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	<title>absolute value &#8211; GRE</title>
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		<title>What&#8217;s Tested on GRE Math</title>
		<link>https://www.manhattanprep.com/gre/blog/whats-tested-on-gre-math/</link>
		
		<dc:creator><![CDATA[Chelsey Cooley]]></dc:creator>
		<pubDate>Mon, 01 Apr 2019 21:49:29 +0000</pubDate>
				<category><![CDATA[Current Studiers]]></category>
		<category><![CDATA[GRE 101]]></category>
		<category><![CDATA[GRE Prep]]></category>
		<category><![CDATA[GRE Quant]]></category>
		<category><![CDATA[GRE Strategies]]></category>
		<category><![CDATA[How To Study]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Basics]]></category>
		<category><![CDATA[Study Tips]]></category>
		<category><![CDATA[Taking the GRE]]></category>
		<category><![CDATA[absolute value]]></category>
		<category><![CDATA[algebra]]></category>
		<category><![CDATA[Arithmetic]]></category>
		<category><![CDATA[Decimals]]></category>
		<category><![CDATA[Divisibility]]></category>
		<category><![CDATA[Executive Reasoning]]></category>
		<category><![CDATA[Exponents]]></category>
		<category><![CDATA[formulas]]></category>
		<category><![CDATA[fractions]]></category>
		<category><![CDATA[Functions]]></category>
		<category><![CDATA[geometry]]></category>
		<category><![CDATA[inequalities]]></category>
		<category><![CDATA[Number Properties]]></category>
		<category><![CDATA[Percents]]></category>
		<category><![CDATA[Ratios]]></category>
		<category><![CDATA[Roots]]></category>
		<category><![CDATA[Sequences]]></category>
		<category><![CDATA[Statistics]]></category>
		<guid isPermaLink="false">https://www.manhattanprep.com/gre/?p=12353</guid>

					<description><![CDATA[<p>GRE Math is a bit like high school math, without some of the hardest parts: for instance, you don’t have to write proofs or show your work! Here’s a quick rundown of the GRE Math skills required to conquer the Quant section, along with some of our best GRE Math tips. GRE Math Rules to [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gre/blog/whats-tested-on-gre-math/">What&#8217;s Tested on GRE Math</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gre">GRE</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><img decoding="async" fetchpriority="high" class="alignnone size-full wp-image-12356" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2019/04/whatstestedongremath.jpg" alt="Manhattan Prep GRE Blog - What's Tested on GRE Math by Chelsey Cooley" width="1200" height="628" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2019/04/whatstestedongremath.jpg 1200w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2019/04/whatstestedongremath-300x157.jpg 300w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2019/04/whatstestedongremath-768x402.jpg 768w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2019/04/whatstestedongremath-1024x536.jpg 1024w" sizes="(max-width: 1200px) 100vw, 1200px" /></p>
<p><span style="font-weight: 400;">GRE Math is a bit like high school math, without some of the hardest parts: for instance, you don’t have to write proofs or show your work! Here’s a quick rundown of the GRE Math skills required to conquer the Quant section, along with some of our best GRE Math tips. </span><span id="more-12353"></span></p>
<h4><b>GRE Math Rules to Memorize</b></h4>
<p>You can’t bring a <a id="bloglink" href="https://www.manhattanprep.com/gre/blog/creating-your-own-gre-quant-cheat-sheets/" target="_blank" rel="noopener">cheat sheet</a> to the GRE, so you’ll need to memorize a number of GRE Math rules. This list isn’t exhaustive, but it does cover the different types of basic math rules and operations you’ll need to know on test day. It <i>doesn’t</i> cover problem-solving skills—we’ll look at those in a moment.</p>
<p><b>Arithmetic:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to add, subtract, multiply, and divide positive and negative numbers</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to round numbers</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to use the order of operations (PEMDAS) to simplify a complicated expression</span></li>
</ul>
<p><b>Algebra:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to simplify one or more equations and solve for the value of a variable or variables</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to find the solutions of a quadratic equation, and how to create a quadratic equation by multiplying binomials</span></li>
</ul>
<p><b>Inequalities and Absolute Values:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">The meanings of ‘inequality,’ ‘absolute value,’ and related terms</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to graph absolute values and inequalities on a number line, and how to interpret what you see on a number line</span></li>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-absolute-value/" target="_blank" rel="noopener"><span style="font-weight: 400;">How to solve equations and simplify expressions containing one or more absolute values</span></a></li>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/manipulating-inequalities-and-absolute-values-on-the-gre/" target="_blank" rel="noopener"><span style="font-weight: 400;">How to simplify an inequality and/or combine multiple inequalities together</span></a></li>
</ul>
