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Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We\u2019re not kidding! <\/i><\/b>Check out our upcoming courses here<\/i><\/b><\/a>.<\/i><\/b><\/p>\n \u2026 when it\u2019s a distance on a number line!<\/span><\/p>\n Okay, that doesn\u2019t quite work as a joke. But it <\/span>does<\/span><\/i> work as a GMAT Quant strategy. Intimidated by absolute value GMAT problems? Read on to learn a quick and painless strategy. <\/span><\/p>\n Absolute values always come out as positive numbers. For instance, the absolute value of -7 is 7:<\/span><\/p>\n |-7| = 7<\/span><\/p>\n Distances <\/span><\/i>are also always positive, both in the real world and on the GMAT. There\u2019s no such thing as a negative distance. That means we can use distances\u2014something we already understand intuitively\u2014to think about absolute value. <\/span><\/p>\n The town of <\/span>Greatport<\/b> is at mile marker 5 on the highway, and the town of <\/span>Fairmont<\/b> is at mile marker 35.<\/span><\/p>\n If you want to travel from Greatport to Fairmont, you calculate the distance like this:<\/span><\/p>\n 35 \u2013 5 = 30<\/span><\/p>\n But if you want to travel from Fairmont back to Greatport, you don\u2019t do this:<\/span><\/p>\n 5 \u2013 35 = -30<\/span><\/p>\n You know intuitively that the distance is still 30 miles, not negative 30, regardless of which direction you\u2019re traveling. What you\u2019re really doing, mathematically, is taking an absolute value. <\/span><\/p>\n |5 \u2013 35| = |-30| = 30<\/span><\/p>\n |35 \u2013 5| = |30| = 30<\/span><\/p>\n The distance between two towns is the <\/span>absolute value of the difference between their mile markers.<\/span><\/i><\/p>\n Let\u2019s add a third town: <\/span>Veltria<\/b>. But I\u2019m not actually going to tell you where Veltria is. All I\u2019m going to tell you is that it\u2019s 5 miles away from Fairmont. <\/span><\/p>\n Here\u2019s the equation that shows that:<\/span><\/p>\n |v \u2013 35| = 5<\/span><\/p>\n By the way, this would be equally correct:<\/span><\/p>\n |35 \u2013 v| = 5<\/span><\/p>\n What this equation <\/span>means<\/span><\/i> is that the distance between Veltria and the 35-mile marker is 5 miles. Your intuition should tell you that Veltria can only be in two different locations: the 30-mile marker or the 40-mile marker. And in fact, those are the two values that fit the equation:<\/span><\/p>\n |30 \u2013 35| = |-5| = 5<\/span><\/p>\n |40 \u2013 35| = |5| = 5<\/span><\/p>\n So, when you see an equation like |10 \u2013 x| = 7, you can read it like this:<\/span><\/p>\n \u201cThe distance between 10 and x is 7.\u201d<\/span><\/p>\n Without actually doing algebra, you can figure out that x can only equal 3 or 17. <\/span><\/p>\n Let\u2019s bring a fourth town into the mix. It\u2019s called <\/span>Halfwayville<\/b>, and here\u2019s an equation that tells you where it\u2019s located:<\/span><\/p>\n |h \u2013 35| = |5 \u2013 h|<\/span><\/p>\n If you see this in an algebra problem on the GMAT, don\u2019t start simplifying it with math. Instead, read it as if it\u2019s telling you about the real world. <\/span><\/p>\n |h \u2013 35| = \u201cThe distance between Halfwayville and the 35-mile marker\u201d<\/span><\/p>\n |5 \u2013 h| = \u201cThe distance between Halfwayville and the 5-mile marker\u201d<\/span><\/p>\n The equals sign between them means that those two distances are the same. In other words,<\/span><\/p>\n \u201cHalfwayville is equally far from the 5-mile marker and the 35-mile marker.\u201d<\/span><\/p>\n There\u2019s only one place Halfwayville could be located: halfway between those two markers! That places it at the 20-mile marker.<\/span><\/p>\n What if they start bringing inequalities into the mix? Let\u2019s locate the town of Easton on the highway. Here\u2019s what you know:<\/span><\/p>\n |e \u2013 35| > 7<\/span><\/p>\n The left side of the inequality is the distance between Easton and the 35-mile marker. So, read this inequality like this:<\/span><\/p>\n \u201cThe distance between Easton and the 35-mile marker is more than 7 miles.\u201d<\/span><\/p>\n In other words,<\/span><\/p>\n \u201cEaston is more than 7 miles from the 35-mile marker.\u201d<\/span><\/p>\n Where could Easton be? Anywhere, as long as it\u2019s at least 7 miles from Fairmont.<\/span><\/p>\n Let\u2019s locate a new town: <\/span>Middleburg<\/b>. This time, all you know about it is this inequality, which has two absolute values:<\/span><\/p>\n |5 \u2013 m| > |35 \u2013 m|<\/span><\/p>\n Read it in plain English:<\/span><\/p>\n \u201cThe distance between Middleburg and the 5-mile marker is greater than the distance between Middleburg and the 35-mile marker.\u201d<\/span><\/p>\n Or:<\/span><\/p>\n \u201cMiddleburg is closer to the 35-mile marker than to the 5-mile marker.