More Fast Math for the GMAT (Part 7)
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A while back, we started a series on Fast Math for the GMAT—here’s the link if you want to start from the beginning.
In our last installment, I gave you two problems to try. We’ve already discussed the first one; here’s the second one again (from the free problem set on mba.com).
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
What do you think?
Step 1: Understand
Those answers…they are seriously far apart. The first two are “clumped,” then the next two, and that last one is totally different.
We’re definitely going to estimate on this one. ☺ Also, just from glancing at the answers, I’m guessing that the correct answer will not be (E). Chances are pretty good that the correct answer will have another “close” answer based on making some small mistake—or based on making the problem just a little harder to estimate.
Jot down the details.
Step 2: What’s the plan?
How do you go from seconds to hours?
60 seconds → 1 minute
60 minutes → 1 hour
So we need 60 twice. But is that…multiplying? Dividing? Glance at the answers again or think it out logically. All of the answers are greater than 18.5, so I must have to multiply. And logically, that makes sense: If I go 18.5 miles in one second, then I should be able to go a lot further in a whole hour.
Okay, now which “clump” of answers is the right clump? 18.5 is a really annoying number, but the clumps are so far apart that I can just call that 20 for now.
(20)(60) = 1,200
Hmm. I still need to multiply by another 60, so answers (A) and (B) are out.
But I’m only multiplying by another 60, so answer (E) is out, too. It’s down to (C) and (D).
If I just multiply by another 60 now…will it be close enough? I’m not sure. I overestimated (from 18.5 to 20) and the two final numbers are pretty close. If the answer is (C), I might think it’s (D) just from the error I introduced in my estimation.
In fact, (1,200)(60) = 72,000. Definitely not good enough. Okay, what should I do next?
The “official” math is this:
(18.5)(60)(60)
The math that I actually did was this:
(20)(60)(60)
Hmm. So I overestimated because I used 20 rather than 18.5. In other words, I overestimated by 1.5—times 60 times 60:
(1.5)(60)(60) = overestimate
The latter two are easy: (60)(60) = 3,600. Oh, and then multiplying by 1.5 is the same thing as increasing something by 50%. So 3,600 + half of 3,600 = 3,600 + 1,800 = 5,400.
My original “answer” was 72,000 but I overestimated by 5,400.
72,000 minus 5,000-ish, is about 67,000. The actual value should be a little less, since I actually want to subtract 5,400. The answer must be (D) 66,600. Answer (C) is too small.
Key Fast Math Takeaways:
(1) If you think you need to do long division or long multiplication, stop for a moment. Reflect. Even if you have to do partial long division or multiplication, how much do you really have to do?
(2) As we discussed last time, don’t start solving on PS until you’ve looked at those answer choices! Sometimes, they contain very important clues about the most efficient way to solve.
* 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.