{"id":18366,"date":"2019-12-04T21:17:28","date_gmt":"2019-12-04T21:17:28","guid":{"rendered":"https:\/\/www.manhattanprep.com\/gmat\/?p=18366"},"modified":"2019-12-04T21:17:45","modified_gmt":"2019-12-04T21:17:45","slug":"quick-gmat-math-hacks","status":"publish","type":"post","link":"https:\/\/www.manhattanprep.com\/gmat\/blog\/quick-gmat-math-hacks\/","title":{"rendered":"Quick GMAT Math Hacks"},"content":{"rendered":"<p><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-18367 size-full\" src=\"https:\/\/www.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2019\/12\/mprep-blogimages-wave1-39-e1575494245444.png\" alt=\"quick GMAT math hacks\" width=\"1200\" height=\"628\" \/><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Here are a few of the most useful quick GMAT math tricks I\u2019ve learned over the years. They won\u2019t show up on every problem, or even on every Quant section. But, if you happen to use one of these GMAT math hacks on test day, it could save you anywhere from a few seconds to a few minutes.\u00a0<\/span><\/p>\n<p><!--more--><\/p>\n<h3><b>Number Properties<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">The product of two consecutive integers is always divisible by two, the product of three consecutive integers is always divisible by three, and so on.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">To check whether a complicated expression is even or odd, plug in 0 and 1. For instance, try the expression 2<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> + <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">. If you plug in 0, you get 0, which is even. If you plug in 1, you get 4, which is also even. So, this expression is always even.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">If you want to find all of the factors of a number by guessing and testing, you can stop when you reach the square root of that number. For instance, if you\u2019re finding all of the factors of 228, you can stop checking numbers when you hit 15, since that\u2019s approximately the square root of 228.\u00a0<\/span><\/li>\n<\/ul>\n<h3><b>Geometry<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">If you double the side length of a shape (such as a square or triangle), its area quadruples. If you halve the side length, its area is quartered.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Learn the <\/span><a href=\"https:\/\/www.manhattanprep.com\/gre\/blog\/gre-geometry-three-ways-to-spot-similar-triangles\/\"><span style=\"font-weight: 400;\">three ways to spot similar triangles<\/span><\/a><span style=\"font-weight: 400;\">, so you\u2019ll instantly recognize that two triangles are similar without having to prove it from scratch.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">If a problem tells you a shape is a rectangle, don\u2019t forget that the shape could be a square! In fact, a square is often a good case to test on <\/span><a href=\"https:\/\/www.manhattanprep.com\/gmat\/blog\/how-to-review-a-data-sufficiency-question\/\"><span style=\"font-weight: 400;\">Geometry Data Sufficiency<\/span><\/a><span style=\"font-weight: 400;\"> problems.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">If a GMAT math problem asks you whether a point is on a line, plug the coordinates of the point into the equation for the line. If you get a valid result, then the point is on the line. For example, the point (2, 6) is on the line y = 2x + 2.<\/span><\/li>\n<\/ul>\n<h3><b>Word Problems<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">The average of a set of numbers always has to be somewhere in the middle of that set. It can\u2019t be larger than the largest number in the set, or smaller than the smallest number. This is useful for weighted average problems: if you average the weights of 6 cats that each weigh 10 pounds, and 8 dogs that each weigh 30 pounds, the result will be somewhere in the middle in between 10 and 30. The more evenly spread the numbers are, the closer the average will actually be to the middle.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Only use a Venn diagram for rare \u201c3-group\u201d overlapping set problems. For almost all overlapping sets, the Overlapping Set Matrix is quicker and easier. <\/span><a href=\"https:\/\/www.manhattanprep.com\/gmat\/blog\/how-to-handle-3-group-overlapping-sets-on-the-gmat\/\"><span style=\"font-weight: 400;\">Both are described in this article<\/span><\/a><span style=\"font-weight: 400;\">.