Avoiding the C-Trap in Data Sufficiency

by , Apr 16, 2014

math_4Have you heard of the C-Trap? Im 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 Marys and Jims annual salaries was twice the difference between Marys and Kates annual salaries. If Marys annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?

(1) Jims annual salary was $30,000 that year.

(2) Kates annual salary was $40,000 that year.

Im going to do something I normally never do at this point in an article: Im going to tell you the correct answer. Im not going to type the letter, though, so that your eye wont inadvertently catch it while youre 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?

Heres 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 thereso you cant 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 doesnt work. Youre predisposed, then, to assume that the second statement, which seemingly supplies the same kind of information, also wont work. Therefore, you dont vet the second statement thoroughly enough before dismissing itand youve just fallen into the trap.

How can you dig yourself out? First of all, just because two statements look similar, dont assume that they either both work or both dont. The test writers are really good at setting traps, so assume nothing.

Second, imagine that youre teaching your 10-year-old niece how to do algebra. Shes never done this before but shes 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, shell be able to solve for the third one. What answer is she going to pick on the above problem?

Hmm. Shed 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.

Its 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 whats 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 youre falling into a trap. Stop, take a deep breath, and scrutinize those statements individually!

Heres 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 Marys salary is the highest.)

The positive difference between Marys and Jims salaries has to be M J, since M is larger. Likewise, the positive difference between Marys and Kates salaries has to be M K, since M is larger.

Heres the translated formula:

M J = 2(M K)

Step 3: Work

By itself, that doesnt look very helpful, but anytime DS gives you a formula that isnt simplified, simplify it. Multiply out the right-hand side and also get like variables together:

M J = 2(M K)

M J = 2M 2K

- J = M 2K

Notice two things: first, negatives are annoying. Second, this formula (so far) doesnt 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 isonly 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) Jims annual salary was $30,000 that year.

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

(2) Kates annual salary was $40,000 that year.

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

The correct answer is (B).

If you dont 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. Youll take longer, though. You may also fall into the trap of assuming that statement (2) wont work because it looks so very similar to statement (1) and that one didnt work.

Key Takeaways: Data Sufficiency

(1) Dont 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. Its 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, youre 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 theres a good chance youre falling into a trap!

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