TIPS FOR PASSING GMAT

Nearly every GMAT includes at least one rate problem. Perhaps fittingly, rate/speed problems are where many examinees waste the most time. The good news? Certain rate problems offer a great chance to “catch up” if you’re running short on time. “Catching up” rate problems can be among the most time-consuming problems on the entire exam, but with a strategic eye for what they’re really asking you can make them some of the quickest.

Take, for example, the question:

Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?

(A) 8

(B) 9

(C) 10

(D) 11

(E) 12

When you’re looking at these “catching up” problems in which two entities are traveling in the same direction at different speeds, what’s important is the difference in rates.  In this case, every time Donovan runs a lap (which takes him 45 seconds), Michael, who has finished in 40 seconds, gets a 5 second “head start” on the next lap.  And since it takes Michael 40 total seconds to run a full lap, he needs 8 of those 5-second head starts in order to run an entire extra lap.  This means that Michael will have to run 9 total laps, as on the first lap there’s no “head start” (and you can check the math: 8 laps x 45 seconds per lap = 9 laps x 40 seconds per lap, as both equal 360 seconds).

More important than this particular question is the take-away. When you’re dealing with “catching up” rate problems—those in which two cars/trains/people are traveling in the same direction and one needs to catch up to or pass the other—you may have a temptation to go about it in a labor-intensive fashion, either setting up ugly algebra or trying to draw out what happens minute-by-minute or mile-by-mile. But what’s truly important is the difference between the two—how much ground does the faster entity gain on the slower in each increment. If you focus on the difference, the math is generally manageable, and you’ll save quite a bit of time en route to a correct answer. “Catching up” problems are a great opportunity to catch up.

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