Math on the Executive Assessment
The Executive Assessment (EA) shares a lot of roots with the GMAT, GMAC’s flagship graduate business school exam. In certain ways, the Executive Assessment feels almost like the GMAT on steroids—it’s even more stereotypically GMAT-like than the GMAT itself, if that’s possible.
One of those ways has to do with the way in which you can solve math problems. Most of the same math content areas are tested on the Executive Assessment, but a higher proportion of released Executive Assessment problems share a certain characteristic: You can use general “Fast Math” principles to make your job much easier—and you can do even more with the overall Fast Math idea on the Executive Assessment.
Here’s the overall idea: Don’t do math that you don’t have to. Don’t do math until you have to. Before you actually do something you think you need to do, lay it out and ask yourself what the best path is through the math—giving heavy consideration to estimation and other shortcuts.
Let’s try some problems out and see how this really works! All problems in this series are from the free problem sets that appear on the official Executive Assessment website.
EA Math Practice Question #1
Give yourself two minutes to complete this first problem. As of September 2017, it appeared as question 2 in the free online Quant Problem Solving problem set.
The table below represents the combined net income of all United States companies in each of five sectors for the second quarter of 1996. Which sector had the greatest net income during the first quarter of 1996?
(A) Basic Materials
(B) Energy
(C) Industrial
(D) Utilities
(E) Conglomerates
Got your answers? Even if you’re not sure, guess—that’s what you want to do on the real Executive Assessment, too, so practice that now (even if your practice consists of saying, “I have no idea, so I’m randomly picking B!”).
Ready? Let’s do this!
The first order of business is to understand what the question wants and what the table tells you.
There are 5 sectors. Each one shows a certain net income for the second quarter and then a percent change from the first quarter. What’s the significance of a negative vs. positive percent change?
Think in terms of real business. If your division had a net income of 4.83 billion this quarter, but that represents a –26% change from last quarter…then last quarter was better and this quarter your boss might not be very happy.
Okay, now what do they want to know? Which sector had the greatest net income in the first quarter… hmm. So we’re going to have to backwards-engineer this somehow.
Start by jotting down the starting point for each sector and whether that one was higher or lower in the first quarter:
BM: 4.83, –26%….Q1↑
E: 7.46, +40%…….Q1 ↓
I: 5, –1%……………..Q1 ↑
U: 8.57, +303%..Q1 ↓
C: 2.07, +10%…….Q1↓
They want to know which one was the highest once we back out the numbers. Sector C is already the lowest by far and it was even lower last quarter, so it’s not that one. Eliminate answer (E).
Sector I only went down by 1% in the second quarter, so basically it was still at about 5 in the first quarter. Call that your baseline point and test the other answers against it.
Was Sector BM above or below 5 in the first quarter? The 4.83 figure reflects about a 25% decline from the previous quarter.
If 4.83 represents about a 25% decline from Q1, then it represents about 75% of Q1. Use this to estimate the value for Q1: If the 4.83 figure is about 75%, then what would 25% be?
You would divide 75% by 3 to find 25%, so do the same with the value 4.83.
4.83 is kind of annoying to divide. Try a number that seems like it’s in the ballpark, like 1.5. (1.5)(3) = 4.5, so the value is around 1.5 (but really a little larger). The 1.5 estimate, then, is on the low side. Keep track of that.
Then, multiply by 4 to find 100%: (1.5)(4) = 6. The value is really a little larger than 6, since 1.5 is a low estimate.
Therefore, sector BM, at 6+, was more than sector I, at 5; eliminate answer (C). Your new baseline point is 6+. Test the remaining answers against this number.
The other two sectors were both lower in Q1. For sector E, 7.46 reflects a 40% increase from Q1. What if the starting number for this sector were 6? What would a 40% increase be?
6 + 40% of 6
To find 40%, find 10%, then multiply by 4. Then add your starting point of 6 back in:
(6)(0.1) = 0.6
(0.6)(4) = 2.4
6 + 2.4 = 8.4
If Q1 were 6, then this sector would have been at 8.4 in the second quarter. It wasn’t; it was only at 7.46. Sector E, therefore, was not as high as sector BM, so eliminate choice (B).
Finally, sector U started at 8.57, but that represented a whopping 303% increase over Q1! If you started at 6 and increase that number by 300%, it would be way over 8.57. Sector U also must have started lower than 6, so eliminate choice (D).
The Basic Materials sector is the last one standing. The correct answer is (A).
You could have done all of the above with very precise calculations—but that’s really annoying when you don’t have access to a calculator or Excel. Note that you didn’t actually have to make very precise calculations because the problem was set up to allow you to estimate even though it didn’t tell you that you could.
