Know the GMAT Code: Story Problems:

by on December 21st, 2016

How are the GMAT test writers going to hide information in plain sight and get you to fall into traps?

Try out this problem in our Know the Code series and then we’ll dig in to figure out what’s going on. Note: this one’s from the GMATPrep® free practice problems.

“*A certain group of car dealerships agreed to donate x dollars to a Red Cross chapter for each car sold during a 30-day period. What was the total amount that was expected to be donated?

“(1) A total of 500 cars were expected to be sold.

“(2) 60 more cars were sold than expected, so that the total amount actually donated was \$28,000.”

(If you are new to Data Sufficiency, start here and come back to this article later.)

1-second Glance. DS. Wall of words! Story—will need to translate.

Read. Put yourself in the story. You’re coordinating all of these donations. This group agreed to donate x dollars per car sold during a certain period.

Then, there’s some curiously-worded language: they’re asking for the amount expected to be donated.

That’s weird—most problems would ask for the amount that was actually donated. So, presumably, the amount actually donated does not match the amount expected to be donated. We’ll need to keep these two different amounts straight, so factor this into your notes. (Also: pay attention to your instincts when you feel that something is unusual—don’t just ignore it and keep going!)

Jot.

\$x / car

C = # of cars expected

Total expected donation = xC

Reflect. Briefly: what could change in this scenario to create a difference between total actually donated and total expected to be donated?

The amount, \$x, donated per car sold could change; maybe the dealerships change their pledge?

It could also be the case that they expect to sell a certain number of cars in the given period, but they might end up selling a different number.

Let’s look at the first statement.

“(1) A total of 500 cars were expected to be sold.”

This is half of the equation but indicates nothing about the dollar amount donated per car. Without any information about the money, it’s impossible to figure out the total amount that was expected to be donated.

Statement (1) is insufficient; eliminate choices (A) and (D).

“(2) 60 more cars were sold than expected, so that the total amount actually donated was \$28,000.”

Here’s where it gets interesting. The information here is more convoluted—be careful.

If C is the # of cars expected to be sold, then the actual number of cars sold is C + 60. If the per-car donation is still \$x, then we can write a new formula for the amount actually donated—and this figure is provided in the statement, too!

Total amount actually donated = (\$x / car)(number of cars actually sold)

28,000 = x(C + 60)

This information is for the actual amount donated, not the expected amount—and the problem asks for the expected amount. Can you do anything with this to figure out x and C?

There is another formula, but that one has three variables: T = xC, where the T is the total expected donation. There isn’t a way to manipulate the two equations to solve for a single numerical value for T.

Statement (2) is not sufficient; cross off answer (B).

Finally, put the two statements together. Now, you have C = 50 and 28,000 = x(C + 60). Plug in and you can solve for x. (Don’t actually solve—this is DS!)

If you have x, can you do anything else? Yes! Statement (1) still tells you C! Multiply those two together to get the desired value: T = xC.

The correct answer is (C).

When you go through this solution, the question might seem pretty straightforward. But it would be easy, during the stress of the test, to fall into a couple of different traps.

First, if your notes aren’t totally clear about the “expected” stuff vs. the “actual” stuff, it would be easy to conclude that statement (2) is sufficient on its own, leading you to incorrect answer (B). That’s where the Reflect stage is so important—if you can establish ahead of time that these two scenarios exist, you’ll be more likely to keep the information straight when you get to statement (2).

Second, once you do put the two statements together, you have to do a sort of double-loop: first, you use the two statements to realize that you can solve for x, and then you have to remember that one of those two pieces of information actually did give you C in the first place. The trap: you already used the given information from the two statements and, since there isn’t anything new elsewhere to use, you think that that’s it—you can find x, but that’s not enough by itself.

How to avoid that trap? Two things. First, write out your work fully and carefully. Second, know what you need to find before you start to solve.

If you have C = 50 written right there, clearly, on your scrap paper and you’ve just said to yourself, “The two together will be sufficient if I can find both C and x,” then you can say to yourself right up front, “Oh, I already have C! Great, all I need to do is find x.” When the two statements together give you x, voila: you’re done.

Key Takeaways for Knowing the Code:

(1) For story problems, put yourself in the story. Pay attention to unusual language cues and take the time to Reflect on what they mean. That 15 or 30 seconds is well spent if you avoid traps or careless mistakes later on!

(2) Write everything down carefully. Before you evaluate a piece of information, remind yourself what you would need to find in order to say that the info is sufficient.

(3) Turn any knowledge you gain into Know the Code flash cards:

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.