Executive Assessment: Quant Strategies for Faster Solutions – Part 6

by on November 29th, 2017

math2Welcome to the sixth 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.

We’re going to revisit a strategy we’ve seen earlier in the series … but I’m not going to tell you which one. Give yourself about 3 to 3.5 minutes for the below 2-Part Integrated Reasoning question (currently #4 in the 2-Part free problem set on the official EA website).

Practice Problem

“Over a period of 5 academic years from Fall 1999 through Spring 2004, the number of faculty at a certain college increased despite a decrease in student enrollment from 5,500 students in Fall 1999.

“In the given expressions, F and S represent the percent change in the number of faculty and students, respectively, over the 5 academic years, and R represents the number of students per faculty member in Fall 1999. The percent change in a quantity X is calculated using the formula ({X_new-X_old}/X_old)(100).

“Select the expression that represents the number of faculty in Fall 1999, and select the expression that represents the number of students per faculty member in Spring 2004. Make only two selections, one in each column.”

Got your answers? Let’s go!

First, let’s get the basic information down on paper. That first paragraph is pretty straightforward—let’s make a table.

The second paragraph … oh, I see. They’re defining F and S in a certain way, so I can’t use those variables to mean the number of faculty members or the number of students. Okay, jot that down. And then there’s this third variable, R, that really is based on the number of each … I’ll jot that down using words, since I can’t use the same variables.

 

So that R thing is just for 1999 … but I can’t use F and S as variables … oh, wait a second. They gave me the number of students in 99—5,500. So I can actually write R as:

 

Okay, now what? What do they want me to find? First … hey, the number of faculty in Fall 1999! That’s right there in that formula. I wonder, can I just rearrange it to isolate “fac?”

R(fac) = 5500

fac = (5500) / R

Check it out! That’s answer choice (B). Done!

The correct answer for the first column, number of faculty in Fall 1999, is (B):  {5500/R}.

And I didn’t even have to use smart numbers! But if I had been uncertain at all, this is where I’d have plugged in some real numbers to see what’s going on.

Okay, what about that second column? The number of students per faculty member in Spring 2004 … that’s more complicated. Let’s try some real numbers for this one.

What will work nicely with 5,500? Let’s say that there were 550 faculty members in 1999. So now I can find … do I need to, though? That’s for 1999 and this column asks about 2004.

Glance at the answers. They all include R, so we do actually have to find R now.

R = students / faculty = 5500 / 550 = 10 / 1 = 10

Now, what happens in 2004? The number of faculty increases, but the number of students decreases.

Let’s see. Oh, and then we’ll have to be able to calculate the percent change … so let’s actually start with the percent change. Let’s take students down by … how about 10%. (Grab your calculator—it’s IR, so you’re allowed!—if you don’t want to figure this out on paper.)

(10%)(5500) = 550

5500 – 550 = 4,950

Remember that S is a 10% decrease; you can also think of this as S = –10% (minus 10%).

Let’s say F, on the other hand, goes up by 20%. (Again, grab your calculator if you like.)

(20%)(550) = (55)(2) = 110
550 + 110 = 660

So F = +20% and the new student / faculty ratio is 4950/ 660 = 7.5.

Think about all of that math that you just did. You had to find R, and you also had to find S and F. So the correct answer should include all three variables. Glance at the answers—it can’t be the first three. If you feel like you’re running low on time right now, you might just guess among the other three.

Here are two ways to finish the problem off from here: the extra-special-cool shortcut and the remaining “official” smart numbers process.

The extra-special-cool shortcut

Again, think about the math that you had to do. The faculty number increased from its starting point, but the student number decreased from its starting point. Look at the remaining three answers. The F part should be 100 + … oh, all three of them say that. That’s not useful.

What about S? Remember that S is a negative. So how should that show up in this expression?

100 – (a negative) will end up getting bigger—not what we want

100 + (a negative), on the other hand, will get smaller

Only one answer uses 100 + S: answer (D). We’re done!

If you’re thinking, “Uh, sorry, but that’s a little too extra-special clever for me … WHAT??” then ignore this shortcut and read the next part.

If the extra-special-cool shortcut does work for you, then you don’t even need to pick numbers and work through any of the math in the first place. If you’re confident in your mathematical reasoning, you can basically just logic your way to answer (D) in the first place. :)

The smart numbers finish

Our last step is to plug into the answers to find our desired solution.

R = 10

S = –10

F = +20

Ignore the first three choices and start with answer (D).

({100+S}/{100+F})R=

({100+(-10)}/{100+20})(10)=

(90/120)(10)=

7.5

That’s a match! The correct answer for the second column is (D).

What did you learn here? Articulate your takeaways before you look at mine below.

Key Takeaways Smart Numbers (especially on IR):

(1) On IR, make sure you understand the story. If you do, you can save yourself a lot of time and trouble, as we did on the first half of the problem; if you don’t understand the story, guess and move on.

(2) On IR problems, it may not be the case that we really need to choose numbers and do the math—we may be able to “think through” what’s happening and go straight to the answers. We did this for the first column and could even do it for the second (though that one was trickier). And if we do need to do some math, we can still choose smart numbers in the same way we would on a regular old math problem from the quant section of the test.

(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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