Why You Should Do the Math on Data Sufficiency GMAT Questions

On GMAT Data Sufficiency questions, it’s important to note that you don’t have to do any calculations to get the right answer. In theory, it’s entirely possible to simply look at a problem and determine that the answer must be D (whilst eating your grey poupon). The question format simply asks you to confirm whether you have enough information to make a decision, not what that decision is or what any specific value is.

The downside of Data Sufficiency questions is that, by not necessarily going through the calculations, it’s very possible to misinterpret the question or reach a premature conclusion without considering every option. While there is no formal requirement of actually calculating anything, I do recommend trying to cement your answer by plugging in a few numbers to confirm your theory. In the worst case, your hunch is validated and you feel confident. In the best case, you recognize a simple mistake or assumption you took for granted and you avoid a glaringly incorrect choice (like Decca records passing on The Beatles in 1962).

Another common trap students fall into on data sufficiency is misunderstanding the information given. If the question is asking you for x, and you think it’s asking you for y, your chances of getting the right answer are reduced to lucky guesses and finger slips of the mouse (much like Australia’s chance of winning the 2014 World Cup). Avoiding doing the math also makes it harder to see if you go down the wrong path. In some instances, it’s worth writing down some numbers just to see what happens. Sometimes just seeing what doesn’t work will lead you down the path of the correct answer.

Let’s highlight this principle with a Data Sufficiency question that a lot of people can narrow down to two choices, but then pick incorrectly:

A certain car rental agency rented 25 vehicles yesterday, each of which was either a compact car or a luxury car. How many compact cars did the agency rent yesterday?

(1) The daily rental rate for a luxury car was $15 higher than the rate for a compact car.

(2) The total rental rates for luxury cars was $105 higher than the total rental rates for compact cars yesterday

(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 but neither statement is sufficient alone.

(D)   Each statement alone is sufficient to answer the question.

(E)    Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Looking at what’s provided in the question stem, there are two types of cars being rented. The total number of cars rented is 25, and every car is either compact or luxury. We only have to determine how many compact cars were rented, so something as small as the number of luxury cars rented would solve our problem very quickly. Looking at the statements, we only have information about prices. The daily rate for the compact car is 15$ less than the luxury vehicle. That’s great (and a little unrealistic), but it doesn’t help us answer the question about the number of vehicles. Statement 2 also talks about money, this time talking about the total revenue instead of a per-car basis. This doesn’t help either, so answer choices A, B and D are all out.

This type of question visibly needs you to combine statements in order to get anywhere. There is a danger in combining statements without thinking, because there is often a relationship that’s just hard enough to detect linking the two statements that gets test-takers thinking they’re on the right track. In this question, the fact that 105$ is 7 times the luxury car premium of 15$ makes it feel like 7 more luxury cars were rented than compact cars. This type of connector is hard enough to see that people feel encouraged that they’ve stumbled upon something useful. Unfortunately, when you’re feeling clever is when you’re most vulnerable to fall into a GMAT trap (Something about pride going before a fall).

Let’s delve into these numbers a little. If 7 more luxury cars got rented than compact cars, and the numbers add up to 25, then that means the company rented 16 luxury cars and 9 compacts. If we stop here, we might think that the answer is C. However, applying arbitrary numbers might make us realize the error of our ways. Let’s say a compact car is 100$ an hour (easy number to work with). This makes the luxury cars 115$. We can quickly calculate that the compact cars will bring in exactly (9×100) 900$. The luxury cars will bring in well over 1600$. These two numbers don’t respect the 105$ difference mentioned in statement 2. Why is that? Maybe I picked the wrong prices? Let’s go smaller: 20$ compacts and 35$ luxury cars. That’s 180$ for the compacts and 525$ for the luxury cars. We’re getting closer, but this still doesn’t work. What’s happening?

The number of cars we chose (16 luxury cars and 9 compacts) has a solution, but it’s not one that makes any real world sense. Solving for the two equations and two unknowns with our chosen number of cars:

L+C = 25
L(x+15) = C*x+105
Replacing L by 16 and C by 9
16(x+15) = 9*x+105
16x+240 = 9x+105
7x = -135
x = -19.286

That’s right, this solution works if we give people 19$ to rent compact cars and only 4$ to rent out luxury cars. Clearly this solution does not work in the real world because it does not mean what we expected. On test day, you don’t have to go through the actual math to solve for x, but being able to recognize that renting out 16 cars at a 15$ premium will yield at least (16*15) = 240$ more dollars for the luxury line than the compact line. The relationship of 7 additional cars only works if we rent a total of 7 cars, all luxury liners. Any other rental will throw off this delicate balance, highlighting that it was nothing but a mathematical mirage.

So what’s the answer to this question? As many of you probably figured out, it’s just going to be answer choice E. There are multiple values that will work (and even be positive) for the two constraints given. Many test takers can solve these questions without having to write a single digit down. However, if you’re ever unsure, write down a few numbers and see what they tell you. The reason some people dislike math is the same reason some people love math: it tells the truth. If your understanding of the question is shoddy, a couple of concrete numbers will tell you more than all the x’s and y’s in an alphabet soup (or a Jerry Springer show).

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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.