<p><b>Functions, Formulas, and Sequences:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">The definition of a function, such as f(x) = 2x, and how to use it</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">The definition of a sequence, such as S</span><span style="font-weight: 400;"><sub>x</sub></span><span style="font-weight: 400;"> = S</span><span style="font-weight: 400;"><sub>x-1</sub></span><span style="font-weight: 400;"> + 3, and how to use it</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to find missing terms in a sequence</span></li>
</ul>
<p><b>Fractions and Decimals:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to add, subtract, multiply, and divide fractions and decimals</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to simplify a fraction</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to simplify a complex expression containing multiple fractions and/or decimals</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to convert back and forth between fractions and decimals</span></li>
</ul>
<p><b>Percents:</b></p>
<ul>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/heres-the-safest-way-to-handle-gre-percentage-problems/" target="_blank" rel="noopener"><span style="font-weight: 400;">How to find a certain percent of a number</span></a></li>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-percentage-problems-part-2-percent-increase-and-percent-decrease/" target="_blank" rel="noopener"><span style="font-weight: 400;">How to find a number that is a certain percent higher or lower than another</span></a></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to convert between percents, fractions, and decimals</span></li>
</ul>
<p><b>Ratios:</b></p>
<ul>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-ratios/" target="_blank" rel="noopener"><span style="font-weight: 400;">The ratio between two given numbers</span></a></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to find unknown values, given information about their ratio with other values</span></li>
</ul>
<p><b>Divisibility:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">The definitions of divisibility terms, such as ‘divisible,’ ‘divisor,’ ‘factor,’ ‘prime factor,’ ‘multiple,’ ‘integer,’ etc. </span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to find divisors, prime factors, and multiples of a number</span></li>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-remainder-problems/" target="_blank" rel="noopener"><span style="font-weight: 400;">How to find the remainder when one number is divided by another</span></a></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to determine whether one number is divisible by another</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">Quick rules for divisibility (such as the rules for whether a number is divisible by 3 or 9)</span></li>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-prime-factorization-and-divisibility-problems/" target="_blank" rel="noopener"><span style="font-weight: 400;">The relationship between divisibility and prime factors</span></a></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">The first 10 prime numbers</span></li>
</ul>
<p><b>Exponents and Roots:</b></p>
<ul>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/lets-have-fun-with-gre-exponents/" target="_blank" rel="noopener"><span style="font-weight: 400;">How to add, subtract, multiply, and divide various combinations of numbers and variables with exponents</span></a></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">The rules about negative versus positive numbers and exponents</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to find the square root of a given number</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">The perfect squares up to 20</span><span style="font-weight: 400;">2</span></li>
</ul>
<p><b>Number Properties:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">What happens when you add, subtract, multiply, and divide positive and negative numbers</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">What happens when you add, subtract, multiply, and divide even and odd numbers</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">Methods to find the units digit of a large unknown number</span></li>
</ul>
<p><b>Statistics:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">The definitions of mean, median, range, mode, quartile, percentile, and standard deviation</span></li>
</ul>
<h4><b>Geometry Rules for GRE Math</b></h4>
<p><span style="font-weight: 400;">Geometry gets its own section, because it involves a lot of rules! Make your geometry flashcards early in your GRE Math studies, and review them often. Here are the basics.</span></p>
<p><b>Basic Triangles:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">The area of a triangle</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">Rules regarding the side lengths and perimeter of a triangle, and the relationship between angles and side lengths</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">The definition and properties of isosceles and equilateral triangles</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">The sum of the angles of a triangle</span></li>
</ul>
<p><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-right-triangles/" target="_blank" rel="noopener"><b>Right Triangles:</b></a></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">The Pythagorean Theorem</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">The ‘special right triangles’ which have integer side lengths, such as the 3-4-5 triangle</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">The properties of 30-60-90 and 45-45-90 triangles</span></li>