\u201d<\/span><\/p>\n Where could Middleburg be? It can\u2019t be off to the left side of Greatport; if it was over there, it would be closer to Greatport. We want it to be closer to Fairmont. It <\/span>could<\/span><\/i> be between Greatport and Fairmont, as long as it\u2019s closer to Fairmont. It could also be over to the right side of Fairmont. Here are all of the possibilities:<\/span><\/p>\n That inequality, |5 \u2013 m| > |35 \u2013 m|, is really just saying that Middleburg is to the right of the halfway point between Greatport and Fairmont.<\/span><\/p>\n What if they give you even less info? Let\u2019s suppose that we\u2019re now in a foreign country, where we don\u2019t know where anything is at all. You see this equation:<\/span><\/p>\n |x \u2013 y| + |y \u2013 z| = |x \u2013 z|<\/span><\/p>\n Read it out piece by piece. We have three towns: Xandria, Yelby, and Zorb. <\/span><\/p>\n On the left side of the equation, we have this:<\/span><\/p>\n \u201cThe distance from Xandria to Yelby, plus the distance from Yelby to Zorb\u201d<\/span><\/p>\n On the right side, we have this: <\/span><\/p>\n \u201cThe distance from Xandria to Zorb\u201d<\/span><\/p>\n In other words, if you drive straight from Xandria to Yelby, then drive from Yelby to Zorb, you\u2019ll cover the exact same distance as you would if you drove directly from Xandria to Zorb. <\/span><\/p>\n What does that mean? <\/span><\/p>\n Suppose that Xandria, Yelby, and Zorb were laid out like this. If you traveled from X to Y, then from Y to Z, you\u2019d be going out of your way:<\/span><\/p>\n There\u2019s actually only <\/span>one<\/b> situation where going through Yelby doesn\u2019t add any distance to your trip. That\u2019s the situation where Yelby is right on the line between Xandria and Zorb.<\/span><\/p>\n In that case, the distances are equal. If you go from X to Y, then from Y to Z, you\u2019ve covered the same distance as going straight from X to Z.<\/span><\/p>\n In other words, this equation:<\/span><\/p>\n |x \u2013 y| + |y \u2013 z| = |x \u2013 z|<\/span><\/p>\n Means this:<\/span><\/p>\n \u201cY is located on the line that goes from X to Z.\u201d<\/span><\/p>\n On a number line\u2014which is where we do most absolute value problems\u2014that just means that Y is in between X and Z, rather than being off to one side. <\/span><\/p>\n Absolute value problems are more intuitive than you might think, even when they\u2019re combined with inequalities! The next time you see an absolute value of a <\/span>difference<\/b>, pause before you start applying algebra rules. Can you think about the problem in terms of distances, instead? If so, you may find that the solution is faster and simpler than you expected! ?<\/span><\/p>\n 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\u2019re not kidding.\u00a0<\/i><\/b>Check out our upcoming courses here<\/i><\/b><\/a>.<\/i><\/b><\/p>\n Chelsey Cooley<\/a> Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We\u2019re not kidding! Check out our upcoming courses here. \u2026 when it\u2019s a distance on a number line! Okay, that doesn\u2019t quite work as a joke. But it does work as a GMAT Quant […]<\/p>\n","protected":false},"author":127,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,873,929,874,52871,930,2,8],"tags":[53232,53233],"yst_prominent_words":[],"class_list":["post-15228","post","type-post","status-publish","format-standard","hentry","category-manhattan-gmat-blog-algebra","category-for-current-studiers","category-gmat-prep","category-gmat-resources","category-gmat-strategies","category-gmat-study-guide","category-how-to-study","category-quant-on-gmat","tag-absolute-value","tag-number-line"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15228","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/users\/127"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/comments?post=15228"}],"version-history":[{"count":2,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15228\/revisions"}],"predecessor-version":[{"id":15274,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15228\/revisions\/15274"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=15228"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=15228"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=15228"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=15228"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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\n![\"Chelsey](\"https:\/\/cdn2.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2015\/11\/chelsey-cooley-150x150.jpg\" "\\"Chelsey")
<\/a>\u00a0is a Manhattan Prep instructor based in Seattle, Washington.<\/strong>\u00a0<\/em><\/i><\/b>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\u2019s degree in linguistics, a 790 on the GMAT, and a perfect 170\/170 on the GRE.\u00a0<\/em><\/i>Check out Chelsey\u2019s upcoming GMAT prep offerings here<\/a>.<\/em><\/i><\/p>\n","protected":false},"excerpt":{"rendered":"