The beauty of the Executive Assessment is that this is a business test, not a math test. They’re not interested in knowing whether you can do precise math calculations on paper. They’re interested in knowing whether you have a general number sense that allows you to reason your way to a conclusion—we call that the “back of the envelope” approach. All my boss really needs to know is which division did best last quarter, not what the exact numbers were, so I can just do a quick-and-dirty approach that addresses the big picture.
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) You’re going to need to practice that! First, you need to get yourself into the mindset that the Executive Assessment isn’t a math test and you actually aren’t just trying to calculate, calculate, calculate. Second, you’re going to need to spend time thinking about how to back-of-the-envelope something in various different situations.
(3) Turn that knowledge into Know the Code flash cards:
EA Math Practice Question #2
Here’s another Executive Assessment problem from the official free practice set (this one is labeled #3 in the PS set on the Executive Assessment website, as of September 2017):
According to the table below, the number of fellows was approximately what percent of the total membership of Organization X?
(A) 9%
(B) 12%
(C) 18%
(D) 25%
(E) 35%”
Before we dive in, what principles do you remember from our discussion of the first Executive Assessment problem?
Think about it.
Keep thinking about it.
Don’t read below yet.
Okay, here are some things I remember. ☺ Don’t do math unless / until I have to. If I do have to do some calculations, lay things out first, then look at everything to decide what the best path is (and to see whether I can spot any shortcuts!).
These principles are reflected in the below graphic:
When a new Executive Assessment problem first pops up, I glance: What have I got, big picture? Without reading the full text, I can see the following things: a table…with some fairly annoying numbers. Also, the answers are percentages, so this is a percent problem of some kind.
The annoying numbers are making me wonder whether I’ll be able to estimate. I’m going to keep an eye out for that possibility as I go to my next step, Read.
Yep, it’s a percent problem. What do they want? Jot it down.
Don’t start solving yet! Go to the second row: Reflect & Organize.
Glance at the Fellows number. Annoying. And then the total? I have to add that up. Ugh.
Look at the answers again. The bottom three are decently far apart—estimation would probably be close enough.
(A) 9%
(B) 12%
(C) 18% → 20% = 1/5
(D) 25% → 25% = 1/4
(E) 35%” → 33.3% = 1/3
But answers (A) and (B) are both around 10%…hmm.
I know! If it does seem to be between those two, then I can estimate whether the number is greater than 10% or less than 10%—that’s not a hard estimate to make.
Great, now that I actually have an angle to solve, I can go ahead and do the work.
Oh, wait, one more annoying part to consider: adding up the five numbers to get the total. I only need to estimate, so I can estimate the individual numbers, first of all. I can also try to put them together into “pairs” that add up to “nice” numbers. Okay, let’s do this.
The first one is 78, which is almost 100. Look for another number that would “pair” well with 100: how about Associate Members, at 27,909? Add them up to get about 28,000, a “nice” number.
Any others?
9,200 and 2,300 equal 11,500, another nice-ish number.
That leaves 35,500—oh, let’s pair that with 11,500 to get an even 47k. Then add in the 28k to get about 75k. Nice!
Now, the top of the fraction is the 9,200 number. Maybe 9k is close enough. What’s 9k / 75k? Or 9 / 75?
Reflect for a moment again. Dividing that fraction is kind of annoying.
I’m trying to find a percent. Percent literally means “of 100”—wouldn’t it have been nice if the fraction had already had 100 on the bottom? SO annoying that it doesn’t…
Hmm…
Is there any way to get that number on the bottom to be 100 instead of 75…?
What did we do with that 75% in the first problem (in the first installment of this series)? Go back and take a look.
(Seriously, go look! See what, if anything, you can figure out on your own before you keep reading.)
To go from 75% to 100%, take the 75% figure, divide by 3 to get 25%, then multiply by 4 to get 100%.
BUT, if I’m going to do that with the bottom of the fraction, then I have to do the same thing to the top of the fraction. I can manipulate a fraction in any way that I like as long as I do the same thing to the top and the bottom.
So, take 9, divide by 3 to get 3, then multiply by 4 to get 12. Boom! The new fraction is 12 / 100. Look at the answers—we have an exact match at 12%. ☺
The correct answer is (B).
What did you learn on this Executive Assessment problem? Think about your takeaways before you read mine.
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) Different problems might have some shortcuts in common; when you learn something on one problem, look for opportunities to apply that learning on different-but-similar-in-some-way problems. The 75% → 100% thing doesn’t require a table or even necessarily a story. It doesn’t even need to be 75% to start—it just requires you to know that you’re trying to get to 100% from a number that’s a little annoying.
(3) Turn that knowledge into Know the Code flash cards:
EA Math Practice Question #3
Our final practice question 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.