GMAT Tip: Becoming Above Average on Average Problems

GMAT Tip: Becoming Above Average on Average Problems
Calculating averages typically involves adding and dividing, but many GMAT average questions can be done without any division (Photograph by Getty Images)
Photograph by Getty Images

This tip on improving your GMAT score was provided by Brian Galvin at Veritas Prep.

In your job or in your life, calculating averages is relatively easy. Just type that code into Microsoft Excel, drag the cursor across your data set, and voila—average!

But on the GMAT—without the help of Excel or a calculator—many students find calculating averages to be a task that takes longer than average. It doesn’t have to, though. There’s a secret about averages that can drastically reduce your calculation time and increase your accuracy:

When the number of terms doesn’t change, average problems can usually be solved just using the sum.

By now you should know that the average can be calculated by:

And for most, the least-enjoyable part of calculating an average is doing that division.  But this can be avoided if the number of values doesn’t change. In that case, you can do all your work using the sum. Consider the following example:

Which of the following series of numbers, if added to the set {1, 6, 11, 16, 21}, will not change the set’s average?

I. 1.50, 7.11, and 16.89

II. 5.36, 10.70, and 13.24

III. -21.52, 23.30, 31.22

(A) I only

(B) II only

(C) III only

(D) II and III only

(E) None

Those decimal places may already be giving you anxiety. Who wants to tally up three different 8-term sets, then divide them, to determine their averages? But there’s a workaround: The division is actually unnecessary.

You should see that the sum of the terms in the original set is 55, making the average of that set 11 (a quick division calculation you should be able to do in your head). And since you don’t want the average to change, you’ll want the new sum of 8 terms to be 88, keeping the average at 11. Since you already have 55 and you want a total of 88, the three new terms have to sum to 33. If you recognize that, this problem really comes down to a quick calculation: Do each of these three sets sum to 33?

From there, you should see that Sets I and II don’t get near enough to 33 to warrant even adding the decimals, and Set III does sum to 33. So the correct answer is C. More important is the takeaway: A great many average problems can be done quickly by simply working with the sum of the values and not performing redundant (and time-consuming) division.

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