Executive Assessment: Fast Math for Faster Solutions – Part 2:
Last time, I gave you a couple of questions to try and then we discussed how to minimize your work on the first one. (If you haven’t read the first installment yet, go do that now.) Today, we’re going to review the second problem.
Here’s the second Executive Assessment problem from the official free practice set (this one is labeled #3 in the PS set on the EA 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?
Before we dive in, what principles do you remember from our discussion of the first 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 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.
“(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.
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 …
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 problem? Think about your takeaways before you read mine.
Join me next time, for another installment in this series.
Key Takeaways for EA 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:
* Executive Assessment questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.