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Here\u2019s a quick <\/span>cheat sheet<\/span><\/a> on how, when, and why to use Smart Numbers to solve GRE Quant problems. <\/span><\/p>\n Smart Numbers is a <\/span>strategy<\/b> for certain GRE Quant problems, usually word problems. It\u2019s not a guessing method\u2014in other words, using Smart Numbers will give you the exact right answer, just like doing algebra will.<\/span><\/p>\n You\u2019ll decide whether to use Smart Numbers by looking at the answer choices (so, it\u2019s most often useful on Discrete Quant problems, which have answer choices!).<\/span><\/p>\n If you see the following in the answer choices, you can definitely use Smart Numbers:<\/span><\/p>\n You can also <\/span>usually<\/span><\/i> use Smart Numbers if you see the following in the answer choices:<\/span><\/p>\n If you see percents, ratios, or fractions, here\u2019s how to make the decision. Read the whole problem, and decide whether you\u2019re dealing with specific numbers, or just with relationships between numbers. <\/span><\/p>\n For instance, does the problem say that <\/span>x<\/span><\/i> equals 12, or that Beryl has sixteen cats? Those are specific numbers, and you probably can\u2019t use Smart Numbers. <\/span><\/p>\n On the other hand, if <\/span>x<\/span><\/i> is 50% more than <\/span>y<\/span><\/i>, or if Beryl has twice as many cats as Jane, those are <\/span>relationships<\/span><\/i>\u2014and you probably <\/span>can<\/span><\/i> use Smart Numbers. <\/span><\/p>\n There are a few other special situations, so I\u2019ll also give you a rule that covers everything\u2014although it takes a little bit more thinking to apply it. If a GRE Discrete Quant problem <\/span>doesn\u2019t tell you the numbers, but just tells you how they relate to each other<\/span><\/i>, you can use Smart Numbers. If it <\/span>does<\/span><\/i> tell you specific numbers, you can\u2019t.<\/span><\/p>\n Suppose you\u2019ve decided to use Smart Numbers because there are variable expressions in your answer choices. For instance, the problem looks like this: <\/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 In this situation, start by choosing numbers that fit all of the facts the problem gives you. In this one, the four numbers you choose have to be consecutive, with <\/span>a<\/span><\/i> being the smallest, and <\/span>d<\/span><\/i> being the largest. <\/span><\/p>\n As long as the numbers fit the facts, you should use the easiest numbers you can think of. For this problem, let\u2019s go for 1, 2, 3, and 4.<\/span><\/p>\n The next step is probably the most important one: <\/span>everywhere you see a variable in the problem\u2014including the answer choices!\u2014replace it with the number you chose<\/b>. You can use a combination of mental math and scratch work to do this, depending on how complex the problem looks. <\/span><\/p>\n By the way, during this step, you should forget about the phrase \u201cin terms of <\/span>d<\/span><\/i>.\u201d \u201cIn terms of\u201d only matters when you\u2019re using variables. Since we\u2019re replacing our variables with numbers, we can just drop it. <\/span><\/p>\n Here\u2019s what that problem would look like, once we\u2019re finished with this step:<\/span><\/p>\n If 1, 2, 3, and 4 are consecutive integers and 1<2<3<4, what is the average of 1, 2, 3, and 4? <\/span><\/p>\n A) 4 \u2013 5\/2 Next, answer the question. What is the average of 1, 2, 3, and 4? It\u2019s 2.5. <\/span><\/p>\n Which of the answer choices equals 2.5? Only (C) does. (By the way, you can often figure this out without doing too much math\u2014for instance, you should eliminate (B) quickly, since it won\u2019t result in a decimal.) <\/span><\/p>\n Let\u2019s try another one. This time, suppose you\u2019re using Smart Numbers because you noticed percents in the answer choices. Your problem might look like this: <\/span><\/p>\n Aloysius spends 50% of his income on rent, utilities, and insurance, and 20% on food. If he spends 30% of the remainder on video games and has no other expenditures, what percent of his income is left after all of the expenditures? <\/span><\/p>\n A) 30% Pick a number that fits everything you\u2019re told in the problem. This problem doesn\u2019t really give us any constraints on the number\u2014except that it\u2019s a dollar amount, so it shouldn\u2019t be negative\u2014so we can pick more or less any number we want. Let\u2019s say that Aloysius\u2019s income is $100.<\/span><\/p>\n You don\u2019t have to replace the variables with numbers in this scenario, because there aren\u2019t any variables! If the problem only has percents or ratios, not variables, you can skip that step. Go right ahead and solve the problem. <\/span><\/p>\n 50% of $100 is $50, and 20% of $100 is $20. That leaves $30 remaining. Aloysius spends 30% of that $30, or $9, on video games. His total expenditures are $50+$20+$9, or $79, with $21 left over. Since $21 is 21% of his original income, the right answer is (B). <\/span><\/p>\n In some situations, using Smart Numbers takes more time than just doing the algebra. If you\u2019re fast and confident with algebra, there will be problems where you\u2019ll save time by \u201cjust doing the math.\u201d However, there are other advantages to using Smart Numbers:<\/span><\/p>\n However, I do have one warning: don\u2019t think of Smart Numbers as a last resort! If you wait until you\u2019ve already spent two minutes on the GRE Quant problem, using Smart Numbers isn\u2019t going to help you. Try using it <\/span>first<\/span><\/i>\u2014after all, there\u2019s no rule saying you have to try algebra before you can do something else. On the GRE, you\u2019re free to use whichever approach works, even if your middle school algebra teacher would disapprove! ?<\/span><\/p>\n See that \u201cSUBSCRIBE\u201d button in the top right corner? Click on it to receive all our GRE blog updates straight to your inbox!<\/i><\/b><\/p>\n Chelsey Cooley<\/a> Here\u2019s a quick cheat sheet on how, when, and why to use Smart Numbers to solve GRE Quant problems.<\/p>\n","protected":false},"author":127,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,2,474284,921840,6,7,9,733445,154333],"tags":[1362494,1362592],"yst_prominent_words":[],"class_list":["post-11947","post","type-post","status-publish","format-standard","hentry","category-gre-math-algebra","category-challenge-problems","category-current-studiers","category-gre-prep-2","category-gre-strategies","category-how-to-study","category-math-gre-strategies","category-study-tips-2","category-taking-the-gre-2","tag-discrete-quant","tag-smart-numbers"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/11947","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/users\/127"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/comments?post=11947"}],"version-history":[{"count":2,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/11947\/revisions"}],"predecessor-version":[{"id":11959,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/11947\/revisions\/11959"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/media?parent=11947"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/categories?post=11947"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/tags?post=11947"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/yst_prominent_words?post=11947"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}What is Smart Numbers?<\/b><\/h4>\n
When can you use Smart Numbers on GRE Quant? <\/b><\/h4>\n
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How does Smart Numbers work?<\/b><\/h4>\n
\n<\/span>B)<\/span> d<\/span><\/i> \u2013 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
\n<\/span>C) 4 \u2013 3\/2
\n<\/span>D) 4 + 3\/2
\n<\/span>E) (4*4 \u2013 6)\/7<\/span><\/p>\n
\n<\/span>B) 21%
\n<\/span>C) 20%
\n<\/span>D) 9%
\n<\/span>E) 0%<\/span><\/p>\nWhy should you use Smart Numbers?<\/b><\/h4>\n
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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 170Q\/170V on the GRE.\u00a0<\/em><\/i>Check out Chelsey\u2019s upcoming GRE prep offerings here<\/a>.<\/em><\/i><\/p>\n","protected":false},"excerpt":{"rendered":"