Avoiding the C-Trap in Data Sufficiency:

by on April 16th, 2014

math_4Have you heard of the C-Trap? I’m not going to tell you what it is yet.

Try this problem from GMATPrep® first and see whether you can avoid it:

* “In a certain year, the difference between Mary’s and Jim’s annual salaries was twice the difference between Mary’s and Kate’s annual salaries. If Mary’s annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?

“(1) Jim’s annual salary was $30,000 that year.

“(2) Kate’s annual salary was $40,000 that year.”

I’m going to do something I normally never do at this point in an article: I’m going to tell you the correct answer. I’m not going to type the letter, though, so that your eye won’t inadvertently catch it while you’re still working on the problem. The correct answer is the second of the five data sufficiency answer choices.

How did you do? Did you pick that one? Or did you pick the trap answer, the third one?

Here’s where the C-Trap gets its name: on some questions, using the two statements together will be sufficient to answer the question. The trap is that using just one statement alone will also get you there—so you can’t pick answer (C), which says that neither statement alone works.

In the trickiest C-Traps, the two statements look almost the same (as they do in this problem), and the first one doesn’t work. You’re predisposed, then, to assume that the second statement, which seemingly supplies the “same” kind of information, also won’t work. Therefore, you don’t vet the second statement thoroughly enough before dismissing it—and you’ve just fallen into the trap.

How can you dig yourself out? First of all, just because two statements look similar, don’t assume that they either both work or both don’t. The test writers are really good at setting traps, so assume nothing.

Second, imagine that you’re teaching your 10-year-old niece how to do algebra. She’s never done this before but she’s pretty bright. She understands your explanation of what variables are and how they work. She knows that, if you give her an equation with 3 variables, and then give her values for 2 of those variables, she’ll be able to solve for the third one. What answer is she going to pick on the above problem?

Hmm. She’d pick (C) also, since that gives her values for two of the three variables in the equation that she can write from the question stem.

It’s obvious, in fact, that using the two statements together will allow you to find all three salaries, in which case you can average them. In the test-prep world, this is what’s known as a Too Good To Be True answer. If your 10-year-old niece, who just learned algebra, could get to the same answer, then chances are you’re falling into a trap. Stop, take a deep breath, and scrutinize those statements individually!

Here’s how to solve the problem.

Step 1: Glance Read Jot

Take a quick glance; what have you got? DS. Story problem: understand the story before writing.

The question asks for the average of the three salaries. What do you actually need to know in order to find an average? Right, the sum. So can you find the sum of the three salaries?

Jot that on your scrap paper: M + J + K = ?

Step 2: Reflect Organize

The first sentence provides an equation, so translate it. (Note that the second sentence says Mary’s salary is the highest.)

The positive difference between Mary’s and Jim’s salaries has to be MJ, since M is larger. Likewise, the positive difference between Mary’s and Kate’s salaries has to be MK, since M is larger.

Here’s the translated formula:

MJ = 2(MK)

Step 3: Work

By itself, that doesn’t look very helpful, but anytime DS gives you a formula that isn’t simplified, simplify it. Multiply out the right-hand side and also get “like” variables together:

MJ = 2(MK)

MJ = 2M – 2K

- J = M – 2K

Notice two things: first, negatives are annoying. Second, this formula (so far) doesn’t look anything like the question: M + J + K = ?

Is there any way to remedy those two things?

Move the –J over: 0 = M – 2K + J.

Notice that 2K is never going to fit the question, which has only K. Move that away from the others: 2K = M + J.

Interesting. The right-hand side now matches part of the question. In fact, you could substitute:

M + J + K = ?

2K = M + J

Therefore, the question becomes 2K + K = ?

If you know what K is—only K!— then you can solve. (Note: we call this process Rephrasing. Use the information given in the question stem to rephrase the question in a more simplified form.)

“(1) Jim’s annual salary was $30,000 that year.”

J = 30,000. If you plug that into M + J + K = ?, it isn’t sufficient. If you plug that into 2K = M + J, you get 2K = M + 30,000, which still isn’t sufficient. Knowing only J doesn’t get you very far. This statement is not sufficient; eliminate answers (A) and (D).

“(2) Kate’s annual salary was $40,000 that year.”

Bingo! If you know Kate’s salary, then you know the sum of all three. This statement is sufficient to answer the question.

The correct answer is (B).

If you don’t rephrase up front, and instead go through all of the work of plugging in the values for statements (1) and (2), then you may still discover the correct answer. You’ll take longer, though. You may also fall into the trap of assuming that statement (2) won’t work because it looks so very similar to statement (1) and that one didn’t work.

Key Takeaways: Data Sufficiency

(1) Don’t just write down the information in the question stem, shrug, and go straight to the statements. Push yourself to try to rephrase the question before you go to the statements.

(2) Use standard math steps and your test-taker savvy to help you know how to simplify. It’s standard algebra to try to get “like” variables together in equations. A negative sticking out in front of an equation is ugly, so that was clue #2. Finally, you’re ultimately trying to match the information in the question (M + J + K = ?), so try to rearrange your rephrased equation to match the question as much as possible. Then see whether you can substitute in to make that question simpler!

(3) Keep an eye out for Too Good to Be True answers. If an answer seems pretty obvious, then there’s a good chance you’re falling into a trap!

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

1 comment

  • Thanks Stacey. I often find myself defaulting to the "C-Trap" on questions such as the above. This is actually my first time hearing of this particular trap, so I will keep this in mind going forward.

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