More Fast Math for the GMAT (Part 6)
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Welcome to the 6th installment of our Fast Math for the GMAT series!
On these two new problems, we’re going to employ some broader principles than the ones you saw in the earlier installments of this series. I won’t say any more yet—try the two problems from the free problem set available on mba.com and then we’ll talk.
Set your timer for 4 minutes and go!
(A) 3⁄10
(B) 7⁄10
(C) 6⁄7
(D) 10⁄7
(E) 10⁄3
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?
(A) 1,080
(B) 1,160
(C) 64,800
(D) 66,600
(E) 3,996,000
We’ll talk about the first one in this installment and the second one in the next installment.
Step 1: Understand what’s going on.
Glance: Wow, that fraction in the first problem is ugly! Glance down at the answers, too. Notice anything?
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?
Also, Answers (A) and (E) are “mirror images” 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’t have a mirror…so if I have to guess, I’m not going to guess that. (And, in fact, if I solve and get (C), I might actually check my work.)
Step 2: Now that you know what’s going on, figure out your plan.
Hmm. Can I tell anything now about whether it’ll be greater or less than 1? The top of the “main” fraction is the number 1. The bottom of the main fraction is 1 + something. That “something” is positive, so the overall fraction is 1 over something bigger than 1.
Is that going to be greater than 1 or less than 1?
1 over (>1) is less than 1. Eliminate answers (D) and (E).
From here, you can just straight up solve. If you’re confident that (C) isn’t going to be right, though, you can also estimate. Why? Because answer (A) is 3⁄10 and answer (B) is 7⁄10. Those are pretty far apart—like 30% and 70%.
Look at that thing again. 2 + 1⁄3 is about 2 (or close enough!). So just the bottom part of the fraction is about 1 + 1⁄2 = 3⁄2.
And then bring the numerator back in: 1 over 3⁄2 just means “take the reciprocal,” which is 2⁄3.
Which answer is closest? Answer (B), 7⁄10. Answer (A) is too far away. Done!
You might be thinking, sure, I see how that works, but the actual math isn’t all that hard…so why not just do it?
Here’s why: When I’m studying I’m not just looking for ways to get this problem right. I’m also looking for legitimate ways to solve the problem using as little time and mental energy as possible—because any time and mental energy saved can be used on other problems in the section.
But if you really want to know, here is the math.
I’m not saying that you shouldn’t solve it this way—but I am saying that you should consider whether there’s a valid path that’s faster / easier…so that you can spend that saved time and mental energy elsewhere.
Key Fast Math Takeaways
(1) You can estimate a lot more than you might think on the GMAT. If the question stem asks for an approximate answer—of course, estimate. But, on PS, also glance at those answers before you begin to solve. Certain characteristics can indicate a good opportunity to estimate.
(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 “dividing line”—for example, some are greater than 0 and some are less than 0. Some are more than 1⁄2 and some are less than 1⁄2 (that one is especially good for probability questions!). And so on.
Are you ready? Read on for Part 7 of the Fast Math series!
* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.
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Stacey Koprince is a Manhattan Prep instructor based in Montreal, Canada. Stacey 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. Check out Stacey’s upcoming GMAT courses here.