Warning: Don’t Fall Into the C Trap on Data Sufficiency Questions

Studying for the GMAT can take over your life. I’m sure many of you are nodding your heads as you read this. If you’re not, you probably haven’t gotten there yet. I sincerely hope that you never do, but it is an almost unavoidable part of studying for this test. Eventually, you start correcting artists in songs (I got one less problem without you… more like one fewer problem) and wondering if your table number is a prime number (how about table 51… oops that’s divisible by 3). The first time you catch yourself using a GMAT specific term, you know you’re really deep in studying for this exam.

Most of the terms you hear are just general math and verbal times that you’ve seen before, but likely not in many years (“gerunds” and “isosceles” come to mind immediately). However, some expressions exist only on the GMAT. As an example, have you come across the term “The C trap” yet? This idiom is used to describe the erroneous assumption that answer choice C is disproportionately chosen on Data Sufficiency questions. As a quick reminder, this choice indicates “both statements taken together are sufficient to answer the question, but neither statement alone is sufficient”. (If you knew it verbatim by heart, congratulations, you’re in GMAT mode).

Why do people select this choice on roughly 30-40% of their data sufficiency questions? The answer is that, since you have two independent statements to evaluate, choosing to use both typically gives you the maximum amount of information. Of course, that doesn’t mean that using both statements is what will provide sufficient information to answer the question. It also doesn’t mean that you can’t get the same information from only one of the two statements. Despite this, test takers consistently feel most comfortable picking answer choice C than any other choice on questions where they’re unsure how to proceed. It seems as if answer choice C makes them feel safe. Unfortunately, time and time again, it’s a trap.

Let’s look at question that highlights this issue:

An animal shelter began the day Tuesday with a ratio of 5 cats for every 11 dogs. If no new animals arrived at the shelter, and the only animals that left the shelter were those that were adopted, what was the ratio of cats to dogs at the end of the day Tuesday?

(1) No cats were adopted on Tuesday.

(2) 4 dogs were adopted on Tuesday.

(A)   Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

(B)   Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

(C)   Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

(D)    EACH statement ALONE is sufficient to answer the question asked

(E)    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Let’s begin by taking stock of what we know. This question is asking about ratios. At a certain shelter, the ratio started off as 5:11 for cats : dogs. During the course of the day, some animals were potentially adopted. The question asks about the ratio at the end of the day. The most important thing to note here is that we being with a ratio but not absolute numbers, which means if we get ratios (i.e. half the cats got adopted) we might know the end ratio. If we get absolute numbers, we have almost no chance of having sufficient data. The stimulus gives us no further information, so we need to start looking at the statements.

For simplicity’s sake, let’s start with statement (1). Remember that you can always start with statement (2) if you prefer (or if it seems easier) as both statements are independent. The first statement tells us that no cats were adopted. However, we don’t know anything about the dogs (other that they’re four legged mammals). This statement alone will clearly be insufficient. We can eliminate answer choices A and D.

Looking now at statement 2, we know that exactly four dogs were adopted over the course of the day. This statement will suffer from the same problem as statement 1: we have no information about the cats. This statement will be insufficient on its own, and answer choice B can be eliminated as well.

Looking now to combine the statements, we can consider that the number of dogs dropped by four while the number of cats remained the same. Since we know about both animals, many people believe that the two statements together are sufficient. This would be true if we knew the actual number of each animal at the beginning of the day. Regrettably, we only know the ratio of one to the other, meaning that a change in absolute number is meaningless.

To use concrete numbers, there could have been 5 cats and 11 dogs at the beginning of the day, and the loss of four dogs would change the ratio to 5:7.  Just as likely, we had 50 cats and 110 dogs at the beginning of the day, and the new ratio would be 50:106 (which we could simplify to 25:53 for completeness’ sake).  Since either of these scenarios (and a dozen more) is possible, the answer must be answer choice E. The statements together do not provide enough information.

There is one caveat worth mentioning with ratios. Since the ratio does not tell us about absolute numbers, adding 10 or subtracting 15 is meaningless because we don’t know the original numbers. There is, however, one interesting exception: If you added 5 cats and 11 dogs, then the ratio would naturally remain unchanged. Indeed, as long as the change was in the ratio of 5:11, the ratio would be known: still 5:11. If the ratio deviates in any way, this does not hold. Interestingly, for subtraction, this problem does not occur because removing 5 cats and 11 dogs introduces the non-negligible possibility that there are now 0 cats and 0 dogs left at the shelter. In general, absolute number data is meaningless on ratios. Keep the one exception (adding by the exact same ratio) in mind when considering these types of problems.

In general, people are far too enticed by answer choice C on Data Sufficiency questions. Indeed, answer choice E was the most common answer for this question, but choice C was not far behind. Having more information is always tempting, even if it has almost no bearing on the actual question. Many students report feeling more secure selecting answer choice C, especially if they don’t know the answer and are guessing (educated guess, hopefully) the correct answer. The problem is that the test makers know that answer choice C is the most popular answer choice and specifically design problems to lure you to that conclusion. However, (as admiral Ackbar warned in 1983) it’s a trap!

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Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.