<?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>Exponents – GMAT</title> <atom:link href="https://www.manhattanprep.com/gmat/blog/tag/exponents/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 17:35:38 +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>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" fetchpriority="high" 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" 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> <item> <title>The GMAT’s G-MASKs</title> <link>https://www.manhattanprep.com/gmat/blog/gmat-masks/</link> <dc:creator><![CDATA[Reed Arnold]]></dc:creator> <pubDate>Fri, 27 Jul 2018 16:50:35 +0000</pubDate> <category><![CDATA[Algebra]]></category> <category><![CDATA[For Current Studiers]]></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[Verbal]]></category> <category><![CDATA[Exponents]]></category> <category><![CDATA[GMAT Masks]]></category> <guid isPermaLink="false">https://www.manhattanprep.com/gmat/?p=16052</guid> <description><![CDATA[<p>You can and should murder me for that pun. But first, a question. What is a simplified way of writing 3x + 3x + 3x? Tough question. You might not have seen something like that before. How are you supposed to know what to do? Easier question. What is a nice, simplified way of writing […]</p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/gmat-masks/">The GMAT’s G-MASKs</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-16084" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/07/gmat-g-masks-reed-arnold.png" alt="Manhattan Prep GMAT Blog - The GMAT's G-MASKs by Reed Arnold" width="1200" height="628" srcset="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/07/gmat-g-masks-reed-arnold.png 1200w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/07/gmat-g-masks-reed-arnold-300x157.png 300w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/07/gmat-g-masks-reed-arnold-768x402.png 768w, https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2018/07/gmat-g-masks-reed-arnold-1024x536.png 1024w" sizes="(max-width: 1200px) 100vw, 1200px" /></p> <p><span style="font-weight: 400;"><iframe loading="lazy" src="https://giphy.com/embed/l3q2K5jinAlChoCLS" width="409" height="480" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p> <p><a href="https://giphy.com/gifs/mashable-l3q2K5jinAlChoCLS"></a></p> <p></span></p> <p><span style="font-weight: 400;">You can and should murder me for that pun.</span><span id="more-16052"></span></p> <p><span style="font-weight: 400;">But first, a question. What is a simplified way of writing 3</span><span style="font-weight: 400;"><sup>x</sup> </span><span style="font-weight: 400;">+ 3</span><span style="font-weight: 400;"><sup>x</sup> </span><span style="font-weight: 400;">+ 3</span><span style="font-weight: 400;"><sup>x</sup></span><span style="font-weight: 400;">?</span></p> <p><span style="font-weight: 400;">Tough question. You might not have seen something like that before. How are you supposed to know what to do?</span></p> <p><span style="font-weight: 400;">Easier question. What is a nice, simplified way of writing x + x + x?</span></p> <p><span style="font-weight: 400;">You probably got this one easily. x + x + x is just 3x.</span></p> <p><span style="font-weight: 400;">Not even an issue, right? But what’s the difference between these two things, really? If I add three of the same number, the outcome should always be three times that number. 2 + 2 + 2 is 3(2) = 6. x + x + x = 3x.</span></p> <p><span style="font-weight: 400;">So 3</span><span style="font-weight: 400;"><sup>x</sup> </span><span style="font-weight: 400;">+ 3</span><span style="font-weight: 400;"><sup>x</sup> </span><span style="font-weight: 400;">+ 3</span><span style="font-weight: 400;"><sup>x</sup> </span><span style="font-weight: 400;">= 3(3</span><span style="font-weight: 400;"><sup>x</sup></span><span style="font-weight: 400;">), which, using my exponent rules, equals 3</span><span style="font-weight: 400;"><sup>x+1</sup> </span><span style="font-weight: 400;">(because 3(3</span><span style="font-weight: 400;"><sup>x</sup></span><span style="font-weight: 400;">) can be written as</span> <span style="font-weight: 400;">3</span><span style="font-weight: 400;"><sup>1</sup></span><span style="font-weight: 400;">(3</span><span style="font-weight: 400;"><sup>x</sup></span><span style="font-weight: 400;">)).</span></p> <p><span style="font-weight: 400;">This is an example of one of the GMAT’s favorite moves: making you think you don’t know how to do something because they’ve put something that looks weird onto a process that you know how to do.</span></p> <p><span style="font-weight: 400;">I call these ‘GMAT masks.’ They’re disguises, nothing more. They are Batman’s cowl and Clark Kent’s glasses, except instead of hiding superheroes, they hide, y’know… math and stuff. They’re designed to blind you to rules you know and processes you can do.