Executive Assessment: Fast Math for Faster Solutions – Part 4
Welcome to the fourth installment of Fast Math for the EA! If you’re just joining us now, head back to the first part and work your way back here.
I have two more problems for you from the official free practice set (these are labeled #5 and #7 in the PS set on the EA website, as of September 2017). Give yourself 4 minutes to complete the set. Good luck!
“Increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by?
“If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 20 minutes?
Did you spot any opportunities to make these problems easier to solve?
Our theme for this set is: Draw / Step It Out. Don’t think “algebra” or formulas or whatever. Pretend your boss just handed you a pen and an envelope and asked you to figure this out. What’s your quick-and-dirty, back-of-the-envelope approach?
Here’s the first problem.
“Increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by?”
So I’m your boss and I’m going to give you a raise. I’m also giving you a choice: You can have a straight 30% raise, or you can have two 15% raises, one after the other. In other words, I’ll apply the first 15% raise to your current salary, and then I’ll apply a second 15% raise … to the new salary.
Do you have a preference? If so, which one would you choose?
First, there is a difference between those two calculations—one will result in a higher salary than the other—so you should definitely have a preference. Next, which one is the higher one?
Let’s say your salary is $100. A straight 30% raise will make your new salary $130.
Now do the two 15% raises. The first 15% raise will get you to $115. Next, don’t do the math, but think about what happens for the second 15% raise. The first time, you took 15% of the starting salary, $100. But this second time, you’re going to take 15% of your new, larger salary of $115. So 15% of that number will be more than $15 and your new-new salary will be more than $130.
In other words, you definitely want the 15% + 15% again raise, not the one-time 30% raise.
Here are the answer choices for the problem. What do you notice?
The answer has to be more than 30%, so eliminate choices (D) and (E). How much more? Okay, let’s go do some math to figure that out.
Increase #1: +15% so the dollar amount goes from $100 to $115
Increase #2: +15%, so the dollar amount goes from $115 to ……?
Take 15% of 115. That’s an annoying number, so use percent benchmarks to solve (percent benchmarks are taught in the original Fast Math series for the GMAT, linked in the very first article in this series).
You want 15%. That’s made up of 10% and 5%.
10% of 115 = 11.5
5% of 115 = half of above = 11.5 / 2 = 5.75
15% = 10% + 5% = 11.5 + 5.75 = 17.25
The new increase is $17.25, but that still needs to be added to the starting point of $115. That math is slightly annoying—but you can make it a bit easier.
Glance at the answers. Hmm, two actually do have a 0.25 at the end (if only one had, you could have just picked that one).
Okay, if you added a straight $15 to $115, you’d get $130. You’re actually adding $17.25, or $2.25 more than $130—in other words, $132.25. You started at $100 and are now at $132.25, so the percentage increase is 32.25.
The correct answer is (A). Nice!
What about the second one?
“If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 20 minutes?”
Again, imagine your boss asking you to figure this out on the back of an envelope right now.
+1 person every 15 seconds…
They want 20 minutes … uhh …
Too annoying. Okay, how many is that in just 1 minute?
+1 in 15 seconds = +4 in 1 minute. Good.
So how to go from 1 minute to 20 minutes? Multiply by 20!
+4 in 1 minute = +4(20) in 20 minutes
The correct answer is (A).
You can do this the “textbook” way: set up a proportion to convert from seconds to minutes and then another one to get to 20 minutes. But that’s like creating busywork. You aren’t required to “show your work”—you just need to select the correct answer. Since you can just logic this one out on paper, go for it.
Join me next time, for another installment in this series.
Key Takeaways for EA Fast Math:
(1) Whenever possible pretend someone’s asking you to do this in the real world. That will take you away from “textbook” math and put you firmly in the realm of just thinking the steps through the way you normally would in the real world.
(2) If the numbers in the problem or answers (or both!) seem annoying (e.g., that second 15% calculation), there’s probably a shortcut somewhere. In this case, we used two techniques: percent benchmarks to find the 17.25 figure more easily and then real-world logic / math sense to make the addition step easier than having to add 115 and 17.25.
(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.