</ul>
<p><b>Circles:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">The relationship between the radius, diameter, circumference, and area of a circle</span></li>
</ul>
<p><b>Quadrilaterals:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">Identifying different types of quadrilaterals</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">The area and perimeter of a square, rectangle, and parallelogram</span></li>
</ul>
<p><b>Other Shapes:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to break down a complex shape into smaller shapes to find its area or perimeter</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">The relationship between the number of sides of a polygon and the sum of its angles</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to find the volume and surface area of basic 3-dimensional figures</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to find the area of the border surrounding another shape</span></li>
</ul>
<p><b>Coordinate Geometry:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to draw points and lines in a plane based on their equations</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to identify the approximate equation of a line or the coordinates of a point based on a graph</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to use algebra to determine whether a particular point is on a particular line</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">Which points appear in which quadrants of the coordinate plane</span></li>
</ul>
<h4><b>GRE Math Problem-Solving Skills</b></h4>
<p><span style="font-weight: 400;">Knowing the rules is only the first part of mastering GRE Math. You’ll also need to learn certain methods for solving different types of problems—and how to recognize those problems in the first place. Here are a few of the most important problem-solving techniques for GRE Math.</span></p>
<p><b>Overall GRE Quant Skills:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to quickly predict whether you’re likely to get a problem right or wrong, so that you can decide whether to guess</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to make quick, reasonable guesses on tough problems</span></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How often to look at the clock during each Quant section, and what to do if you’re behind on time</span></li>
</ul>
<p><b>Discrete Quant/Word Problems:</b></p>
<ul>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-word-problems-tricks-traps/" target="_blank" rel="noopener"><span style="font-weight: 400;">How to translate text into equations</span></a></li>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-what-is-a-variable-really/" target="_blank" rel="noopener"><span style="font-weight: 400;">How to identify unknown values in a problem and turn them into variables</span></a></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">Strategies for common specific types of word problems, such as overlapping sets, rates, weighted averages, and </span><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-percent-change-questions/" target="_blank" rel="noopener"><span style="font-weight: 400;">percent change</span></a></li>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/a-step-by-step-guide-to-multiple-workers-gre-rates-problems/" target="_blank" rel="noopener"><span style="font-weight: 400;">How to translate a problem about rates and work into a rate/work/time equation</span></a></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to translate a problem about parts and wholes into equations involving percents, fractions, decimals, and/or ratios</span></li>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/using-smart-numbers-to-avoid-algebra-on-the-gre/" target="_blank" rel="noopener"><span style="font-weight: 400;">How and when to use Smart Numbers to solve a Discrete Quant problem</span></a></li>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-backsolving/" target="_blank" rel="noopener"><span style="font-weight: 400;">How and when to work backwards to solve a Discrete Quant problem</span></a></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">How and when to test cases</span></li>
</ul>
<p><b>Quantitative Comparisons:</b></p>
<ul>
<li style="font-weight: 400;"><span style="font-weight: 400;">How to simplify the quantities and the given information</span></li>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/heres-how-to-know-which-cases-to-test-on-gre-quantitative-comparison-problems/" target="_blank" rel="noopener"><span style="font-weight: 400;">How to choose appropriate cases</span></a></li>
<li style="font-weight: 400;"><span style="font-weight: 400;">Strategies to prove answer choice D</span></li>
</ul>
<p><b>Data Interpretation:</b></p>
<ul>
<li style="font-weight: 400;"><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-data-interpretation/" target="_blank" rel="noopener"><span style="font-weight: 400;">How to interpret information from various types of graphs, including line graphs, bar graphs, and pie charts</span></a></li>
</ul>
<h4><b>Polishing Your GRE Math Skills</b></h4>
<p><span style="font-weight: 400;">Memorizing math rules and mastering problem-solving strategies are starting points for GRE Math. However, even if two people know exactly the same list of math techniques, they can end up with very different GRE Math scores. The difference lies in what the GRE is </span><i><span style="font-weight: 400;">really</span></i><span style="font-weight: 400;"> testing: executive reasoning skills.</span></p>
