![\"Manhattan](\"https:\/\/www.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2018\/01\/smart-numbers-speed-gmat-quant-chelsey-cooley.png\")
<\/p>\n<\/p>\n
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 <\/i><\/b>Are you having trouble finishing GMAT Quant word problems within two minutes? Here\u2019s a technique that will help. <\/span><\/p>\n First of all, this technique is only for Problem Solving problems. It won\u2019t work on Data Sufficiency. <\/span><\/p>\n It also doesn\u2019t work on <\/span>every <\/span><\/i>Problem Solving problem. There are <\/span>two<\/b> scenarios where smart numbers will work:<\/span><\/p>\n In both scenarios, the clues are in the answer choices. This means you have to build a new habit. From now on, <\/span>you have to read the answer choices before you choose an approach<\/b>. This will feel strange at first. If you\u2019re anything like me, you\u2019ll want to start writing down variables and equations before you even finish reading the problem, let alone the answer choices. <\/span><\/p>\n The problem is, once you\u2019ve started writing down a bunch of algebra, you\u2019ve already committed yourself to doing the problem with algebra. But algebra isn\u2019t usually the smartest approach on these problems. The GMAT doesn\u2019t give you enough time to test out an algebraic approach, then start over with smart numbers. Read the answer choices early, and <\/span>start<\/b> with smart numbers. <\/span><\/p>\n It\u2019s a little easier to apply smart numbers when there are percents, fractions, or ratios in the answer choices, so we\u2019ll start there. Here\u2019s an example problem:<\/span><\/p>\n Team A and Team B are raising money for a charity event. The ratio of money collected by Team A to money collected by Team B is 5:6. The ratio of the number of students on Team A to the number of students on Team B is 2:3. What is the ratio of money collected per student on Team A to money collected per student on Team B? <\/span><\/p>\n (A) 4:5 Step one: read through the <\/span>entire<\/span><\/i> problem, including the answer choices. It\u2019s okay to jot down the given information on your paper, but <\/span>don\u2019t<\/b> start writing equations. <\/span><\/p>\n Step two: identify the <\/span>simple unknowns<\/b>. In this step, ask yourself: what number or numbers would I most like to know? In this problem, you\u2019d like to know the number of students on each team and the amount of money raised by each team. <\/span><\/p>\n Step three: choose your numbers. The numbers should fit what the problem tells you, and they should be easy to do math with. For instance, you can\u2019t just pick any number for the number of students on Team A and the number of students on Team B. You need to pick numbers that have a 2:3 ratio, in order to match what the problem says. <\/span><\/p>\n Here\u2019s what your scratch paper might look like after this step:<\/span><\/p>\n Team A: $50, 2 students<\/span><\/p>\n Team B: $60, 3 students<\/span><\/p>\n Step four: solve the problem, using your numbers instead of the variables. <\/span>Don\u2019t write down equations with variables! <\/b>Instead, just do math with the numbers you\u2019ve already picked. <\/span><\/p>\n Team A: $50 \/ 2 students = $25\/student<\/span><\/p>\n Team B: $60 \/ 3 students = $20\/student<\/span><\/p>\n 25:20 = 5:4<\/span><\/p>\n The answer to this problem is 5:4. Choose (B) and move on to the next problem!<\/span><\/p>\n If there are <\/span>variables<\/b> in the answer choices, rather than relationships, you\u2019ll need to do one extra step before picking the answer. The first four steps are exactly the same, so practice them on your own with this problem before reading further.<\/span><\/p>\n If <\/span>a<\/span><\/i>, <\/span>b<\/span><\/i>, <\/span>c<\/span><\/i>, and <\/span>d<\/span><\/i> are consecutive integers and <\/span>a<\/span><\/i> < <\/span>b<\/span><\/i> < <\/span>c<\/span><\/i> < <\/span>d<\/span><\/i>, what is the average (arithmetic mean) of <\/span>a<\/span><\/i>, <\/span>b<\/span><\/i>, <\/span>c<\/span><\/i>, and <\/span>d<\/span><\/i> in terms of <\/span>d<\/span><\/i>?