Do Weighted Average Problems Faster

August 11, 2006

Today let's take a look at a very specific type of problem, one you can expect to see at least once on the GMAT, probably in the form of a Problem Solving question. Weighted averages are not particularly tricky, but they can be very time-consuming, and when you only have a couple of minutes per problem, that can be just as bad.

I've got a great shortcut for weighted average problems, one that very few students seem to have seen before. It's best explained in the context of an actual problem, so let's start there.

If Jason purchased two suits for $179 each and three suits for $189 each, what is the average price Jason paid for each suit?

(A) $183.00
(B) $184.00
(C) $185.00
(D) $185.50
(E) $186.50

If you've learned how to compute weighted averages, you know exactly how to set up this problem:

(179)(2) + (189)(3)

Lots of calculations ensue, the clock ticks away, and if all goes well, you find the correct answer. It's (C), $185.00.

Before launching into the shortcut, think about this question as if it were set on a number line. The relevant part of the number line for this question is between 179 and 189, inclusive. Because 189 is weighted more heavily, imagine that the average is pulled in the direction of 189--which turns out to be in line with the correct answer.

An Easier Approach

Now think of a different number line: this time between 0 and 10, inclusive. If you were calculating the weighted average of 2 0's and 3 10's, the average would nudge toward 10. The calculations are much simpler in that case:

(0)(2) + (10)(3)

30 divided by 5 is 6. Again, despite the fact that we're looking at a number line 179 points lower than the original, the weighted average is exactly 6 larger than the lower number and 4 smaller than the higher number. This is no accident. In a matter of speaking, weighted averages don't care what the end points are, they just care about the weights.

By now, it may be clear how to apply this to do the example problem above more quickly. Instead of using 179 and 189 as your datapoints, use 0 and 10. Find the weighted average of 2 0's and 3 10's, then add 179.

To immediately put this tip to work for you, try Problem Solving question #137 in The Official Guide for GMAT Quantitative Review . It's on page 80. Another very similar example is PS #11 in the The Official Guide for GMAT Review, on page 153. With a little practice, you'll be doing even the hardest weighted average problems faster than you ever have before.

About the author: Jeff Sackmann is a GMAT tutor based in New York City. He has created many resources for GMAT preparation, including the popular Total GMAT Math and Total GMAT Verbal, as well as 1,800 practice GMAT math questions.