<p><span style="font-weight: 400;">“Executive reasoning” refers to the type of high-level thinking you use when you have to make tough decisions, quickly, with limited time and information. You’ll need to do that, over and over again, as you take the GRE! You don’t get to spend all the time you’d like on every GRE Math problem. You also don’t get to test out multiple approaches to each problem until you find the perfect one. You need to set priorities and make the strategic moves that will maximize your score—even though that sometimes means guessing on ones you might be able to get right.</span></p>
<p><span style="font-weight: 400;">Don’t think that memorizing math rules is the main goal of your GRE Math studies. You should also spend plenty of time doing problems. And when you do problems, at least some of the time, do them in </span><b>timed, random sets</b><span style="font-weight: 400;"> and </span><b>use a timer while you practice</b><span style="font-weight: 400;">. Also, when you fill out your </span><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/gre-problem-log-quant/" target="_blank" rel="noopener"><span style="font-weight: 400;">problem log</span></a><span style="font-weight: 400;">, review problems that you spent too much time on, or where you picked an inefficient approach, even if you got them right in the end. </span></p>
<p><span style="font-weight: 400;">There are other GRE Math skills, too. One GRE Math skill is your ability to handle test anxiety and mental fatigue. GRE Math experts are those who improve their test-taking stamina ahead of time so that they won’t get worn out on test day. They also address test anxiety head-on, rather than ignoring it and hoping that it goes away! Check out our </span><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/managing-gre-anxiety-before-test-day/" target="_blank" rel="noopener"><span style="font-weight: 400;">GRE anxiety reduction tips</span></a><span style="font-weight: 400;"> for some ways to do this yourself. The GRE Math section also tests focus: can you pay careful attention to every single problem and avoid missing details and making careless mistakes? Luckily, </span><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/your-attention-please/" target="_blank" rel="noopener"><span style="font-weight: 400;">focus can be trained</span></a><span style="font-weight: 400;">, and there are many ways to </span><a id="bloglink" href="https://www.manhattanprep.com/gre/blog/careless-gre-math-mistakes/" target="_blank" rel="noopener"><span style="font-weight: 400;">avoid careless errors on test day</span></a><span style="font-weight: 400;">. </span></p>
<p><span style="font-weight: 400;">You might not need geometry and inequalities in graduate school or in your career. However, you’ll definitely need some of the core GRE Math skills: executive reasoning, decision-making, focus, attention, and the ability to stay relaxed under pressure. Studying GRE Math is a unique chance to push yourself, grow, and hone your skills. ?</span></p>
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<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&#038;utm_medium=blog&#038;utm_content=CooleyBioGREBlog&#038;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-pin-nopin="true" /></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 170Q/170V on the GRE. </em></i><i><em><a id="bloglink" href="https://www.manhattanprep.com/gre/classes/#instructor/48" target="_blank" rel="noopener noreferrer">Check out Chelsey’s upcoming GRE prep offerings here</a>.</em></i></p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gre/blog/whats-tested-on-gre-math/">What&#8217;s Tested on GRE Math</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gre">GRE</a>.</p>
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		<item>
		<title>GRE Math for People Who Hate Math: Absolute Value</title>
		<link>https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-absolute-value/</link>
		
		<dc:creator><![CDATA[Chelsey Cooley]]></dc:creator>
		<pubDate>Wed, 10 May 2017 17:19:56 +0000</pubDate>
				<category><![CDATA[Algebra]]></category>
		<category><![CDATA[Current Studiers]]></category>
		<category><![CDATA[GRE Prep]]></category>
		<category><![CDATA[GRE Quant]]></category>
		<category><![CDATA[GRE Strategies]]></category>
		<category><![CDATA[How To Study]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[Study Tips]]></category>
		<category><![CDATA[absolute value]]></category>
		<category><![CDATA[GRE Math]]></category>
		<category><![CDATA[GRE Math for People Who Hate Math]]></category>
		<guid isPermaLink="false">http://www.manhattanprep.com/gre/?p=10315</guid>

					<description><![CDATA[<p>You can attend the first session of any of our online or in-person GRE courses absolutely free. Ready to take the plunge? Check out our upcoming courses here. Think of an absolute value as a simple machine that looks like this: &#124;&#124;. You put a value into it, and the machine answers a single question [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-absolute-value/">GRE Math for People Who Hate Math: Absolute Value</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gre">GRE</a>.</p>
