<?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>Positives and Negatives – GMAT</title> <atom:link href="https://www.manhattanprep.com/gmat/blog/tag/positives-and-negatives/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>Fri, 30 Aug 2019 17:34:38 +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>GMAT Number Properties: Practice Questions</title> <link>https://www.manhattanprep.com/gmat/blog/gmat-number-properties-practice-questions/</link> <dc:creator><![CDATA[Chelsey Cooley]]></dc:creator> <pubDate>Fri, 01 Feb 2019 21:27:08 +0000</pubDate> <category><![CDATA[For Current Studiers]]></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[combinatorics]]></category> <category><![CDATA[divisibility]]></category> <category><![CDATA[GMAT Code]]></category> <category><![CDATA[number properties]]></category> <category><![CDATA[Odds and Evens]]></category> <category><![CDATA[Positives and Negatives]]></category> <category><![CDATA[Primes]]></category> <category><![CDATA[remainders]]></category> <guid isPermaLink="false">https://www.manhattanprep.com/gmat/?p=16892</guid> <description><![CDATA[<p>The best thing about GMAT Number Properties problems is that the numbers are nice and easy. There’s no need to worry about fractions, decimals, or percents! On the flip side, whoever writes GMAT Number Properties questions loves to make simple concepts seem complicated. These problems are often written in “GMAT code” rather than plain English, […]</p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/gmat-number-properties-practice-questions/">GMAT Number Properties: Practice Questions</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="alignnone size-full wp-image-16946" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2019/02/gmat-number-properties.png" alt="Manhattan Prep GMAT Blog - GMAT Number Properties: Practice Questions by Chelsey Cooley" width="1200" height="628" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2019/02/gmat-number-properties.png 1200w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2019/02/gmat-number-properties-300x157.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2019/02/gmat-number-properties-768x402.png 768w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2019/02/gmat-number-properties-1024x536.png 1024w" sizes="(max-width: 1200px) 100vw, 1200px" /></p> <p><span style="font-weight: 400;">The best thing about GMAT Number Properties problems is that the numbers are nice and easy. There’s no need to worry about fractions, decimals, or percents!</span><span id="more-16892"></span></p> <p><span style="font-weight: 400;">On the flip side, whoever writes GMAT Number Properties questions loves to make simple concepts seem complicated. </span><a id="bloglink" href="https://www.manhattanprep.com/gmat/blog/cracking-gmat-code/" target="_blank" rel="noopener"><span style="font-weight: 400;">These problems are often written in “GMAT code” rather than plain English</span></a><span style="font-weight: 400;">, and to start solving them, you need to translate them first.</span></p> <p><span style="font-weight: 400;">If you do these tricky Number Properties practice problems, you’ll get to practice translating GMAT code, as well as working on some important math skills.</span></p> <h4><b>What Types of Problems Fall Under GMAT Number Properties? </b></h4> <p><span style="font-weight: 400;">On the GMAT, Number Properties questions cover four broad categories. The first of those is divisibility and primes. Here are the key skills you’ll need: </span></p> <ul> <li><b>Know the language. <span style="font-weight: 400;">Be able to define the following terms: </span>prime, factor, multiple, integer, prime factor<span style="font-weight: 400;">, and </span>divisor<span style="font-weight: 400;">.</span></b></li> <li style="font-weight: 400;"><span style="font-weight: 400;">Know </span><b>how</b><span style="font-weight: 400;"> and </span><b>when</b><span style="font-weight: 400;"> to divide a number into its prime factors.</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">Understand how a number’s prime factors relate to its divisibility.</span></li> </ul> <p><span style="font-weight: 400;">The next topic is remainders. Remainders aren’t tested nearly as often as divisibility, although the two ideas are related! You should know:</span></p> <ul> <li style="font-weight: 400;"><span style="font-weight: 400;">How to calculate remainders, and how to find numbers that have a particular remainder</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">The clues that tell you to start thinking about remainders: words and phrases like ‘remaining,’ ‘left over,’ and ‘divided into groups’</span></li> </ul> <p><span style="font-weight: 400;">GMAT Number Properties also covers odds and evens, and positives and negatives. These two topics go hand in hand. You’ll need to know what happens when you add, subtract, multiply, and divide odd and even, or positive and negative, numbers. </span></p> <p><span style="font-weight: 400;">Finally, combinatorics and probability are rare and challenging GMAT Number Properties problem types. We won’t look at these problems here, because they’re covered in </span><a id="bloglink" href="https://www.manhattanprep.com/gmat/blog/help-i-cant-handle-gmat-probability-and-combinatorics-part-1/" target="_blank" rel="noopener"><span style="font-weight: 400;">this article</span></a><span style="font-weight: 400;">. They’re also rare and often difficult, which makes them great candidates for guessing!