Sample Data Sufficiency GMAT Questions

We’ve already covered why studying with official practice questions is the best way to prepare for the GMAT.  But even if you come up with the correct answer to an official problem, you still might not understand the underlying principles used to create that particular question, leaving yourself open to traps and pitfalls set by the test writers.  In the explanations below, I will use some of the core tenets of the Menlo Coaching GMAT curriculum to breakdown two official GMAT data sufficiency questions and provide important principles for correctly attacking this question type in the future. 

GMAT data sufficiency questions are surprisingly sophisticated, and most students do not truly understand the game or leverage all the hints present in these complex problems. The difficulty in data sufficiency questions often comes more from the particular construct and the inherent logic than from the math itself. Essentially, GMAT data sufficiency questions assess who is good at spotting the con and who is hypervigilant, two extremely important skills in business. Try the following example from the official practice tests:

Data Sufficiency GMAT Sample Question #1


If t and x are integers, what is the value of x?

(1)
(2)

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer & Explanation
Correct answer is (E). 

In all of my classes and tutoring sessions, I emphasize how important it is to “spot the con” and to critically analyze your decision-making process when working through GMAT problems. This frequently missed question is a wonderful example of what happens when you don’t remain critical. In statement (1), you are given a piece of information that the test writers purposefully want you to determine is insufficient. You look at statement (1), glance at statement (2), and immediately realize that x and t could be positive or negative in statement (1) alone, making it insufficient. People feel good about themselves for identifying this fact and quickly pick (C), since adding statement (2) seems to guarantee that x and t are positive 2 and positive 3, respectively. 

Anytime the test writers can create a scenario in which you have a dopamine response and feel good about finding a trap, you are likely to stop being critical. The positive/negative issues present in this question are a shiny penny—so many people pick (C) because they only focus on the positive/negative ambiguity in statement (1), and statement (2) guarantees they are positive. However, when taken together, all that statements (1) and (2) tell you is that the ratio of x:t must be 2:3 and x and t must be positive. This still leaves an infinite number of possibilities for the two values: 2 and 3, 4 and 6, 6 and 9, 8 and 12, etc. Since the value for x cannot be determined, the correct answer is (E).

If both statements together still result in an infinite number of possibilities for the value of x, why do a majority of high-performing students still pick (C), thinking x must be 2? Because they don’t understand the con and they let their guard down! Just because you find one “con” in a question (in this example, the positive/negative issue), does not mean there aren’t others still present! 

All hard questions on this exam work as follows: good test takers find the first “con” in the problem and are satisfied to stop at that point; the best test takers remain highly critical even after that infusion of dopamine from identifying the first “con” and keep looking for traps, eventually proving the correct answer. As in business, success on the GMAT requires hypervigilance—one lazy moment and you get a very doable question wrong!

Data Sufficiency GMAT Sample Question #2

The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes?

(1) The cost of the phone call was greater than $3.35
(2) The cost of the phone call was less than $4.16

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer & Explanation
Correct answer is (B). 

This problem highlights how important it is to read carefully and to look for potential interpretation errors in GMAT math questions. It also shows how it is often easier to manipulate the question stems to match the statements in data sufficiency questions than to change the statements to match the questions (what you naturally want to do). Here is the incredibly well-made “con” in this question:
 
A majority of high performing students do not properly interpret how to determine the cost—the instructions say $0.75 for the first 3 minutes NOT $0.75 per minute for the first three minutes. However, most people carelessly calculate the charge as if it were per minute. If you do that improper interpretation, then the question stem seems to be asking this in terms of cost: a 15-minute call would be 3 x ($0.75) + 12 ($0.20) or $2.25 + $2.40 = $4.65, so the question would be “Did the phone call cost more than $4.65?” Statement (1) would give you a definitive “No” to the question (cost would always be less than $4.65) and thus be sufficient. Statement (2) would allow for the cost to be both below and above $4.65, so the “Maybe” answer would make it insufficient. With the improper interpretation, you seem to have done everything correct when picking (A). But the correct answer is (B)!
 
The proper interpretation:
 
The first three minutes in total cost $0.75 and each minute after the first three costs $0.20 per minute. A 15-minute call would cost $0.75 + 12 ($0.20) or $3.15. So, after changing the question to ask about cost (in order to match the statements) it becomes: Did the call cost more than $3.15?
 
Now you see that statement (1) gives a maybe answer since it allows for both a yes and a no answer to the question. Statement (2), however, guarantees that the cost will always be greater than $3.15, so it is sufficient, yielding the correct answer of (B).
 
Questions that are designed to elicit one particular mistake are dangerous on this test: if you make that mistake, it will feel like you have gotten the question correct when you really have not. To avoid these “designer mistakes,” you must always be critical and try to find the trap or interpretation mistake in all GMAT quant questions. Additionally, this problem shows how it is often easier to change the question to match the statements in data sufficiency: it is much faster to change the time to cost in the question stem, than to change each statement to match the time in the question.