GMAT by the Numbers: Problem Solving

Now that you’ve learned how to approach Problem Solving questions on the GMAT, let’s add one more dimension to your understanding of how they work.

Take a moment to try this question. Following is performance data from thousands of people who have studied with Kaplan over the decades. Through analyzing this data, we will show you how to approach questions like this one most effectively and how to avoid similarly tempting wrong answer choice types on Test Day.

  1. The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y, where y ≤ 16,000. What would be the total weekly revenue, in dollars, from the sale of cars priced at $15,000?
    1. 50,000
    2. 750,000
    3. 850,000
    4. 7,500,000
    5. 750,000,000

Explanation

The first—and in many ways most important—step in Problem Solving is to understand what you’re solving for. This problem gives you an equation: x = 800,000 – 50y, with x representing the number of cars sold and y representing their price. You’re given the price, so y = 15,000. But you aren’t solving for x. Rather, you’re solving for the total revenue. You’ll therefore find the number of cars sold (x), then multiply by their price ($15,000).

Substituting 15,000 for y in the equation, you get:

Multiplying 50,000 cars by $15,000 yields revenue of $750,000,000. (E) is correct.

Notice that the math involved here is not extremely challenging, yet fewer than half of test takers select the right answer. That’s because two wrong answers are actually right answers—but to the wrong questions. (A), the most popular incorrect choice, is the value of x. It’s easy to assume that you’re solving for a variable given by the problem, but often you won’t be. (B), the other commonly selected wrong answer, is the value of 50y. These “intermediate values” that you generated on your way to the right answer make for very tempting wrong answers—so tempting in this problem that more test takers choose them than the right answer! Be clear about what you need to solve for, and you’ll avoid the biggest Problem Solving pitfall.

More GMAT by the Numbers . . .

To see more questions with answer choice statistics, be sure to review the full-length CATs in your online resources.