Executive Assessment: Quant Strategies for Faster Solutions – Part 5
Welcome to the fifth installment of Quant Strategies for the EA! If you’re just joining us now, head back to the first part and work your way back here.
I’m super excited about the problem we’re going to talk about today. The textbook math is really annoying—but there’s a fantastic shortcut that’s going to save us all kinds of time.
Try this Problem Solving (PS) problem from the official free EA practice set (labeled #1 in the PS set on the EA website, as of November 2017) and then we’ll talk!
“Dick and Jane each saved $3,000 in 1989. In 1990 Dick saved 8 percent more than in 1989, and together he and Jane saved a total of $5,000. Approximately what percent less did Jane save in 1990 than in 1989?
This problem is going to hinge on a strategy that we first discussed way back in the Fast Math for EA series. Glance at the answer choices. Notice anything?
They’re seriously far apart. When the answers are that far apart, we don’t have to solve for an exact number; we just need to estimate. In this case, we can estimate quite heavily.
That’s level 1 of the awesome solution. Here’s how I found level 2.
(My thought process) “Okay, so I know their starting points, $3k each in 89 … (jotting down) and then D saved 8% more … and then I know the new total for D and J, but I have to figure out by what percent J went down.
“I’ll have to figure out D’s new amount and then subtract from $5k to find J’s new amount and then find what percent that is of J’s original amount … ugh. That’s annoying.
“Is there an easier way? I know I can estimate (glancing at answers again) … ”
And that’s when it hit me. I could just try the answers and see which one works. They’re so very far apart that I can estimate quite heavily, and they’re in order, so all I’ll need to try is (B) and (D); if those ones aren’t right, I’ll be able to tell whether I need to go higher or lower.
Let’s do this!
Dick started with $3k and saved 8% more. I know I can estimate heavily, so let’s call that 10%—way easier. So he saved $3,300↓ in 1990. (Note: That arrow signals to me that I’ve overestimated; the real value is a little under $3,300. This is a good habit to get into when estimating, just to make sure—though the answers are so far apart in this problem that I probably don’t need to keep track of this.)
Okay, back to the problem. Together, D and J saved $5k, so J must have saved about $1,700↑. (Really, a little bit more, since D is a little less than $3,300.)
In 1989, J saved $3,000. Check the answers to see which “percent less” gets us down to about $1,700. Start with answer (B). (In general, start with answer B or D when working backwards.)
(B) 25%. First, take 25% of $3,000.
Divide by 4: that’s $750.
Now, subtract $750 from $3,000.
What do you get? Hmm, $2,250.
That’s too much left; she’s only supposed to have $1,700 left.
So (B) is not the correct answer; cross it off.
Should the correct percentage be higher or lower?
We need her to have saved less, so she needs to have lost more. The percentage should be greater than 25%.
Next, go to (D), 59%. That’s about 60%. Glance at the problem details again. She started at $3,000 and needs to go down to about $1,700. That means she still keeps more than half (half would be $1,500), so she can’t have lost 60%. She must have lost less.
Go look at the answers. There’s only one that’s more than 25% but less than 59%: answer (C), 41%.
If you want to check your reasoning, do the numbers make sense generally? She started at $3k and is now at about $1,700. Does it make sense that she lost about 40%?
Yes! That (roughly) seems about right—she kept a couple of hundred dollars more than she would have if she’d lost exactly 50%. Done!
The correct answer is (C).
I could show you the “textbook” algebra here…but I’m not going to. I want you to get into the same habit that I have. I’m not okay with just plugging and chugging away at algebra. Most of the time on this test, I don’t need to—so why make the test experience any more annoying than it has to be? Start looking for opportunities to make this test easier.
Key Takeaways for EA Quant Strategies:
(1) Get into the habit of glancing at the answers before you decide how to solve. If the answers are really far apart, you can most likely estimate—the farther apart they are, the more heavily you can estimate.
(2) If the answers are also relatively “nice” numbers (as in this case: They are about 10%, 25%, 40%, 60% and 70%, all nice percentages), then you may also be able to Work Backwards—just try the answers to see what works. When you have a combo of far-apart and nice answers, look out! You can really accelerate your solution process.
(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.