{"id":18545,"date":"2020-01-24T21:49:57","date_gmt":"2020-01-24T21:49:57","guid":{"rendered":"https:\/\/www.manhattanprep.com\/gmat\/?p=18545"},"modified":"2021-03-29T17:15:34","modified_gmt":"2021-03-29T17:15:34","slug":"gmat-quant-tips-mental-math","status":"publish","type":"post","link":"https:\/\/www.manhattanprep.com\/gmat\/blog\/gmat-quant-tips-mental-math\/","title":{"rendered":"GMAT Quant Tips: Mental Math"},"content":{"rendered":"

\"gmat<\/span><\/p>\n

If your goal is to take some time pressure off of the <\/span>quantitative section of the GMAT<\/span><\/a>, you should ask yourself: what are the skills I will need over and over during that section, and what are the skills I will only need once or twice? Too often I see my own students spending hours to get incrementally faster at, for example, weighted averages; that\u2019s an area where understanding the basic concept is probably sufficient. Instead, invest the most time in the thing you\u2019ll be doing the most often: calculation!\u00a0<\/span><\/p>\n

<\/p>\n

One of the questions you\u2019ll hear me ask in my classroom a lot is, \u201cDo you really need paper for that?\u201d There\u2019s a massive speed (and arguably accuracy) benefit to learning to do calculations in your head. To help me give some examples, I enlisted the help of my dad, a retired math teacher! He feels the same way about mental math that I do, so I asked him to write some questions that he thinks students shouldn\u2019t need a pencil for, and I would try to solve them as quickly as I possibly could. Here are some of the questions he asked me and my answers.<\/span><\/p>\n

Dad<\/b>: Margo counted a total of 1800 sheep and cows during the week she visited New Zealand. If she counted five sheep for every cow, how many more sheep than cows did Margo count?<\/span><\/p>\n

Ryan<\/b>: Well, there are actually lots of ways to do this. It\u2019s a 5 to 1 ratio, which means there are 6 parts total (represented by the 1800). So if I divide by 6, that\u2019s 300, which is the cow part of the ratio. So there are 300 cows, and there are 1500 sheep, and the difference between those is 1200. But if the numbers were trickier, you could just say the difference is 4 parts out of 6, or 2 parts out of 3, so the answer is just two-thirds of the total.<\/span><\/p>\n

Dad<\/b>: Let\u2019s say that Steph Curry made 40% of his 3-point field goal attempts last year. If he made 280 3-pointers, how many 3-pointers did he attempt?<\/span><\/p>\n

Ryan<\/b>: One nice way to deal with percents is with benchmarks: 1%, 5%, 10%, 50%. I think 10% is going to be an easy benchmark here. If 280 is 40% of the total, I could divide by 4 to get 70, which is 10% of the total, which means 700 is 100% of the total. So that would be 700 3-pointers attempted.<\/span><\/p>\n

Dad<\/b>: If the dinner bill came to $44 and you wanted to leave a 15% tip, how much money would you leave altogether? (Assume there\u2019s no tax involved.) What if you wanted to leave a 20% tip?\u00a0<\/span><\/p>\n

Ryan<\/b>: This is another benchmarking question. 10% is easy, because you just move the decimal point. A 10% tip, in other words, would be $4.40, so a 20% tip would just be twice that much, which would be $8.80. That\u2019s the easiest, so I\u2019ll start there. 15% is a little trickier, because I also need a 5% benchmark. The 10% we already know is $4.40; the 5% would be half that, which is $2.20. If I add those two together, that\u2019s going to get us to 15%. So $4.40 plus $2.20 is $6.60; that would be a 15% tip.<\/span><\/p>\n

Dad<\/b>: At Ikea, Sonam bought a square table whose area was 1.44 sq. meters.\u00a0 How many centimeters long was each side of the table?<\/span><\/p>\n

Ryan<\/strong>: Well, I don\u2019t want to convert to square centimeters; I would rather just keep working in meters, then convert at the very end. So if the table is 1.44 square meters, then that\u2019s 1.2 meters on each side, and I know that because 144 is the square of 12. That means that 1.2 times 1.2 would be 1.44. This is where it pays to know your perfect squares; if you don\u2019t just recognize that 144 is a perfect square, then this problem is going to be very difficult. So let\u2019s see: if each side of the table is 1.2 meters, that means it\u2019s 120 centimeters, since I have to multiply by 100, which I can do by moving the decimal point two places to the right.<\/span><\/p>\n

Ryan<\/b>: So here\u2019s my question for you, which I think is particularly relevant to the <\/span>Integrated Reasoning<\/span><\/a> section of the GMAT. When students asked you \u201cwhy do we need mental math when we have calculators,\u201d what did you say?<\/span><\/p>\n

Dad<\/b>: The more you practice doing mental math, the more facile you become with numbers, because you\u2019re constantly thinking about shortcuts. It\u2019s going to improve your mathematical ability all around, but even beyond that, it\u2019s quicker as you develop more confidence, and you\u2019ll realize it\u2019s a much more fun way to do something then taking out a calculator and pushing a bunch of buttons. Plus, there\u2019s an error factor with calculators, because students will often mis-key something, which leads to another issue: I taught middle schoolers, and when they used calculators, I always wanted them to consider what an appropriate answer would be or not be. Before you hit the equals button, give me a ballpark figure. Now go ahead and press equals, and see if you were close.<\/span><\/p>\n

GMAT Mental Math – Takeaways<\/b><\/h3>\n

Hopefully, these problems have given you a few ideas about how to improve your calculation speed; if you\u2019re studying for the GMAT, you\u2019ll find plenty more speed tips in Manhattan Prep\u2019s \u201c<\/span>Foundations of GMAT Math<\/span><\/a>\u201d book. But before you go, I do have one final tip for you: every so often, complete a study session wherein you solve absolutely everything in your head. You may be slow at first, but it\u2019s a great way to improve. When I was studying for the test, I would do problems during my lunch break, but I would sometimes forget to bring my pencil with me, so I had to really hone my mental math skills! In retrospect, those study sessions were probably some of the most effective ones.<\/span><\/p>\n

NEXT:\u00a0<\/b>GMAT Quant Tips: Mental Math – Part 2<\/a><\/p>\n

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

\n

\"ryan-jacobs\"Ryan Jacobs<\/a>\u00a0is a Manhattan Prep instructor based in San Francisco, California.<\/strong>\u00a0He has an MBA from UC San Diego, a 780 on the GMAT, and years of GMAT teaching experience. His other interests include music, photography, and hockey.\u00a0Check out Ryan\u2019s upcoming GMAT prep offerings here<\/a>.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

If your goal is to take some time pressure off of the quantitative section of the GMAT, you should ask yourself: what are the skills I will need over and over during that section, and what are the skills I will only need once or twice? Too often I see my own students spending hours […]<\/p>\n","protected":false},"author":25,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[52871],"tags":[233,319,325,372],"yst_prominent_words":[57337,55251,57338,57336,53635,53997,57340,57330,57342,57341,57331,57343,57332,56905,55938,57339,54679,57333],"class_list":["post-18545","post","type-post","status-publish","format-standard","hentry","category-gmat-strategies","tag-gmat","tag-gmat-quant","tag-gmat-quant-tips","tag-gmat-tips"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/18545","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\/25"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/comments?post=18545"}],"version-history":[{"count":6,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/18545\/revisions"}],"predecessor-version":[{"id":19350,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/18545\/revisions\/19350"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=18545"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=18545"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=18545"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=18545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}