### Executive Assessment: Fast Math for Faster Solutions (Part 3)

Welcome to the third installment of Fast Math for the Executive Assessment! If you’re just joining us now, you might want to go back to the first part and work your way back here.

I have another problem for you from the official free practice set (this one is labeled #4 in the PS set on the Executive Assessment website, as of September 2017):

“The regular price per can of a certain brand of soda is $0.40. If the regular price per can is discounted 15 percent when the soda is purchased in 24-can cases, what is the price of 72 cans of this brand of soda purchased in 24-can cases?

“(A) $16.32

“(B) $18.00

“(C) $21.60

“(D) $24.48

“(E) $28.80”

What did you think about this problem?

I found it pretty annoying. ☺ I mean, sure, I didn’t find it crazy hard to find the 15% discount off of $0.40:

10% of 0.40 is 0.04…

another 5% is half of that, or 0.02…

so the discount is $0.06…

and the discounted price is $0.34

And then I want to buy 72 cans, so it’s just (72)(0.34)…*aaagh,* *but I don’t have a calculator*.

I refuse to do that out the long way. Seriously! There’s got to be an easier way.

Picture this: You’re standing in the convenience store. You want to buy this soda. You’ve just figured out that it’s going to cost you $0.34 a can…and you know you want 72 cans…but you don’t have a calculator on you (your phone died) and you don’t even have pen and paper. Also, you forgot your credit card. (It’s been a long day.)

So how are you going to figure out whether you have enough cash on you to buy all 72 cans?

That’s not a rhetorical question. Close your eyes, picture yourself there, and try to figure out what you’d do.

Thinking?

Thinking?

Okay, here’s my idea. In the real world, I wouldn’t literally need to calculate to the penny—I’d just need to estimate to make sure I have *enough* cash. But this is a math test and the answers are down to the penny…so don’t I have to calculate exactly here?

Glance at the answers.

If the answers had been of the variety $10.01, $10.02, $10.03…, then yes, I’d have to calculate to the penny. But they’re not. They’re each at least a couple of dollars apart, so I can estimate. How?

Let’s see. It’s going to cost me $0.34 to buy one can. How many could I buy for a dollar?

I can get 3 cans (basically—technically, it’ll cost me $1.02 for 3 cans, but close enough!). So 3 cans for $1…how many do I want again? Oh yeah, 72 cans. So that’s going to cost me about 72 / 3 = $24.

Oh. Look at the answers. There’s only one that’s close—answer (D). Done!

You can also, by the way, do this same estimation from the math I set up before I got frustrated by my lack of a calculator: (72)(0.34). Just look at it in a different way, now that you’ve realized you can estimate. Since 0.34 is about 1/3, you’re just taking about one-third of 72…it’s the same math! $24.

What we just did is classic back-of-the-envelope math. You don’t need an exact number—you just need a quick-and-dirty, good-enough estimate. We certainly weren’t allowed to do that on math tests in school, but the Executive Assessment is *not* a math test.

Well, yes, it is, somewhat. But not in the way that you’re used to from school. We do have to know various math formulas and rules, but the Executive Assessment is really mostly interested in how well you can reason about math. After all, in the real world, you’re never going to be forced to do math on paper without the benefit of Excel or a calculator. But you are going to need to be able to think about mathematical concepts and draw conclusions—not in the “what’s the answer to this math problem” sense, but in a “what should we do about this problem that our division is facing?” sense.

So, while the Executive Assessment looks a whole lot like a traditional math test, it really isn’t at all. Most of the time, you can get to the answer through a combination of strategic approaches, like the back-of-the-envelope approach discussed above. That’s what you’re looking to learn and practice as you study for this exam.

**Key Takeaways for Executive Assessment Fast Math**

(1) You often don’t need to calculate exact values. Look for opportunities to estimate and do back-of-the-envelope calculations wherever possible.

(2) If the numbers in the problem or answers (or both!) seem annoying, there’s probably an opportunity to estimate somewhere. Also, get in the habit of glancing at the answers to see how far apart they are (when they’re just plain numbers)—the farther apart they are, the better the opportunity to estimate.

(3) Turn that knowledge into Know the Code flash cards:

##### * Executive Assessment 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 and Los Angeles, California.** 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.

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