</span></p> <p><span style="font-weight: 400;">If you need a refresher on the GMAT Number Properties rules and strategies, the </span><a id="bloglink" href="https://www.manhattanprep.com/gmat/store/strategy-guides/number-properties/" target="_blank" rel="noopener"><span style="font-weight: 400;">Number Properties Strategy Guide</span></a><span style="font-weight: 400;"> is the first place to go. </span><a id="bloglink" href="https://www.manhattanprep.com/gmat/store/strategy-guides/foundations-of-gmat-math/" target="_blank" rel="noopener"><span style="font-weight: 400;">Foundations of GMAT Math</span></a><span style="font-weight: 400;"> also starts from scratch and covers the basics of divisibility. </span></p> <h4><b>GMAT Number Properties Practice Questions</b></h4> <p><span style="font-weight: 400;">These problems each test Number Properties topics, and each one contains some “GMAT code” that you’ll need to translate. Go ahead and work through them now! If you’re feeling brave, set a countdown timer for 12 minutes.</span> <span style="font-weight: 400;">That’s about how much time you’d have for these on test day. </span></p> <p><b>GMAT Number Properties: Divisibility, Primes, and Remainders</b></p> <p><span style="font-weight: 400;">1. Is </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;">/10 an integer?</span></p> <p style="padding-left: 30px;"><span style="font-weight: 400;">(1) </span><em><span style="font-weight: 400;">x</span></em><span style="font-weight: 400;">/40 is an integer<br /> </span><span style="font-weight: 400;">(2)</span><i><span style="font-weight: 400;"> x</span></i><span style="font-weight: 400;">/5 is an integer</span></p> <p><span style="font-weight: 400;">2. If 1000 is divisible by 5</span><i><span style="font-weight: 400;">jk</span></i><span style="font-weight: 400;">, </span><i><span style="font-weight: 400;">j</span></i><span style="font-weight: 400;"> and </span><i><span style="font-weight: 400;">k</span></i><span style="font-weight: 400;"> are positive integers, and </span><i><span style="font-weight: 400;">j</span></i><span style="font-weight: 400;"> > </span><i><span style="font-weight: 400;">k</span></i><span style="font-weight: 400;">, what is the largest possible value of </span><i><span style="font-weight: 400;">k</span></i><span style="font-weight: 400;">?</span></p> <p style="padding-left: 30px;"><span style="font-weight: 400;">(A) 5<br /> </span><span style="font-weight: 400;">(B) 8<br /> </span><span style="font-weight: 400;">(C) 10<br /> </span><span style="font-weight: 400;">(D) 20<br /> </span><span style="font-weight: 400;">(E) 50</span></p> <p><span style="font-weight: 400;">3. Is the number of students in a certain club divisible by 15?</span></p> <p style="padding-left: 30px;"><span style="font-weight: 400;">(1) If the club were divided as evenly as possible into six teams, three of the teams would each have one extra student.<br /> </span><span style="font-weight: 400;">(2) The club can be evenly divided into teams of five students each, with no students left over. </span></p> <p><b>GMAT Number Properties: Evens, Odds, Positives, and Negatives</b></p> <p><span style="font-weight: 400;">4. If </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> and </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> are positive integers, is </span><i><span style="font-weight: 400;">xy</span></i><span style="font-weight: 400;">+1 even?</span></p> <p style="padding-left: 30px;"><span style="font-weight: 400;">(1) </span><i><span style="font-weight: 400;">x </span></i><span style="font-weight: 400;">+ </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> is even<br /> </span><span style="font-weight: 400;">(2) 3</span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is odd</span></p> <p><span style="font-weight: 400;">5. If</span><i><span style="font-weight: 400;"> x</span></i><span style="font-weight: 400;"> < 0 < </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;">, which of the following must be negative?</span></p> <p style="padding-left: 30px;"><span style="font-weight: 400;">(A) (</span><i><span style="font-weight: 400;">xy</span></i><span style="font-weight: 400;">)</span><span style="font-weight: 400;">²<br /> </span><span style="font-weight: 400;">(B)</span><i><span style="font-weight: 400;"> x</span></i><span style="font-weight: 400;">²</span><i><span style="font-weight: 400;"> y<br /> </span></i><span style="font-weight: 400;">(C)</span><i><span style="font-weight: 400;"> x</span></i><span style="font-weight: 400;"> + </span><i><span style="font-weight: 400;">y<br /> </span></i><span style="font-weight: 400;">(D)</span><i><span style="font-weight: 400;"> x</span></i><span style="font-weight: 400;">²</span><span style="font-weight: 400;"> + </span><i><span style="font-weight: 400;">xy<br /> </span></i><span style="font-weight: 400;">(E)</span><i><span style="font-weight: 400;"> xy</span></i><span style="font-weight: 400;">²</span></p> <p><span style="font-weight: 400;">6. If </span><i><span style="font-weight: 400;">abc</span></i><span style="font-weight: 400;"> ≠ 0, is </span><i><span style="font-weight: 400;">ab</span></i><span style="font-weight: 400;"> > 0?