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										<content:encoded><![CDATA[<p><img decoding="async" class="alignnone size-full wp-image-10331" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/gre-math-people-who-hate-math-absolute-value-chelsey-cooley.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Absolute Value by Chelsey Cooley" width="1200" height="628" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/gre-math-people-who-hate-math-absolute-value-chelsey-cooley.png 1200w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/gre-math-people-who-hate-math-absolute-value-chelsey-cooley-300x157.png 300w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/gre-math-people-who-hate-math-absolute-value-chelsey-cooley-768x402.png 768w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/gre-math-people-who-hate-math-absolute-value-chelsey-cooley-1024x536.png 1024w" sizes="(max-width: 1200px) 100vw, 1200px" /></p>
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<p><b><i></i></b><span style="font-weight: 400;">Think of an absolute value as a simple machine that looks like this: ||. You put a value into it, and the machine answers a single question for you: how far away from zero was the value that you put in?</span></p>
<p><span style="font-weight: 400;">The basic operation of the machine is simple. Take any number, put it into the machine, and find out how far from zero that number is. The absolute value of 12, |12|, is equal to 12. The absolute value of -10, |-10|, is equal to 10. That’s because -10 is 10 units away from zero.</span></p>
<p><span style="font-weight: 400;">It starts to get complicated when the GRE asks you to put things into the machine that are more complex than simple numbers. Imagine that somebody else is operating the machine. She puts values in, but she doesn’t tell you what those values are. All you can see is the </span><i><span style="font-weight: 400;">answer</span></i><span style="font-weight: 400;"> that the machine gives when it receives those values.</span><span id="more-10315"></span></p>
<p><span style="font-weight: 400;">Suppose that the absolute value machine operator – call her Abby, for short – puts a value into the machine, and the machine answers ‘5’. That’s equivalent to saying that |</span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;">| = 5, in a GRE problem. What could </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> be? What did Abby put into the machine? Any value that’s 5 units away from zero. She could’ve inserted either a -5 or a +5, and you would’ve gotten the same result. </span></p>
<p><span style="font-weight: 400;">What if you put something more complex into the absolute value machine? Suppose that Abby takes an unknown again, but this time, before putting it in the machine, she multiplies it by two and adds one. That is, the expression she puts in is 2</span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> + 1. Then, the machine answers ‘7’. You now know that 2</span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> + 1 is 7 units away from zero. </span></p>
<p><span style="font-weight: 400;">That allows you to simplify as follows:</span></p>
<p style="padding-left: 30px;"><span style="font-weight: 400;">|2</span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> + 1| = 7</span></p>
<p style="padding-left: 30px;"><span style="font-weight: 400;">2</span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> + 1 = 7 OR 2</span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> + 1 = -7</span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> = 3 OR </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> = -4</span></p>
<p><span style="font-weight: 400;">Next, Abby tells you, she’s going to put two values into the machine. She won’t tell you what the values are. But she does tell you that </span><b>the machine gave the same response to both of them</b><span style="font-weight: 400;">. What do you know about the values? </span></p>
<p><span style="font-weight: 400;">The two values might or might not be the same, but they’re definitely equally far away from zero:</span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-10316" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-1.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Absolute Value by Chelsey Cooley" width="510" height="252" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-1.png 510w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-1-300x148.png 300w" sizes="(max-width: 510px) 100vw, 510px" /></p>
<p><span style="font-weight: 400;">This scenario is analogous to the equation |x| = |y|. You don’t know what </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> is, and you don’t know what </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;"> is. You don’t know whether the two variables are equal, and you don’t know whether they’re positive or negative. However, you </span><i><span style="font-weight: 400;">do</span></i><span style="font-weight: 400;"> know that they’re equally far from zero. Either they’re equal (x = y), or one is on the opposite side of zero from the other (x = -y).  </span></p>
<p><span style="font-weight: 400;">Now, Abby puts a value into the machine, but she won’t even tell you what the machine says. Instead, she just tells you that </span><b>the answer the machine gave is less than 10</b><span style="font-weight: 400;">. In other words, |x| < 10. What can you say about the value she used?</span></p>
