{"id":15827,"date":"2012-12-21T09:25:55","date_gmt":"2012-12-21T16:25:55","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=15827"},"modified":"2012-12-21T23:34:20","modified_gmt":"2012-12-22T06:34:20","slug":"number-sense-for-the-gmat","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/number-sense-for-the-gmat\/","title":{"rendered":"Number Sense for the GMAT"},"content":{"rendered":"

\"\"First, a practice problem. Remember,\u00a0no calculator<\/a>.<\/p>\n

I. \u00a047\/150
\nII.\u00a0111\/330
\nIII.\u00a0299\/900<\/p>\n

1) Rank those three in order from smallest to biggest.<\/p>\n

    \n
  1. I, II, III<\/li>\n
  2. I, III, II<\/li>\n
  3. II, I, III<\/li>\n
  4. II, III, I<\/li>\n
  5. III, I, II<\/li>\n
      \n <\/p>\n

      Number sense<\/h2>\n

      Many GMAT Quantitative Problems, like the foregoing one, test\u00a0number sense<\/strong>.\u00a0 What is number sense?\u00a0 Number sense is a good intuition for what happens to different kinds of numbers (positive, negative, fractions, etc.) when you perform various arithmetic operations on them.<\/p>\n

      Number sense is what allows some folks to \"see\" shortcuts such as\u00a0estimation<\/a>\u00a0or\u00a0visual solutions<\/a>.\u00a0 For example, in the problem above, there's absolutely no need to do any detailed calculations: in fact, folks with number sense can probably do all the math they need to do in their heads.<\/p>\n

       <\/p>\n

      Examples of a few number sense facts<\/h2>\n

      1. Making the numerator of a fraction bigger makes the whole fraction bigger.<\/p>\n

      2. Making the denominator of a fraction bigger makes the whole fraction smaller.<\/p>\n

      3. (big positive) + (small negative) = something positive<\/p>\n

      4. (small positive) + (big negative) = something positive<\/p>\n

      5.\u00a0 Multiplying by a positive decimal less than one makes something smaller.<\/p>\n

      6.\u00a0 Dividing by a positive decimal less than one makes something smaller.<\/p>\n

      Of course, it would be near impossible to make anything like a complete list.\u00a0 The left-brain reductionist dreams of something like an exhaustive list one could study, but number sense is all about left-brain pattern matching.\u00a0\u00a0 If you're not familiar with the distinction of left\/right hemisphere, see this\u00a0GRE post<\/a>\u00a0which touches on similar issues.<\/p>\n

       <\/p>\n

      How do you get number sense?<\/h2>\n

      If you don't have it, how do you get it?\u00a0 That's not an easy question.\u00a0 There's no magical shortcut to number sense, but here are some concrete suggestions.<\/p>\n

      1. Do only mental math.\u00a0 You shouldn't be using a calculator to practice for the GMAT anyway.\u00a0 Try to do simpler math problems without even writing anything down.\u00a0\u00a0 Furthermore, look for opportunities every day, in every situation, to do some simple math or simple estimation (e.g. there are about 20 cartons of milk on the grocery store's shelf --- about how much would it cost to buy all twenty?)<\/p>\n

      2. Look for patterns with numbers.\u00a0 Add & subtract & multiply & divide all kinds of numbers --- positive integers, negative integers, positive fractions, negative fractions, and look for patterns.<\/p>\n

      3.\u00a0 This is a BIG one --- in any GMAT practice problem that seemed (to you) to demand incredibly long calculations, but which had a very elegant solution of which you would have never dreamt ---- that problem & its solution are pure gold.\u00a0 In a journal, write down what insights were used to simplify the problem dramatically.\u00a0 Force yourself to articulate this, and return to this solution and to your notes on it often.\u00a0 Over time, you should develop an array of problems like this, and if you study those solutions, you probably wills start to see patterns.<\/p>\n