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">You\u2019ll sometimes see rates problems that look like this: if it takes four people twelve days to sew eight jackets, how long does it take ten people to sew ten jackets? A quick trick for approaching these is to start with the original statement, and then \u201cscale\u201d it upwards or downwards. Here\u2019s what that might look like:\u00a0<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 90px;\"><i><span style=\"font-weight: 400;\">It takes 4 people 12 days to sew 8 jackets.<\/span><\/i><\/p>\n<p style=\"padding-left: 90px;\"><i><span style=\"font-weight: 400;\">1 person will take 4 times as long to do the same amount of work, so it will take 1 person 48 days to sew 8 jackets.\u00a0<\/span><\/i><\/p>\n<p style=\"padding-left: 90px;\"><i><span style=\"font-weight: 400;\">If that 1 person sews \u215b as many jackets, it will take \u215b as many days. So, it takes 1 person 6 days to sew 1 jacket.\u00a0<\/span><\/i><\/p>\n<p style=\"padding-left: 90px;\"><i><span style=\"font-weight: 400;\">If a person takes 6 days to sew a jacket, then it will take 10 people 6 days to sew 10 jackets (one per person). The answer is 6.<\/span><\/i><\/p>\n<h3><b>Fractions, Decimals, and Percents<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">When a fraction has zeroes on the end of both the numerator and the denominator, chop off the same number of zeroes from each (just make sure you count carefully!). 1,000,000 \/ 5,000 simplifies to 1,000 \/ 5.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Likewise, if a fraction has decimals in both the numerator and denominator, you can simplify by moving both decimal places by the same amount and in the same direction. For instance, 0.0007 \/ 0.14 = 0.007 \/ 1.4 = 0.07 \/ 14 = 0.7 \/ 140 = 7 \/ 1,400.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Use <\/span><a href=\"https:\/\/www.manhattanprep.com\/gre\/blog\/heres-the-safest-way-to-handle-gre-percentage-problems\/\"><span style=\"font-weight: 400;\">this technique to directly translate percent problems from English into math<\/span><\/a><span style=\"font-weight: 400;\"> without having to convert between decimals and percents.\u00a0<\/span><\/li>\n<\/ul>\n<h3><b>Working with Numbers<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">You can use a similar \u2018scaling\u2019 technique to calculate percents, fractions, or decimals. For instance, if you want to find 0.1% of 50,000, start like this:\u00a0<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 90px;\"><i><span style=\"font-weight: 400;\">10% of 50,000 is 5,000.<\/span><\/i><\/p>\n<p style=\"padding-left: 90px;\"><i><span style=\"font-weight: 400;\">So, 1% of 50,000 is a tenth of 5,000, or 500.\u00a0<\/span><\/i><\/p>\n<p style=\"padding-left: 90px;\"><i><span style=\"font-weight: 400;\">So, 0.1% of 50,000 is a tenth of 500, or 50. The answer is 50.\u00a0<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">To quickly divide a number by 5, divide it by 10 first, then multiply by 2. For example, 1,880\/5 = 1,880\/10 * 2 = 188 * 2 = 376.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Arithmetic can be easier if you \u201csplit up\u201d or rearrange the numbers before you do the math. Suppose that you need to calculate 117 &#8211; 98. Rewrite this as 117 &#8211; 100 + 2, or 17 + 2, which equals 19.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Use a similar technique to quickly calculate the square of a number that\u2019s close to an easy value.<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 90px;\"><span style=\"font-weight: 400;\">79\u00b2<\/span><span style=\"font-weight: 400;\">\u00a0= (80 &#8211; 1)\u00b2<\/span><span style=\"font-weight: 400;\">\u00a0= 80\u00b2<\/span><span style=\"font-weight: 400;\">\u00a0&#8211; 2(80) + 1 = 6,400 &#8211; 160 + 1 = 6241<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">To find a good common denominator, think of a value (if there is one) that both numbers are divisible by. Divide <\/span><b>one<\/b><span style=\"font-weight: 400;\"> of the two numbers by that value. Then, multiply that by the other number.\u00a0<\/span>\n<ul>\n<li style=\"font-weight: 400;\">For example, to find a common denominator between 25 and 15, note that both are divisible by 5. So, divide 25 by 5, which gives you 5, then multiply that by 15, giving you 75. 75 would be a good common denominator.<\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-weight: 400;\">It can be useful to memorize the approximate square roots of 2 and 3: \u221a<\/span><span style=\"font-weight: 400;\">2\u2248<\/span><span style=\"font-weight: 400;\">1.4<\/span><span style=\"font-weight: 400;\"> and\u221a<\/span><span style=\"font-weight: 400;\">3\u2248<\/span><span style=\"font-weight: 400;\">1.7<\/span><span style=\"font-weight: 400;\">. To remember this, at least if you\u2019re in the US, think of two dates: Valentine\u2019s Day is on 2\/14 and St. Patrick\u2019s Day is on 3\/17.