<p><span style="font-weight: 400;">She could’ve used any value that’s fewer than 10 units away from zero. +5 would’ve worked, and -7 would’ve worked, and 0 would’ve worked. 11, however, wouldn’t work. Neither would -1000. You can actually draw the possibilities out on a number line: </span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-10317" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-2.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Absolute Value by Chelsey Cooley" width="447" height="106" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-2.png 447w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-2-300x71.png 300w" sizes="(max-width: 447px) 100vw, 447px" /></p>
<p><span style="font-weight: 400;">Finally, how about a scenario with both variables and inequalities? You put two variables into the absolute value machine. The machine gives a smaller number in response to the first variable and a larger number in response to the second variable. That is, the machine says that |x| < |y|. </span></p>
<p><span style="font-weight: 400;">All it’s really saying is that </span><i><span style="font-weight: 400;">x is closer to zero than y is</span></i><span style="font-weight: 400;">. That doesn’t tell you anything about whether </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 or negative, and it doesn’t tell you anything about which one of them is greater. </span><i><span style="font-weight: 400;">x </span></i><span style="font-weight: 400;">could be closer to zero than </span><i><span style="font-weight: 400;">y</span></i><span style="font-weight: 400;">, but also greater:</span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-10318" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-3.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Absolute Value by Chelsey Cooley" width="472" height="85" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-3.png 472w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-3-300x54.png 300w" sizes="(max-width: 472px) 100vw, 472px" /></p>
<p><span style="font-weight: 400;">Or, </span><i><span style="font-weight: 400;">x</span></i><span style="font-weight: 400;"> could be smaller:</span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-10319" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-4.png" alt="Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Absolute Value by Chelsey Cooley" width="441" height="96" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-4.png 441w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/cc-46-image-4-300x65.png 300w" sizes="(max-width: 441px) 100vw, 441px" /></p>
<p><span style="font-weight: 400;">Either way, |x| < |y|. </span></p>
<p><b>You don’t have to think about the ‘absolute value machine’ every time you see an absolute value GRE problem.</b><span style="font-weight: 400;"> That would be time-consuming and inefficient. However, you </span><i><span style="font-weight: 400;">should</span></i><span style="font-weight: 400;"> spend some time thinking about it now. If you really grasp where the rules come from, you’ll be less likely to make mistakes when memorizing them and when applying them on test day. You’ll also be better prepared to handle those quirky GRE problems that don’t </span><i><span style="font-weight: 400;">quite </span></i><span style="font-weight: 400;">fit. ?</span></p>
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<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&#038;utm_medium=blog&#038;utm_content=CooleyBioGREBlog&#038;utm_campaign=GRE%20Blog" target="_blank" rel="noopener noreferrer"><img decoding="async" loading="lazy" class="alignleft" title="Chelsey Cooley Manhattan Prep GRE Instructor" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2015/11/chelsey-cooley-150x150.jpg" alt="Chelsey Cooley Manhattan Prep GRE Instructor" width="150" height="150" data-pin-nopin="true" /></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 170Q/170V on the GRE. </em></i><i><em><a id="bloglink" href="https://www.manhattanprep.com/gre/classes/#instructor/48" target="_blank" rel="noopener noreferrer">Check out Chelsey’s upcoming GRE prep offerings here</a>.</em></i></p>
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<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gre/blog/gre-math-for-people-who-hate-math-absolute-value/">GRE Math for People Who Hate Math: Absolute Value</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gre">GRE</a>.</p>
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		<title>Manipulating Inequalities and Absolute Value on the GRE</title>
		<link>https://www.manhattanprep.com/gre/blog/manipulating-inequalities-and-absolute-values-on-the-gre/</link>
		
		<dc:creator><![CDATA[Stacey Koprince]]></dc:creator>
		<pubDate>Mon, 03 Dec 2012 14:14:22 +0000</pubDate>
				<category><![CDATA[Challenge Problems]]></category>
		<category><![CDATA[Current Studiers]]></category>
		<category><![CDATA[GRE Prep]]></category>
		<category><![CDATA[GRE Quant]]></category>
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		<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Basics]]></category>
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		<category><![CDATA[absolute value]]></category>
		<category><![CDATA[inequalities]]></category>
		<guid isPermaLink="false">http://www.manhattanprep.com/gre/blog/?p=4803</guid>

					<description><![CDATA[<p>Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here. Most people dislike absolute value, and inequalities can tie us up into knots. Put them together, and we can have some major headaches! Let&#8217;s test one [&#8230;]</p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gre/blog/manipulating-inequalities-and-absolute-values-on-the-gre/">Manipulating Inequalities and Absolute Value on the GRE</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gre">GRE</a>.</p>