</span></p> <p style="padding-left: 30px;"><span style="font-weight: 400;">(1)</span><i><span style="font-weight: 400;"> ab</span></i><span style="font-weight: 400;">²</span><i><span style="font-weight: 400;">c</span></i><span style="font-weight: 400;"> > 0<br /> </span><i><span style="font-weight: 400;">(2) abc</span></i><span style="font-weight: 400;">²</span><span style="font-weight: 400;"> > 0</span></p> <h4><b>How to Review GMAT Number Properties Questions</b></h4> <p><span style="font-weight: 400;">The secret to reviewing a GMAT Number Properties problem is to </span><b>break it into little pieces</b><span style="font-weight: 400;">. It’s not (usually) the math that’s tough. The challenge is figuring out what the GMAT is trying to tell you, and doing so quickly and calmly.</span></p> <p><span style="font-weight: 400;">You might not understand every piece of a problem the first time you see it, especially if you’re under pressure from using a timer. That’s what the review process is for. Try to spot the little clues and pieces of information in each problem and analyze what each one means. Your goal is to find any pieces of this problem that you might be able to use to solve other, different problems in the future. </span></p> <p><span style="font-weight: 400;">As always, </span><b>do as much of the hard work yourself as possible</b><span style="font-weight: 400;">. That means starting by reviewing your own work, </span><i><span style="font-weight: 400;">without</span></i><span style="font-weight: 400;"> looking at the answers. Then, just check the answer to see if you got it right. If not, look at the problem one more time. Now that you know the answer, can you figure it out? </span></p> <ol> <li style="font-weight: 400;"><span style="font-weight: 400;">(A)</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">(C)</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">(C)</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">(B)</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">(C)</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">(E)</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">(B)</span></li> </ol> <h4><b>Explanations</b></h4> <p><i><span style="font-weight: 400;">Problem 1:</span></i></p> <p><span style="font-weight: 400;">This is a </span><a id="bloglink" href="https://www.manhattanprep.com/gmat/blog/how-data-sufficiency-works/" target="_blank" rel="noopener"><span style="font-weight: 400;">Data Sufficiency</span></a><span style="font-weight: 400;"> problem. The question is really asking whether </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is a multiple of 10. </span></p> <p><span style="font-weight: 400;">The first statement tells you that </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is a multiple of 40. So, </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> could be a number like 40, 80, 400, or even 0 or -40. All of these numbers are multiples of 10. So, </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is definitely a multiple of 10, and the first statement is sufficient.</span></p> <p><span style="font-weight: 400;">However, the second statement only tells you that </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is a multiple of 5. If </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is a multiple of 5, it might be a multiple of 10, or it might not be. For instance, </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> could be 20, but it could also be 15. Since you don’t know whether </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is a multiple of 10 or not, this statement is insufficient. The answer is (A).</span></p> <p><i><span style="font-weight: 400;">Problem 2: </span></i></p> <p><span style="font-weight: 400;">This is a difficult problem to untangle at first. However, what it’s really saying isn’t that complicated!</span></p> <p><span style="font-weight: 400;">5</span><i><span style="font-weight: 400;">jk</span></i><span style="font-weight: 400;"> divides evenly into 1000. So we can divide 1000 evenly by 5, </span><i><span style="font-weight: 400;">j</span></i><span style="font-weight: 400;">, and </span><i><span style="font-weight: 400;">k</span></i><span style="font-weight: 400;">. </span></p> <p><span style="font-weight: 400;">We can go ahead and divide 1000 by 5, and we get 200. We don’t know what </span><i><span style="font-weight: 400;">j</span></i><span style="font-weight: 400;"> and </span><i><span style="font-weight: 400;">k</span></i><span style="font-weight: 400;"> are yet, but we must be able to divide 200 by them. </span></p> <p><span style="font-weight: 400;">There are a lot of different pairs of numbers that you could divide 200 by. Of those pairs, we’re looking for the one that has the biggest value for </span><i><span style="font-weight: 400;">k</span></i><span style="font-weight: 400;">. Start writing out the possible pairs of divisors: </span></p> <p><i><span style="font-weight: 400;">jk</span></i><span style="font-weight: 