</span></p> <p><span style="font-weight: 400;">Here’s another example I use in my classes.</span></p> <p><span style="font-weight: 400;">Put a minute on the clock and try to simplify the following:</span></p> <p><span style="font-weight: 400;"> (x-y)/(√x + √y)</span></p> <p><span style="font-weight: 400;">Maybe you were able to do this, in which case you </span><i><span style="font-weight: 400;">probably</span></i><span style="font-weight: 400;"> were able to see through the GMAT’s disguise. But most students struggle to get through that.</span></p> <p><span style="font-weight: 400;">Try another. Give yourself a minute to simplify:</span></p> <p><span style="font-weight: 400;">(x²</span><span style="font-weight: 400;"> – y²</span><span style="font-weight: 400;">)/(x+y)</span></p> <p><span style="font-weight: 400;">How’d you do? A lot of people get this one in about 15 seconds (if you haven’t, brush up on your common quadratics forms! This is one of the GMAT’s favorites).</span></p> <p><span style="font-weight: 400;">You might have recognized that the numerator could be simplified to (x+y)(x-y). Then the (x+y) canceled out of top and bottom, leaving you with just (x-y). But what about that first expression? The one you probably didn’t see how to simplify when given a minute?</span></p> <p><span style="font-weight: 400;">Turns out, it’s the exact same problem.</span></p> <p><span style="font-weight: 400;">Try it again. Specify what you did in the second, easier problem and try to replicate that same logic on the first.</span></p> <p><span style="font-weight: 400;">Maybe you realize that (x-y), though it doesn’t appear in the most common form of a difference of squares, can be written as ((√x)²</span><span style="font-weight: 400;"> – (√y)²</span><span style="font-weight: 400;">).</span></p> <p><span style="font-weight: 400;">This makes it look much more like the standard form of a difference of squares! We can now write it as (√x + √y)*(√x – √y). And then the (√x + √y) cancels on top and bottom, leaving just (√x – √y).</span></p> <p><span style="font-weight: 400;">How about:</span></p> <p><span style="font-weight: 400;">(3</span><span style="font-weight: 400;"><sup>2x</sup></span><span style="font-weight: 400;"> – 5</span><span style="font-weight: 400;"><sup>2x</sup></span><span style="font-weight: 400;">)/(3</span><span style="font-weight: 400;"><sup>x</sup></span><span style="font-weight: 400;"> + 5</span><span style="font-weight: 400;"><sup>x</sup></span><span style="font-weight: 400;">)</span></p> <p><span style="font-weight: 400;">Same logic. Different mask.</span></p> <p><span style="font-weight: 400;">This is partly why I warn my students that it’s not enough to just memorize a flashcard. It’s one thing to know the most general appearance of formula, and another thing to be able to recognize that it should be used when it has a mask on.</span></p> <p><span style="font-weight: 400;">What is x if x²</span><span style="font-weight: 400;"> = 4</span><span style="font-weight: 400;"><sup>30</sup></span><span style="font-weight: 400;">?</span></p> <p><span style="font-weight: 400;">What is x if x²</span><span style="font-weight: 400;"> = 36?</span></p> <p><span style="font-weight: 400;">If on the second you remembered to say ‘+/- 6’ but on the first you just said ‘4</span><span style="font-weight: 400;"><sup>15</sup></span><span style="font-weight: 400;">’ you fell for a GMAT mask. It’s like the least fun Halloween costume ever.</span></p> <p><span style="font-weight: 400;"><iframe loading="lazy" src="https://giphy.com/embed/ctD357Rv3SCNG" width="480" height="363" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p> <p><a href="https://giphy.com/gifs/david-bowie-cracked-actor-gif-ctD357Rv3SCNG"></a></p> <p></span></p> <p><span style="font-weight: 400;">You’re used to solving the second equation, and you had ‘+/- 6’ drilled into you after all the times you forgot about it (and maybe you just did! Hey, don’t forget that on the GMAT, numbers can be negative unless specified otherwise). But 4</span><span style="font-weight: 400;"><sup>30</sup></span><span style="font-weight: 400;"> is weird. That’s a number we don’t deal with day-to-day, unless we happen to be God, and we’re counting all the stars for fun. So sometimes we let the appearance shake us.