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										<content:encoded><![CDATA[<p><b><i>Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! </i></b><a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/" target="_blank" rel="noopener"><b><i>Check out our upcoming courses here</i></b></a><b><i>.</i></b></p>
<hr />
<p>Most people dislike absolute value, and inequalities can tie us up into knots. Put them together, and we can have some major headaches! Let&#8217;s test one out.</p>
<p>Set your timer for 1 minute and 15 seconds for this Quantitative Comparison problem and GO!<span id="more-4803"></span></p>
<blockquote>
<p align="center">* |x — 2| > 3</p>
<p> </p>
<p><span style="text-decoration: underline;">Quantity A</span>                                                                 <span style="text-decoration: underline;">Quantity B</span></p>
<p>The minimum possible                                              The minimum possible</p>
<p>value of |<em>x</em> — 3.5|                                                        |<em>x</em> — 1.5|</p></blockquote>
<p>What did you get? (Do you remember the 4 QC answer choices? I didn&#8217;t list them above! If you don&#8217;t know what they are, go look them up. I&#8217;ll wait. And the pain of having to look them up will help convince you that you need to memorize these.)</p>
<p>We have a given:</p>
<p style="padding-left: 30px;">|<em>x</em> — 2| > 3</p>
<p>So, first, let&#8217;s figure out what this actually means. For what values of <em>x</em> is this inequality true?</p>
<p>When an inequality or an equation contains an absolute value sign, we have to think of this as <em>two</em> equations (or inequalities). The first one is the actual inequality that we were given, without the absolute value sign:</p>
<p style="padding-left: 30px;"><em>x</em> — 2 > 3</p>
<p>The second one is the negative of the first one. Choose one side (it doesn&#8217;t matter which one, but it&#8217;s easiest to choose whichever side is simpler) and make it negative. If you have an equation (= sign), then that&#8217;s all you need to do. If you have an inequality, though, then things are a bit more complicated. With inequalities, we also have to reverse the direction of the inequality (think of it as multiplying by a negative). So, in the above case, we would get this:</p>
<p style="padding-left: 30px;"><em>x</em> — 2 < -(3)</p>
<p>You&#8217;ll notice that I put parentheses around the 3. I don&#8217;t really need to do that in this case, because it&#8217;s only a 3, but this could make a difference on a different problem, so it&#8217;s a good idea to get into the habit of including parentheses, just in case.</p>
<p>All right, we have these two equations:</p>
<p style="padding-left: 30px;"><em>x</em> — 2 > 3</p>
<p style="padding-left: 30px;"><em>x</em> — 2 < -(3)</p>
<p>Simplify each one. <em>x</em> — 2 > 3 becomes <em>x</em> > 5. And <em>x</em> — 2 < -(3) becomes <em>x</em> < -1. The original equation, then, is telling us that <em>x</em> could be greater than 5 or less than -1.</p>
<p>Because we&#8217;re dealing with absolute value in general, it might be useful to illustrate this on a number line (particularly because, if we glance at Quantities A and B, we can see that we&#8217;re not done with absolute value yet!). Our number line will include 0 not only because we always include 0 on number lines but also because the question is about absolute value—which means negative vs. non-negative is a key issue here.</p>
<p><img decoding="async" class="aligncenter" style="margin: 5px; padding: 0; border: 0;" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2012/11/stacey-gre-1.jpg" alt="gre absolute value" /></p>
<p>What does absolute value mean again? Absolute value turns negative numbers positive (or, in the case of 0, leaves the number the same). Absolute value is really telling us the <em>distance</em> a number is <em>from zero</em> on the number line, regardless of direction. What&#8217;s the closest possibility for <em>x</em>? On the -1 side, <em>x</em> could be just a bit more than 1 unit away from zero.</p>
<p>Take any number in the world and put an absolute value symbol around it. What&#8217;s the smallest possible value you can think of, once the absolute value symbol has been applied?</p>
<p>Right. Zero. The absolute value of zero is zero. The absolute value of anything else is at least a tiny bit bigger than zero, because absolute value gets rid of any negative signs. So the smallest possible value for anything inside an absolute value symbol is zero.</p>
<p>Now, why did I ask you that? Take a look at Quantity A:</p>
<p style="padding-left: 30px;">The minimum possible value of |<em>x</em> — 3.5|</p>
<p>I asked you that because that&#8217;s what the problem wants me to find: the minimum possible value once that absolute value sign has been applied. Can we make it come out to zero? What would <em>x</em> have to be in order for the overall value to be zero?</p>
<p>The value of <em>x</em> would have to be 3.5. Now, I know I can&#8217;t make <em>x</em> = 3.5 because, glancing at my number line, I can see that <em>x</em> has to be bigger than 5 or smaller than -1. Of the <em>possible</em> values for <em>x</em>, which is closest to 3.5?</p>
<p>We should look at the line that start at a little bit bigger than 5. What if we plug in this value?</p>