      4.\u00a0 Similar to #3: search the two fora,\u00a0GMAT Club<\/a>\u00a0and\u00a0Beat the GMAT<\/a>, for similarly difficult questions, and look for elegant solutions.\u00a0 That's a great place to ask the experts (including yours truly) for more detailed explanations of their choices in the solution.<\/p>\n

      5.\u00a0 Here's a variant on a game you can play, alone or with others who also want practice.\u00a0 Pick four single digit numbers at random --- some repeats are allowed.\u00a0\u00a0 You could roll a die four times, and use the results.\u00a0 Now, once you have those four numbers, your job is to use all four of them, and any arithmetic, to generate each number from 1 to 20.\u00a0 By \"any arithmetic,\" I mean any combination of:<\/p>\n

      a. add, subtract, multiply, divide<\/p>\n

      b. exponents<\/p>\n

      c. parentheses & fractions<\/p>\n

      For example, if the four numbers I picked were {1, 2, 3, 4}, I could get 2 from<\/p>\n

      (4 \u2013 3) + (2 \u2013 1)<\/p>\n

      or
      \n      \"\"<\/a><\/p>\n

      or
      \n      \"\"<\/a><\/p>\n

      For any one number, you only need to come up with it in one way.\u00a0 Here, I show three ways just to demonstrate the possibilities.\u00a0 Using similar combination, you have to get every number from 1-20 with these four, or with whatever four you pick.\u00a0\u00a0 Actually, the set {1, 2, 3, 4} is a very good warm-up set.\u00a0 When you want more of a challenge, use {2,3,3,5}. \u00a0 \ud83d\ude42<\/p>\n

       <\/p>\n

      Practice problem<\/h2>\n

      Here's a practice problem that demands number sense. If you didn't get anywhere with the practice problem, you may want to study the solution below carefully.<\/p>\n

      2)\u00a0https:\/\/gmat.magoosh.com\/questions\/54<\/a><\/p>\n

       <\/p>\n

      Practice problem solution<\/h2>\n

      1) Notice that all three of these are close to fractions that equal 1\/3.\u00a0 The fractions that equal 1\/3 would be, respectively, 50\/150, 110\/330, and 300\/900.\u00a0\u00a0 First of all, only the second one has a higher denominator, so the second one is more than 1\/3 and the other two are less than 1\/3.\u00a0 Therefore, II is the greatest.<\/p>\n

      Now, from I and III, which is greater.\u00a0 Well, think about it this way.\u00a0 50\/150 = 300\/900, because both of those equal 1\/3.\u00a0\u00a0 How much less than one third is each one of these?\u00a0 Well, 147\/150 is 3\/150 less than 1\/3, and 299\/900 is 1\/900 less than 1\/3.\u00a0 Well, clearly, 3\/150 > 1\/900 (the latter has a smaller numerator\u00a0and<\/em>\u00a0a larger denominator!)\u00a0 Therefore, starting from 1\/3, 147\/150 goes down further than does 299\/900.\u00a0 Therefore, 147\/150, dropping down a larger distance, must be the minimum value.\u00a0 Therefore, the correct order is I, III, II.\u00a0 Answer =\u00a0B<\/strong><\/p>\n

      This post was written by Mike McGarry, GMAT expert at Magoosh<\/a>, and originally posted here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

      First, a practice problem. Remember,\u00a0no calculator. I. \u00a047\/150 II.\u00a0111\/330 III.\u00a0299\/900 1) Rank those three in order from smallest to biggest. I, II, III I, III, II II, I, III II,…<\/p>\n","protected":false},"author":133,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,783,243,736],"tags":[],"class_list":["post-15827","post","type-post","status-publish","format-standard","hentry","category-gmat","category-magoosh-blog","category-blog","category-quant-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/15827","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/users\/133"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=15827"}],"version-history":[{"count":2,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/15827\/revisions"}],"predecessor-version":[{"id":16076,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/15827\/revisions\/16076"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=15827"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=15827"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=15827"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}