400;"> = 1*200</span></p> <p><i><span style="font-weight: 400;">jk</span></i><span style="font-weight: 400;"> = 2*100</span></p> <p><i><span style="font-weight: 400;">jk</span></i><span style="font-weight: 400;"> = 4*50</span></p> <p><i><span style="font-weight: 400;">jk</span></i><span style="font-weight: 400;"> = 5*40</span></p> <p><i><span style="font-weight: 400;">jk</span></i><span style="font-weight: 400;"> = 10*20</span></p> <p><span style="font-weight: 400;">Since </span><i><span style="font-weight: 400;">k</span></i><span style="font-weight: 400;"> has to be smaller than </span><i><span style="font-weight: 400;">j</span></i><span style="font-weight: 400;">, </span><i><span style="font-weight: 400;">k</span></i><span style="font-weight: 400;"> must be the smaller number in the pair. Of all of these pairs, the one that has the greatest value for k is </span><i><span style="font-weight: 400;">jk</span></i><span style="font-weight: 400;"> = 10*20, where </span><i><span style="font-weight: 400;">k</span></i><span style="font-weight: 400;"> will equal 10. </span></p> <p><i><span style="font-weight: 400;">Problem 3: </span></i></p> <p><span style="font-weight: 400;">This problem is about remainders as well as divisibility. The question asks whether the number of students is divisible by 15. According to the first statement, if you divide the number of students by 6, you get a remainder of 3 (the number of leftover students.) </span></p> <p><span style="font-weight: 400;">So the first statement says that the number of students could be 9, or 15, or 21, or any other number that has a remainder of 3 when divided into 6 groups. Some of these values are divisible by 15 and others aren’t. Since the number of students might or might not be divisible by 15, this statement is insufficient. </span></p> <p><span style="font-weight: 400;">The second statement says that the number of students is divisible by 5. However, the number might be divisible by 15 (for instance, if it equals 15 or 30) or it might not be (if it equals 10 or 20). This statement is also insufficient. </span></p> <p><span style="font-weight: 400;">Put the two statements together. Notice that all of the numbers that fit the first statement are multiples of 3. That isn’t a coincidence! Imagine dividing the students into three groups. You could create each group by combining two of the six smaller groups together, then adding one of the three leftover students. Since the students could be divided evenly into three groups, the number of students is a multiple of three. </span></p> <p><span style="font-weight: 400;">Putting the two statements together tells us that the number of students is a multiple of both 3 and 5. If a number is a multiple of 3 and a multiple of 5, it’s a multiple of 15. The two statements are sufficient together and the answer is (C).</span></p> <p><i><span style="font-weight: 400;">Problem 4:</span></i></p> <p><span style="font-weight: 400;">When this problem asks whether </span><i><span style="font-weight: 400;">xy </span></i><span style="font-weight: 400;">+ 1 is even, it’s really asking whether </span><i><span style="font-weight: 400;">xy</span></i><span style="font-weight: 400;"> is odd. And since </span><i><span style="font-weight: 400;">xy</span></i><span style="font-weight: 400;"> can only be odd if both </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> and </span><i><span style="font-weight: 400;">y </span></i><span style="font-weight: 400;">are odd, you can rewrite the question like this: </span></p> <p><span style="font-weight: 400;">“Are </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> and </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> both odd?”</span></p> <p><span style="font-weight: 400;">Statement 1 tells you that </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> and </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> are either both odd or both even. Since you don’t know whether they’re both odd, the statement is insufficient.</span></p> <p><span style="font-weight: 400;">Statement 2 tells you that </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is odd. However, </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> could be odd or even, so the statement is insufficient.</span></p> <p><span style="font-weight: 400;">Putting the two statements together, </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is odd (from statement 2), and </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> and </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> are the same (from statement 1). So, </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> and </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> are both odd, and </span><i><span style="font-weight: 400;">xy</span></i><span style="font-weight: 400;"> + 1 is even. The two statements together are sufficient, and the answer is (C). </span></p> <p><i><span style="font-weight: 400;">Problem 5: </span></i></p> <p><span style="font-weight: 400;">The question says that </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is negative and </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> is positive. Look through the answer choices to find one that will always turn out