<p style="padding-left: 30px;"><em>|slightly bigger than </em>5 — 3.5|</p>
<p>Do the math but keep the &#8220;slightly bigger than&#8221; language: that would equal something |<em>slightly bigger than </em>1.5| or > 1.5. The value in Quantity A, then, is something just slightly bigger than 1.5.</p>
<p>What about Quantity B? Use the same thought process. In order for the value of |<em>x</em> — 1.5| to be zero, <em>x</em> would have to be 1.5. It can&#8217;t be 1.5, but what&#8217;s the closest possible value that it can be? In this case, we need to go in the other direction: 1.5 is closer to -1 than it is to +5.</p>
<p>This time, we&#8217;re doing this math:</p>
<p style="padding-left: 30px;"><em>|slightly smaller than </em>-1 — 1.5|</p>
<p style="padding-left: 30px;"><em>|slightly smaller than </em>-2.5|</p>
<p>Now here&#8217;s a weird little twist: I know I&#8217;m going to drop the negative sign since I&#8217;ve got an absolute value symbol, right? Think of this as dividing by a negative: we also need to flip the inequality sign. So this becomes: <em>slightly larger than</em> +2.5 or > 2.5.</p>
<p>Which is the larger value? Quantity B. The correct answer is B.</p>
<p>Now, you might look at all of that and think, I can&#8217;t think it through like that. I&#8217;d mess that up. If so, that&#8217;s okay. Here&#8217;s another (slightly longer) way to approach it. You&#8217;ll have to test more cases, but you might find the process more straightforward.</p>
<p>Do everything the same up to the point where we began examining Quantity A. We know that <em>x</em> > 5 and <em>x</em> < -1, and we've drawn our number line. Then test <span style="text-decoration: underline;">both</span> ends of the possible ranges (slightly less than -1 and slightly more than 5) for both Quantity A and Quantity B.</p>
<p>First, try the -1 end of the range. <em>x</em> < |-1 — 3.5| < |-4.5|. Next, apply the absolute value symbol. If <em>x</em> < |-4.5|, then applying the absolute value symbol gives us <em>x</em> > +4.5 (remember, we flip both the sign and the inequality symbol). Next, try 5: x > |5 — 3.5| > |1.5|. We don&#8217;t need to flip the sign this time because the number is already positive. x > 1.5. Here&#8217;s how it would look on the number line.</p>
<p><img decoding="async" class="aligncenter" style="margin: 5px; padding: 0; border: 0;" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2012/11/stacey-gre-2.jpg" alt="gre inequalities" /></p>
<p>So for Quantity A, the smallest possible value (the one closest to zero) is something just a bit bigger than 1.5. Now, do the same thing for Quantity B: test both ends of the range.</p>
<p>This time, we&#8217;ve got <em>x</em> < |-1 — 1.5| < |-2.5|. Applying the absolute value symbol to this negative value, we get <em>x</em> > 2.5. The other possibility is x > |5 — 1.5| > |3.5|, or x > 3.5. In this case, the smallest possible value (the one closest to zero) is something just a bit bigger than 2.5, so Quantity B is greater and the answer is B.</p>
<h4><strong>Key Takeaways for Inequality and Absolute Value Problems</strong></h4>
<p>(1) Equations or inequalities containing absolute value symbols actually represent two different equations (or inequalities), not just one. Make sure that you&#8217;re solving for both!</p>
<p>(2) If you have an inequality inside of an absolute value symbol (as we did when we tested possible values here), you have to flip the sign when the value of the number is negative—just as we would if we were solving a normal inequality.</p>
<p>(3) Try drawing things out. Absolute value problems are really about negative vs. non-negative, so a number line will often help to sort out what the problem is really telling/really asking. ?</p>
<p>*©Manhattan Prep</p>
<hr />
<p><em><strong>Can’t get enough of Stacey’s GMAT mastery? Attend the first session of one of <a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/" target="_blank" rel="noopener noreferrer">her upcoming GMAT courses</a> absolutely free, no strings attached. Seriously.</strong></em></p>
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<p><a id="bloglink" href="https://www.manhattanprep.com/instructors/stacey-koprince/" target="_blank" rel="noopener noreferrer"><img decoding="async" loading="lazy" class="alignleft wp-image-9719 size-thumbnail" src="https://cdn2.manhattanprep.com/gmat/wp-content/uploads/sites/18/2015/06/stacey-koprince-150x150.png" alt="stacey-koprince" width="150" height="150" /></a><em><strong><a id="bloglink" href="https://www.manhattanprep.com/instructors/stacey-koprince/" target="_blank" rel="noopener noreferrer">Stacey Koprince</a> is a Manhattan Prep instructor based in Montreal, Canada and Los Angeles, California.</strong> Stacey has been teaching the GMAT, GRE, and LSAT  for more than 15 years and is one of the most well-known instructors in the industry. Stacey loves to teach and is absolutely fascinated by standardized tests. <a id="bloglink" href="https://www.manhattanprep.com/gmat/classes/#instructor/86" target="_blank" rel="noopener noreferrer">Check out Stacey’s upcoming GMAT courses here</a>.</em></p>
<p>The post <a rel="nofollow" href="https://www.manhattanprep.com/gre/blog/manipulating-inequalities-and-absolute-values-on-the-gre/">Manipulating Inequalities and Absolute Value on the GRE</a> appeared first on <a rel="nofollow" href="https://www.manhattanprep.com/gre">GRE</a>.</p>
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