<\/span><\/p>\n (A)<\/span> d<\/span><\/i> \u2013 5\/2 Step one: Read the entire problem! You know you can use smart numbers because the answer choices are written in terms of the variable <\/span>d<\/span><\/i>. <\/span><\/p>\n Step two: The simple unknowns are the four unknown values, <\/span>a<\/span><\/i>, <\/span>b<\/span><\/i>, <\/span>c<\/span><\/i>, and <\/span>d<\/span><\/i>. <\/span><\/p>\n Step three: Choose some small, simple consecutive integers, like 1, 2, 3, and 4. <\/span><\/p>\n Step four: Solve the problem. You\u2019ll end up with a <\/span>number<\/b> as your answer. The arithmetic mean of 1, 2, 3, and 4 is (1 + 2 + 3 + 4)\/4, which equals 5\/2. <\/span><\/p>\n Step five: This is the trickiest part. You know what your answer should equal: it should come out to 5\/2. However, the answer choices are expressions with variables, not numbers. To finish the problem, you need to determine <\/span>which of those expressions comes out to 5\/2<\/b>. <\/span><\/p>\n To do that, you have to replace the variable <\/span>d<\/span><\/i> with a number. Don\u2019t replace <\/span>d <\/span><\/i>with 5\/2! You chose a value for <\/span>d <\/span><\/i>earlier in the problem: <\/span>d<\/span><\/i> equals 4. Plug in 4 to each answer choice.<\/span><\/p>\n (A) 4 \u2013 5\/2 = 3\/2 Answer choice (C) comes out to 5\/2. Since we know that the right answer to the problem is 5\/2, it\u2019s a match! (C) is the right answer.<\/span><\/p>\n Using smart numbers to solve GMAT Quant problems will probably feel unnatural at first. That goes away with consistent practice. Part of what the GMAT tests is your ability to learn new approaches and unusual ways of thinking\u2014think about how weird Data Sufficiency problems seemed when you first saw one! <\/span><\/p>\n The best way to practice is to consistently use smart numbers whenever you get the opportunity, even if you don\u2019t feel comfortable with them yet. Try this exercise to really drive the concept home, as well. Open your <\/span>Official Guide to the GMAT<\/span><\/a> to the Problem Solving section. Skim through the problems, <\/span>only looking at the answer choices<\/b>. You\u2019ll notice that most problems have numerical answer choices, but many problems have variables, fractions, percents, or ratios. Whenever you see any of those things in the answer choices, stop and read the entire problem from beginning to end. Then, try to solve it using smart numbers. Finally, take notes: did it work? Why or why not? Did you do all of the steps correctly? If you really get stuck, check out the explanations in <\/span>GMAT Navigator<\/span><\/a>\u2014when a GMAT Quant problem can be solved using smart numbers, we\u2019ll walk you through exactly how to do it. ?<\/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. Are you having trouble finishing GMAT Quant word problems within two minutes? Here\u2019s a technique that will help.<\/p>\n","protected":false},"author":127,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[873,929,874,52871,930,2,24,8],"tags":[619,52794],"yst_prominent_words":[54235,53704],"class_list":["post-15061","post","type-post","status-publish","format-standard","hentry","category-for-current-studiers","category-gmat-prep","category-gmat-resources","category-gmat-strategies","category-gmat-study-guide","category-how-to-study","category-problem-solving","category-quant-on-gmat","tag-problem-solving-2","tag-smart-numbers"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15061","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=15061"}],"version-history":[{"count":3,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15061\/revisions"}],"predecessor-version":[{"id":15114,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15061\/revisions\/15114"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=15061"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=15061"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=15061"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=15061"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nHow Do I Know to Use Smart Numbers?<\/b><\/h4>\n
\n
How Do I Do It? <\/b><\/h4>\n
\n<\/span>(B) 5:4
\n<\/span>(C) 5:6
\n<\/span>(D) 5:9
\n<\/span>(E) 9:5<\/span><\/p>\n
\n<\/span>(B) d<\/span> \u2013 <\/span><\/i>2
\n<\/span>(C)<\/span> d<\/span><\/i> \u2013 3\/2
\n<\/span>(D)<\/span> d<\/span><\/i> + 3\/2
\n<\/span>(E) (4<\/span>d<\/span><\/i> \u2013 6)\/7<\/span><\/p>\n
\n<\/span>(B) 4 \u2013 2 = 2
\n<\/span>(C) 4 \u2013 3\/2 = 5\/2
\n<\/span>(D) 4 + 3\/2 = 11\/2
\n<\/span>(E) (16-6)\/7 = 10\/7<\/span><\/p>\nHow Can I Practice?<\/b><\/h4>\n
\n
\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 GRE prep offerings here<\/a>.<\/em><\/i><\/p>\n","protected":false},"excerpt":{"rendered":"