How to Solve Data Sufficiency Questions on the GMAT

On the GMAT quantitative section, you have just over 2 minutes on average to answer each question in front of you. Sometimes, those two minutes go by in a flash and you feel like the question should take at least 4 minutes in order to even make a reasonable guess. Other times, you think you can solve the question in a matter of seconds, and wonder why anyone would take a full 2 minutes on a question that you can eyeball without putting pen to paper (or marker to dry erase board). Because the 2 minute benchmark is an average, not a maximum, figuring out how much time to spend on each question is a crucial part of doing well on this test.

Some questions can be solved quickly, using your conceptual understanding or your familiarity with math without spending copious amounts of time writing out possibilities or formulae. Others can require you to do the calculations from beginning to end in order to get a definitive answer. The latter situation occurs frequently in problem solving questions where the answer choices are close, or in data sufficiency questions.

Let’s look at a question that illustrates both of these notions in one single question:

At a certain auto dealership, 500 cars were sold last week. If a different number of cars were sold on each day, did the dealership sell at least 50 cars on Friday of that week?

(1)    On Monday, the dealership sold 76 cars, which was the third-highest number of cars sold on any day that week.
(2)    On Saturday, the dealership sold 78 cars, which was the highest number of cars sold on any day that week.

(A)   Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B)   Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C)   BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.
(D)   EACH statement ALONE is sufficient.\
(E)    Statements (1) and (2) TOGETHER are NOT sufficient.

This question is about maximizing values in order to see whether we HAVE to sell at least 50 cars on one day of the week. Statement (1) is a perfect example of not having to do much computation to get an answer. If we ignore statement (2), we sold 76 cars on Monday, but that was the third highest of the week, so any other day could have been 20 cars or 200 cars. It’s entirely possible that 200 cars were sold on the highest day, which could easily have been Friday. Similarly, Friday could have been the worst day with 20 cars sold. This statement is insufficient on its own, so let’s eliminate it as well as answer choices A and D.

Statement 2 gives us a crucial piece of information. Since the dealership’s best day was 78 cars sold, we can maximize the sales for all days from Saturday to Thursday and see how many cars could have been sold Friday. Since every day was a different amount, the number of cars sold from Saturday to Thursday could have been 78, 77, 76, 75, 74 and 73 (in any order for the six days). We must do this to calculate the smallest number of cars we could sell on Friday. In this case, breaking down the addition of 6 double digit numbers into a multiplication component and an addition component gets us the answer quicker. This is really (70×6) + (8+7+6+5+4+3), which is 420 + 33, or 453. This is the greatest number of cars that were sold in the 6 days other than Friday.

If the dealership sold 453 cars in 6 days, then the smallest number of cars sold on Friday is 47. This number is below 50, so it’s possible that the dealership didn’t sell 50 cars on Friday (however they did sell one Canyonero). However, it’s entirely possible that they sold more than 50 cars on Friday as well. Friday they could have sold 77 cars, or 73 cars, or 61 cars, or any number between 47 (the minimum) and 77 (the maximum allowed since 78 was Saturday and they all have different amounts). This statement is thus insufficient, and answer choice B can be eliminated as well. This leaves C or E as possible choices.

Combining the statements, statement (1) adds virtually nothing to the situation. The dealership could have still easily sold 77 or 47 cars on Friday, so we don’t know on which side of 50-car threshold Friday is on. Therefore the answer choice must be E, we still need additional information to answer this question.

How could the answer have been different? Let’s look at what would have happened had the statements been slightly different (Butterfly-effect-style). Had statement 2 given us a lower limit, like say 77 cars, then the calculations would have yielded 447 cars at a minimum (quite logically 6 less than we calculated because we went down by 1 car for each of 6 days). This would have meant at least 53 cars on Friday, and statement (2) would have been sufficient on its own. Had the statement said they sold 100 cars on Saturday, it would have been quite obvious without doing any calculations that they could have sold less than 50 cars on Friday while respecting the rules of the question.

A quasi-infinite number of data sufficiency questions can be created from the same skeleton by simply changing the numbers one way or another. When studying for the GMAT, it’s useful to sometimes imagine how the crux of a question could change if the numbers were slightly modified. This helps cement one’s understanding of the commonly tested concepts. Naturally, on test day, you have to answer the question in front of you, but having a good sense of how long you should spend on a question or statement will help you achieve success in a timely manner.

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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.

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