Executive Assessment: Fast Math for Faster Solutions - Part 3
Welcome to the third installment of Fast Math for the EA! If youre 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 EA 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 didnt 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 its just (72)(0.34) aaagh but I dont have a calculator.
I refuse to do that out the long way. Seriously! Theres got to be an easier way.
Picture this: Youre standing in the convenience store. You want to buy this soda. Youve just figured out that its going to cost you $0.34 a can and you know you want 72 cans but you dont have a calculator on you (your phone died) and you don't even have pen and paper. Also, you forgot your credit card. (Its been a long day.)
So how are you going to figure out whether you have enough cash on you to buy all 72 cans?
Thats not a rhetorical question. Close your eyes, picture yourself there, and try to figure out what youd do.
Thinking?
Thinking?
Okay, heres my idea. In the real world, I wouldnt literally need to calculate to the pennyId just need to estimate to make sure I have enough cash. But this is a math test and the answers are down to the pennyso dont 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, Id have to calculate to the penny. But theyre not. Theyre each at least a couple of dollars apart, so I can estimate. How?
Lets see. Its going to cost me $0.34 to buy one can. How many could I buy for a dollar?
I can get 3 cans (basicallytechnically, itll 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 thats going to cost me about 72 / 3 = $24.
Oh. Look at the answers. Theres only one thats closeanswer (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 ... its the same math! $24.
What we just did is classic back-of-the-envelope math. You dont need an exact numberyou just need a quick-and-dirty, good-enough estimate. We certainly werent allowed to do that on math tests in school, but the EA is not a math test.
Well, yes, it is, somewhat. But not in the way that youre used to from school. We do have to know various math formulas and rules, but the EA is really mostly interested in how well you can reason about math. After all, in the real world, youre 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 conclusionsnot in the whats 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 EA looks a whole lot like a traditional math test, it really isnt 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. Thats what youre looking to learn and practice as you study for this exam.
Join me next time, for another installment in this series.
Key Takeaways for EA Fast Math:
(1) You often dont 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, theres probably an opportunity to estimate somewhere. Also, get in the habit of glancing at the answers to see how far apart they are (when theyre 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.