Why The GMAT Poses ‘Gotcha’ Questions

The GMAT is a frustrating test.

For most of us who have been successful enough academically to even sit for a graduate school entrance exam, we’ve been able to get through challenging mid-term and final exams by knowing the information inside and out, by showing our work and explaining our contentions, and by trusting in the fact that the hardest exams are at the very least fair. Most of our educational history has stayed true to the adage “you get out of it what you put into it” – if you pay attention in the lectures, do the reading and assignments, and pore over your notes before the test, you’ll remember enough to do well on test day.

And then the GMAT throws stuff like this at you:

a, b, c, and d are consecutive integers such that the product abcd = 5040.  What is the value of d?

(1) d is prime

(2) a > b > c > d

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;
4. EACH statement ALONE is sufficient to answer the question asked;
5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

And you do the work the way you always have. You factor out 5040 by recognizing that it ends in a 0, so it’s divisible by 10, and the sum of the digits is 9 so it’s a multiple of 9. So, with two consecutive integers already in hand, you divide out the rest to find that 5040 is the product of 7*8*9*10. And it takes a little work and some application of what you studied, but you see the reward when you read statement 1:  if d is prime, then it has to be 7, the only prime number in that list of consecutive integers you just factored. So, statement 1 is sufficient. And, statement 2 leads you to the same conclusion – if d is the smallest one, well that’s 7 again (10>9>8>7), so statement 2 should also be sufficient and the answer should be D. And then you go to review your answer later and you see this:

Solution: A. Explanation: For statement 2, two sets of four consecutive integers could multiply to 5040:  (7)(8)(9)(10) and (-7)(-8)(-9)(-10). Strategy tip: remember to consider negative values of variables.

But what you’re really hearing is that taunt from the playground when you were a kid playing “Simon Says”:

“Simon didn’t say positive – you lose”

If you get mad at those “gotcha” questions, those in which you do all the actual math correctly and efficiently within the time limit but which get you with that technicality of “but what about a negative?” or “but what about a noninteger?” or “but did you consider whether you’re actually dividing by zero?”, you’re not alone.

It’s frustrating to do all the “work” right and still get the question wrong, and it can certainly seem unfair or just plain cheap for the test to use these kinds of tricks against you. Why does this mathematical game of “Simon Says” have any merit when it comes to your suitability to attend a top business school? Why does Darden or Ross or Booth or, yes, Simon (the Simon GSB at Rochester) care about these gotcha, Simon Says questions?

Because they’re not just “Simon Says” questions; they’re actually somewhat analogous to “Steve Says,” as in Steve Jobs would have told you that these questions have takeaways relevant to business strategy.  On the GMAT, gotcha situations like negative numbers and nonintegers can prove to be threats to your answer (if you get it wrong) or opportunities to succeed (if you see them and get it right). While it’s not a perfect substitute for business-case decision making, the GMAT uses these devices because they’re parallel to the threats and opportunities that face business leaders all the time.