negative. </span></p> <p><span style="font-weight: 400;">(A) can’t be negative, since perfect squares are never negative. Similarly, (B) is the product of two positive numbers, so (B) can’t be negative. Eliminate (A) and (B). </span></p> <p><span style="font-weight: 400;">(C) could be either positive or negative. For instance, if </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> = -100 and </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> = 5, </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> + </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> is negative. But if </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> = -5 and </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> = 100, </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> + </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> is positive. (D) can also be positive—for instance, if </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> = -10 and </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> = 1. Eliminate (C) and (D).</span></p> <p><span style="font-weight: 400;">(E) is the only answer choice that must be negative. </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;">²</span><span style="font-weight: 400;"> </span><span style="font-weight: 400;">is positive, and </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is negative, so their product will be negative. </span></p> <p><i><span style="font-weight: 400;">Problem 6: </span></i></p> <p><span style="font-weight: 400;">The question states that </span><i><span style="font-weight: 400;">abc</span></i><span style="font-weight: 400;"> does not equal 0, so none of the unknown values equals zero. The product of two numbers is positive if they’re both positive or both negative: in other words, if they have the same sign. So, you can rewrite the question: </span></p> <p style="padding-left: 30px;"><span style="font-weight: 400;">“Do </span><i><span style="font-weight: 400;">a</span></i><span style="font-weight: 400;"> and </span><i><span style="font-weight: 400;">b</span></i><span style="font-weight: 400;"> have the same sign?” </span></p> <p><span style="font-weight: 400;">Statement 1 states that </span><i><span style="font-weight: 400;">ab</span></i><span style="font-weight: 400;">²</span><i><span style="font-weight: 400;">c</span></i><span style="font-weight: 400;"> > 0. </span><i><span style="font-weight: 400;">b²</span></i><span style="font-weight: 400;"> </span><span style="font-weight: 400;">is definitely positive, since it’s a square. Therefore, it’s safe to divide both sides of the inequality by </span><i><span style="font-weight: 400;">b</span></i><span style="font-weight: 400;">²</span><span style="font-weight: 400;">, which simplifies it to </span><i><span style="font-weight: 400;">ac</span></i><span style="font-weight: 400;"> > 0. However, because there’s no information about the sign of</span><i><span style="font-weight: 400;"> a</span></i><span style="font-weight: 400;"> or the sign of </span><i><span style="font-weight: 400;">b</span></i><span style="font-weight: 400;">, this statement is insufficient. </span></p> <p><span style="font-weight: 400;">Statement 2 states that </span><i><span style="font-weight: 400;">abc</span></i><span style="font-weight: 400;">²</span><span style="font-weight: 400;"> > 0. Since </span><i><span style="font-weight: 400;">c</span></i><span style="font-weight: 400;">²</span><span style="font-weight: 400;"> is definitely positive, you can divide both sides of the inequality by it, and find that </span><i><span style="font-weight: 400;">ab</span></i><span style="font-weight: 400;"> > 0. This answers the original question! So, statement 2 is sufficient and the answer to the problem is (B). <img decoding="async" class="emoji" draggable="false" src="https://s.w.org/images/core/emoji/11/svg/1f4dd.svg" alt="?" /></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" rel="noopener"><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" rel="noopener noreferrer">Chelsey Cooley</a><a href="https://www.manhattanprep.com/instructors/chelsey-cooley/?utm_source=manhattanprep.com%2Fgre%2Fblog&utm_medium=blog&utm_content=CooleyBioGREBlog&utm_campaign=GRE%20Blog" target="_blank" rel="noopener noreferrer"><img decoding="async" 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" data-pagespeed-url-hash="1615980074" data-pagespeed-onload="pagespeed.CriticalImages.checkImageForCriticality(this);" data-pagespeed-loaded="1" /></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/gmat/classes/#instructor/336" target="_blank" rel="noopener noreferrer">Check out Chelsey’s upcoming GMAT prep offerings here</a>.</em></i></p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/gmat-number-properties-practice-questions/">GMAT Number Properties: Practice Questions</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p> ]]></content:encoded> </item> <item> <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 […]</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" 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… 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;">—————- </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> ]]></content:encoded> </item> </channel> </rss>