![\"Manhattan](\"https:\/\/www.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2018\/03\/more-fast-math-gmat-part-6-stacey-koprince.png\")
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Guess what?\u00a0You can attend the first session of any of our online or in-person GMAT courses absolutely free\u2014we\u2019re not kidding!\u00a0Check out our upcoming courses here<\/a>.<\/em><\/strong><\/span><\/p>\n Welcome to the 6th installment of our <\/span>Fast Math for the GMAT<\/span><\/a> series!<\/span><\/p>\n On these two new problems, we\u2019re going to employ some broader principles than the ones you saw in the earlier installments of this series. I won\u2019t say any more yet\u2014try the two problems from the free problem set available on mba.com<\/a><\/span> and then we\u2019ll talk.<\/span><\/p>\n Set your timer for 4 minutes and go!<\/span><\/p>\n (B)\u00a07<\/sup>\u204410<\/sub><\/span><\/p>\n (C)\u00a06<\/sup>\u20447<\/sub><\/span><\/p>\n (D)\u00a010<\/sup>\u20447<\/sub><\/span><\/p>\n (E) 10<\/sup>\u20443<\/sub><\/span><\/p>\n \u00a0<\/p>\n The Earth travels around the Sun at a speed of approximately 18.5 miles per second. This approximate speed is how many miles per hour?<\/span><\/p>\n (A) 1,080<\/span><\/p>\n (B) 1,160<\/span><\/p>\n (C) 64,800<\/span><\/p>\n (D) 66,600<\/span><\/p>\n (E) 3,996,000<\/span><\/p>\n We\u2019ll talk about the first one in this installment and the second one in the next installment.\u00a0<\/span><\/p>\n \u00a0<\/p>\n Step 1: Understand what\u2019s going on.<\/span><\/p>\n Glance: Wow, that fraction in the first problem is ugly! Glance down at the answers, too. Notice anything?<\/span><\/p>\n Answers (A) through (C) are less than 1 and answers (D) and (E) are greater than 1. Is there a way to tell whether the correct answer is greater or less than 1?\u00a0<\/span><\/p>\n Also, Answers (A) and (E) are \u201cmirror images\u201d and so are (B) and (D). That makes sense, because chances are the most common trap answer will be someone solving correctly but just reversing the fraction by accident. Answer (C) doesn\u2019t have a mirror\u2026so if I have to guess, I\u2019m not going to guess that. (And, in fact, if I solve and get (C), I might actually check my work.)<\/span><\/p>\n \u00a0<\/p>\n Step 2: Now that you know what\u2019s going on, figure out your plan.<\/span><\/p>\n Hmm. Can I tell anything now about whether it\u2019ll be greater or less than 1? The top of the \u201cmain\u201d fraction is the number 1. The bottom of the main fraction is 1 + something. That \u201csomething\u201d is positive, so the overall fraction is 1 over something bigger than 1.<\/span><\/p>\n Is that going to be greater than 1 or less than 1?<\/span><\/p>\n 1 over (>1) is less than 1. Eliminate answers (D) and (E).<\/span><\/p>\n From here, you can just straight up solve. If you\u2019re confident that (C) isn\u2019t going to be right, though, you can also estimate. Why? Because answer (A) is<\/span> 3<\/sup>\u204410<\/sub><\/span>\u00a0and answer (B) is<\/span> 7<\/sup>\u204410<\/sub><\/span>. Those are pretty far apart\u2014like 30% and 70%.<\/span><\/p>\n Look at that thing again. 2 + <\/span>1<\/sup>\u20443<\/sub><\/span> is about 2 (or close enough!). So just the bottom part of the fraction is about 1 + <\/span>1<\/sup>\u20442<\/sub> = 3<\/sup>\u20442<\/sub><\/span>.<\/span><\/p>\n And then bring the numerator back in: 1 over 3<\/sup>\u20442<\/sub><\/span>\u00a0just means \u201ctake the reciprocal,\u201d which is <\/span>2<\/sup>\u20443<\/sub><\/span>.\u00a0<\/span><\/p>\n Which answer is closest? Answer (B), 7<\/sup>\u204410<\/sub><\/span>. Answer (A) is too far away. Done!<\/span><\/p>\n You might be thinking, sure, I see how that works, but the actual math isn\u2019t all that hard\u2026so why not just do it?<\/span><\/p>\n Here\u2019s why: When I\u2019m studying I\u2019m not just looking for ways to get <\/span>this<\/span><\/i> problem right. I\u2019m also looking for legitimate ways to solve the problem using as little time and mental energy as possible\u2014because any time and mental energy saved can be used on other problems in the section.