The Most Important Moment in a Problem-Solving Question

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This tip for improving your GMAT score was provided by David Newland at Veritas Prep.

Most of what you do during a problem-solving question is dictated by the problem itself and by the rules of math. There are certain ways to combine exponents, a right triangle has certain features, and an equation is solved according to set rules, with no real choices for you to make. Data-sufficiency problems may allow you more options (such as evaluating statement 1 or statement 2 first) but with problem-solving questions, the proper course is often not really a matter of choice.

However, there are moments—often just one but occasionally two, or even more—when you have to make a decision that is not dictated by the problem or by the rules of math. This is when you have to slow down and think about how to proceed. This is the “moment” that can make this question work for you or can send you off in the wrong direction.

Try this ratio problem from the Veritas Arithmetic book and see if you can recognize the “moment”:

The number of hours it took three truck drivers to drive a certain distance was in the ratio of 3 to 4 to 7. If they drove a combined total of 420 hours, how many hours did the trucker who drove the slowest drive?

A) 280
B) 210
C) 180
D) 90
E) 70

If are you looking for it, the “moment” is very clear on this problem. Your big decision is deciding what the numerator in your ratio will be. The rest of the problem is automatic. You know that 14 hours is the total hours in the ratio and that 420 is the total miles. Your big decision is what number to choose to represent the slowest driver. You automatically have 14 as the denominator in the ratio S/ 14, where S represents the slowest trucker. This means that the proportion is S/ 14 = x/ 420. With x as the solution to the question.

You may think that the answer is obvious, and it should be. Yet many people who think that the answer is obvious have actually set it up incorrectly. Overall, more than 1/3 of students miss this question despite knowing how to work with ratios. Essentially, those students all miss this question for the same reason: They set up this ratio incorrectly.

An extra five seconds to 10 seconds can eliminate any regrettable “simple mistakes” on this one. As you are deciding how to represent the slowest driver, you must slow down yourself and recognize that you are making one of those rare decisions that is not dictated by the problem. Ask “would the slower driver be represented by a 3 in this ratio or by a 7?” If it is DISTANCE, the slower driver will have the lower number. But since this question is about TIME, the slowest driver takes the most time to cover the same distance. So the proper equation is 7/ 14 = x/ 420.

Now you can go back to autopilot since the simple math is automatic. 7/ 14 = 1/2, so x = 210, and the answer is B.

Recognizing the “moment” where you actually need to make a choice, and slowing down to make the right choice can help prevent simple mistakes. It can also help you to get started correctly on a problem. If you are working with a problem involving fractions and you are choosing your own numbers, do not simply use 10 or 100. Recognize this moment as one in which you are making the choices and slow down. Choose numbers that make the problem simpler and that work with the fractions or other limitations of the problem.

Other examples of “important moments” in problem-solving questions include: choosing your own numbers for a problem that has variables in the answer choices; setting up equations that require some interpretation on your part—such as equations on age problems (in 5 years, Bob will by twice as old as Jill); and working with percentages derived from ratios.

While most of what you do in problem solving is dictated by the question and the rules of math on nearly every problem, you will get your “moment” to shine.

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