></p> <div> <hr size="2" /> </div> <p>Got that? Why don’t you try it out on this problem? Note: don’t set a time limit. This is likely tougher than anything you’ll see on the real GMAT!</p> <p><em>From <span style="text-decoration: underline">Advanced GMAT Quant</span>, copyright 2011 Manhattan GMAT; duplication or further distribution requires permission</em><br /> <img decoding="async" src="//cdn.manhattanprep.com/images/gmat/aq-3.jpg" alt="Advanced GMAT Quant excerpt 3" /><br /> Think you got it? Here’s one way someone might think it through, using our Polya-inspired process:</p> <p><img decoding="async" src="//cdn.manhattanprep.com/images/gmat/aq-4.jpg" alt="Advanced GMAT Quant excerpt 4" /><br /> <img decoding="async" src="//cdn.manhattanprep.com/images/gmat/aq-5.jpg" alt="Advanced GMAT Quant excerpt 5" /><br /> Of course, a <span style="text-decoration: underline">great</span> student isn’t going to stop there. What are some other possibilities? Maybe there’s a better or more efficient way (You’ll note that the text below refers to this solution as the “third” one – yes, there’s also a different, second solution in the book, but I didn’t excerpt that one here today.)</p> <p><img decoding="async" src="//cdn.manhattanprep.com/images/gmat/aq-6.jpg" alt="Advanced GMAT Quant excerpt 6" /></p> <div> <hr size="2" /> </div> <p>That was just one question. Plus, we don’t get to study test questions in advance – all of these questions we study will <span style="text-decoration: underline">not</span> be the exact, actual questions we see on the test. As a result, we need to learn how to derive generally applicable takeaways from any questions we study. What kinds of questions do we need to ask ourselves when trying a practice problem? What generally applicable lessons are we learning? And how will we recognize a similar-but-different problem in the future?</p> <p>Let’s start with questions to ask while doing the problem:</p> <p><em>From <span style="text-decoration: underline">Advanced GMAT Quant</span>, copyright 2011 Manhattan GMAT; duplication or further distribution requires permission</em><br /> <img decoding="async" src="//cdn.manhattanprep.com/images/gmat/aq-7.jpg" alt="Advanced GMAT Quant excerpt 7" /><br /> And don’t forget:<br /> <img decoding="async" src="//cdn.manhattanprep.com/images/gmat/aq-8.jpg" alt="Advanced GMAT Quant excerpt 8" /><br /> Finally, you’re not done studying until you’ve analyzed that problem (save this for after you finish trying it):<br /> <img decoding="async" src="//cdn.manhattanprep.com/images/gmat/aq-9.jpg" alt="Advanced GMAT Quant excerpt 9" /></p> <div> <hr size="2" /> </div> <p>That’s all I’ve got for you today “ let us know what you think below. If you’ve got any questions, ask away. And good luck with your quest for that 90<sup>th</sup>-plus percentile quant score!</p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/announcing-the-new-advanced-gmat-quant-strategy-guide/">Announcing the New Advanced GMAT Quant Strategy Guide</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p> ]]></content:encoded> </item> </channel> </rss>