<\/span><\/p>\n But if you really want to know, here is the math. <\/span><\/p>\n I\u2019m not saying that you <\/span>shouldn\u2019t<\/span><\/i> solve it this way\u2014but I am saying that you should consider whether there\u2019s a valid path that\u2019s faster \/ easier\u2026so that you can spend that saved time and mental energy elsewhere.<\/span><\/p>\n (1) You can estimate a lot more than you might think on the GMAT. If the question stem asks for an approximate answer\u2014of course, estimate. But, on PS, also glance at those answers before you begin to solve. Certain characteristics can indicate a good opportunity to estimate.<\/span><\/p>\n (2) What kinds of characteristics? The most common one is simply answers that are spread out. You can also usually estimate when the answers fall on either side of some \u201cdividing line\u201d\u2014for example, some are greater than 0 and some are less than 0. Some are more than 1<\/sup>\u20442<\/sub><\/span>\u00a0and some are less than 1<\/sup>\u20442<\/sub><\/span>\u00a0(that one is especially good for probability questions!). And so on.<\/span><\/p>\n Are you ready? Read on for Part 7 of the Fast Math series!<\/a><\/p>\n Can\u2019t get enough of Stacey\u2019s GMAT mastery? Attend the first session of one of\u00a0her upcoming GMAT courses<\/a>\u00a0absolutely free, no strings attached. Seriously.<\/strong><\/em><\/p>\n Guess what?\u00a0You can attend the first session of any of our online or in-person GMAT courses absolutely free\u2014we\u2019re not kidding!\u00a0Check out our upcoming courses here. Welcome to the 6th installment of our Fast Math for the GMAT series! On these two new problems, we\u2019re going to employ some broader principles than the ones you saw […]<\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[873,929,52871,930,2,24,8,9],"tags":[53022,53023],"yst_prominent_words":[54235,57266,56340,57265,57262,53868,53653,57263,57243,57221,53877,57267,53635,53781,57268,53997,53787,53784,53867],"class_list":["post-15261","post","type-post","status-publish","format-standard","hentry","category-for-current-studiers","category-gmat-prep","category-gmat-strategies","category-gmat-study-guide","category-how-to-study","category-problem-solving","category-quant-on-gmat","category-taking-the-gmat","tag-fast-math","tag-fast-math-for-the-gmat"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15261","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\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/comments?post=15261"}],"version-history":[{"count":13,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15261\/revisions"}],"predecessor-version":[{"id":19612,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15261\/revisions\/19612"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=15261"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=15261"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=15261"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=15261"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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\n(A)\u00a03<\/sup>\u204410<\/sub><\/span><\/p>\n![\"Manhattan](\"https:\/\/www.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2018\/01\/quant-process-1.png\")
<\/p>\n![\"Manhattan](\"https:\/\/www.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2018\/01\/quant-process-2.png\")
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<\/p>\nKey Fast Math Takeaways<\/b><\/h4>\n
* GMATPrep<\/span>\u00ae<\/span> questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.<\/span><\/h6>\n
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\n![\"stacey-koprince\"](\"https:\/\/cdn2.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2015\/06\/stacey-koprince-150x150.png\")
<\/a>Stacey Koprince<\/a> is a Manhattan Prep instructor based in Montreal, Canada.<\/strong>\u00a0Stacey has been teaching the GMAT, GRE, and LSAT for more than 15 years and is one of the most well-known instructors in the industry. Stacey loves to teach and is absolutely fascinated by standardized tests.\u00a0Check out Stacey\u2019s upcoming GMAT courses here<\/a>.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"