</span></p> <p><span style="font-weight: 400;">This doesn’t just happen in GMAT Quant. The Verbal section is full of masks. Masks are the fluff in Sentence Correction that separate singular nouns from plural verbs. </span><a id="bloglink" href="https://www.manhattanprep.com/gmat/blog/2018/08/07/gmat-verbal-fair-part-2/" target="_blank" rel="noopener"><span style="font-weight: 400;">They’re the arguments in Critical Reasoning that seem to be about different topics but are all actually about rates and totals, or questions of causation, or sample biases</span></a><span style="font-weight: 400;">. They’re in Reading Comp, because in all the myriad of topics in the passages they give you, </span><span style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gmat/blog/2017/10/19/what-really-matters-gmat-reading-comp/" target="_blank" rel="noopener">they keep asking about the same stuff</a>.</span></p> <p><span style="font-weight: 400;">This is why on the GMAT, you have to review questions and specify the processes you used. Even on an easy question, you think you understand perfectly.</span></p> <p><span style="font-weight: 400;">You know that 60/12 is 5. But why? How deep can you get with that? If you can explain to me why 60 is divisible by 12 in terms of prime numbers—which are the heart of divisibility—you’ll be much closer to being able to explain to me how (60 * 35) is divisible by 28. If you can explain that, you can explain how 60! is divisible by 11</span><span style="font-weight: 400;"><sup>5</sup></span><span style="font-weight: 400;">, even though those numbers look so much more disgusting. But really? it’s all the same mask.</span></p> <p><span style="font-weight: 400;">60 is divisible by 12 because the prime factors of 12, 2*2*3, are also in the prime factorization of 60 (which are 2*2*3*5).</span></p> <p><span style="font-weight: 400;">(60*35) is divisible by 28 because the prime factorization of 28, 2*2*7, is also in the prime factorization of 60*35 (which is (2*2*3*5*5*7).</span></p> <p><span style="font-weight: 400;">60! is divisible by 11</span><span style="font-weight: 400;"><sup>5</sup></span><span style="font-weight: 400;"> because the prime factors of 11</span><span style="font-weight: 400;"><sup>5</sup></span><span style="font-weight: 400;">, (11*11*11*11*11), are also in the prime factorization of 60 (which is… well, it’s a very long list, but 60! = 1*2*3*4*5…*58*59*60, and 11 shows up 5 times in that product string, at 11, 22, 33, 44, and 55).</span></p> <p><span style="font-weight: 400;">How do you get good at seeing through masks? You have to really pinpoint why you’re doing process—even on an easy question where it seems obvious—and work to understand questions and concepts at their deepest level, not just at a superficial familiarity. And when something looks just </span><i><span style="font-weight: 400;">weird, </span></i><span style="font-weight: 400;">run through your rolodex of commonly tested rules or formulas and see if you can’t spot which one seems to ‘line up’ best with the situation at hand. Perhaps you’ll realize what you have in front of you is just a regular old process trying to disguise itself.</span></p> <p><span style="font-weight: 400;">Look past the masks, and you’ll often find the same old friends underneath. Superman’s glasses weren’t ever that effective a disguise, anyway. ? </span></p> <p><span style="font-weight: 400;"><iframe loading="lazy" src="https://giphy.com/embed/pqFbHWj0vRqmY" width="480" height="400" frameBorder="0" class="giphy-embed" allowFullScreen></iframe></p> <p><a href="https://giphy.com/gifs/superman-challenger23-pqFbHWj0vRqmY"></a></p> <p></span></p> <hr /> <p><b><i>Want some more GMAT tips from Reed? Attend the first session of one of his </i></b><a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/#instructor/366" target="_blank" rel="noopener"><b><i>upcoming GMAT courses </i></b></a><b><i>absolutely free, no strings attached. Seriously.</i></b></p> <hr /> <p><em><strong><a id="bloglink" href="https://www.manhattanprep.com/instructors/reed-arnold/" target="_blank" rel="noopener">Reed Arnold</a><a href="https://www.manhattanprep.com/instructors/reed-arnold/?utm_source=manhattanprep.com%2Fgmat%2Fblog&utm_campaign=GMAT%20Blog&utm_medium=blog&utm_content=Reed%20Arnold%20Bio%20Link" target="_blank" rel="noopener"><img decoding="async" loading="lazy" class="alignleft wp-image-12946 size-thumbnail" src="https://d27gmszdzgfpo3.cloudfront.net/gmat/wp-content/uploads/sites/18/2017/01/reed-arnold-150x150.png" width="150" height="150" data-pin-nopin="true" /></a> is a Manhattan Prep instructor based in New York, NY.</strong> He has a B.A. in economics, philosophy, and mathematics and an M.S. in commerce, both from the University of Virginia. He enjoys writing, acting, Chipotle burritos, and teaching the GMAT. <a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/#instructor/366" target="_blank" rel="noopener">Check out Reed’s upcoming GMAT courses here.</a></em></p> <p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gmat/blog/gmat-masks/">The GMAT’s G-MASKs</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gmat">GMAT</a>.</p> ]]></content:encoded> </item> </channel> </rss>