Executive Assessment: Quant Strategies for Faster Solutions - Part 5
Welcome to the fifth installment of Quant Strategies for the EA! If youre just joining us now, head back to the first part and work your way back here.
Im super excited about the problem were going to talk about today. The textbook math is really annoyingbut theres a fantastic shortcut thats 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 well 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?(A) 8%
(B) 25%
(C) 41%
(D) 59%
(E) 70%
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?
Theyre seriously far apart. When the answers are that far apart, we dont have to solve for an exact number; we just need to estimate. In this case, we can estimate quite heavily.
Thats level 1 of the awesome solution. Heres 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.
Ill have to figure out Ds new amount and then subtract from $5k to find Js new amount and then find what percent that is of Js original amount ugh. Thats annoying.
Is there an easier way? I know I can estimate (glancing at answers again)
And thats when it hit me. I could just try the answers and see which one works. Theyre so very far apart that I can estimate quite heavily, and theyre in order, so all Ill need to try is (B) and (D); if those ones arent right, Ill be able to tell whether I need to go higher or lower.
Lets do this!
Dick started with $3k and saved 8% more. I know I can estimate heavily, so lets call that 10%way easier. So he saved $3,300 in 1990. (Note: That arrow signals to me that Ive overestimated; the real value is a little under $3,300. This is a good habit to get into when estimating, just to make surethough the answers are so far apart in this problem that I probably dont 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: thats $750.
Now, subtract $750 from $3,000.
What do you get? Hmm, $2,250.
Thats too much left; shes 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%. Thats 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 cant have lost 60%. She must have lost less.
Go look at the answers. Theres only one thats 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 rightshe kept a couple of hundred dollars more than she would have if shed lost exactly 50%. Done!
The correct answer is (C).
I could show you the textbook algebra herebut Im not going to. I want you to get into the same habit that I have. Im not okay with just plugging and chugging away at algebra. Most of the time on this test, I dont need toso 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 estimatethe 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 Backwardsjust 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.