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">To estimate other square roots, think of a perfect square that\u2019s as close as possible to the value you\u2019re dealing with. (You have your perfect squares memorized, right\u2026?) Estimate based on that\u2014so, for instance, \u221a<\/span><span style=\"font-weight: 400;\">79<\/span><span style=\"font-weight: 400;\"> is a bit smaller than \u221a<\/span><span style=\"font-weight: 400;\">81<\/span><span style=\"font-weight: 400;\">, which equals 9.\u00a0<\/span><\/li>\n<\/ul>\n<h3><b>What Next?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Math isn\u2019t the most important part of the GMAT math section! <\/span><a href=\"https:\/\/www.manhattanprep.com\/gmat\/blog\/what-the-gmat-really-tests\/\"><span style=\"font-weight: 400;\">Strong executive reasoning skills trump math knowledge<\/span><\/a><span style=\"font-weight: 400;\">. So, while these tips and tricks are useful, if you\u2019re having a tough time with the math section, incorporate some work on <\/span><a href=\"https:\/\/www.manhattanprep.com\/gmat\/blog\/everything-know-gmat-time-management-part-3\/\"><span style=\"font-weight: 400;\">timing<\/span><\/a><span style=\"font-weight: 400;\">, <\/span><a href=\"https:\/\/www.manhattanprep.com\/gmat\/blog\/which-gmat-problems-should-i-guess-on-part-3-making-great-guesses-on-quant-problems\/\"><span style=\"font-weight: 400;\">guessing<\/span><\/a><span style=\"font-weight: 400;\">, <\/span><a href=\"https:\/\/www.manhattanprep.com\/gmat\/blog\/the-4-math-strategies-everyone-must-master-part-1\/\"><span style=\"font-weight: 400;\">problem-solving strategies<\/span><\/a><span style=\"font-weight: 400;\">, and <\/span><a href=\"https:\/\/www.manhattanprep.com\/gmat\/blog\/how-to-handle-gmat-stress-without-freaking-out\/\"><span style=\"font-weight: 400;\">stress management<\/span><\/a><span style=\"font-weight: 400;\">. But keep some pages in your notes for these GMAT math tricks, plus any others you may come across while studying: you never know what may turn out to be useful. <\/span><\/p>\n<hr \/>\n<p><b><i>You can attend the first session of any of our online or in-person GMAT courses absolutely free! We\u2019re not kidding. <\/i><\/b><a href=\"https:\/\/www.manhattanprep.com\/gmat\/classes\/\"><b><i>Check out our upcoming courses here<\/i><\/b><\/a><b><i>.<\/i><\/b><b><i><br \/>\n<\/i><\/b><b><i><\/i><\/b><\/p>\n<hr \/>\n<p><b><i><em><strong><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 loading=\"lazy\" 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>\u00a0is a Manhattan Prep instructor based in Seattle, Washington.<\/strong>\u00a0<\/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\u2019s degree in linguistics, a 790 on the GMAT, and a perfect 170Q\/170V on the GRE. <a href=\"https:\/\/www.manhattanprep.com\/gmat\/classes\/#instructor\/336\"><span style=\"font-weight: 400;\">Check out Chelsey\u2019s upcoming GMAT prep offerings here<\/span><\/a><span style=\"font-weight: 400;\">.<\/span><\/em><\/i><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here are a few of the most useful quick GMAT math tricks I\u2019ve learned over the years. They won\u2019t show up on every problem, or even on every Quant section. But, if you happen to use one of these GMAT math hacks on test day, it could save you anywhere from a few seconds to [&hellip;]<\/p>\n","protected":false},"author":127,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[52871],"tags":[233,283,285],"yst_prominent_words":[54052,56921,56895,56917,53635,53917,56927,56923,53997,56928,54189,56912,56894,56913,56910,56907,56911,56905,56896],"class_list":["post-18366","post","type-post","status-publish","format-standard","hentry","category-gmat-strategies","tag-gmat","tag-gmat-math","tag-gmat-math-strategy"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/18366","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=18366"}],"version-history":[{"count":1,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/18366\/revisions"}],"predecessor-version":[{"id":18368,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/18366\/revisions\/18368"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=18366"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=18366"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=18366"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=18366"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}