GMAT Hacks: When the Mean is the Median
Blogs Barbara Simon - 11-15-10
When you have a set of consecutive numbers (integers, evens, odds, multiples), the mean is equal to the median. To locate the median, find the average of the endpoints.
To extend the usefulness of this tip a bit further: this technique can also be used to find the sum of large sequences of numbers. Say that, instead of looking for the mean of the set of integers from 1 to 50, you wanted to the sum of that set of integers.
The sum of a set of numbers is equal to the average times the number of terms. The number of terms is usually easy to come up with: in this case it's 50. The average, as we now know, is also easy: we know it's 25.5. The sum of the numbers in the set, then, is 25.5 times 50, or 1275. That's much easier than adding up all of the numbers, or even finding all the pairs of numbers
As usual, when it looks like the GMAT is asking you to perform a lengthy calculation, there's a way around it. This is just one more example of how the GMAT isn't an arithmetic test, it's a thinking skills test.
This is an excerpt from a longer article by Jeff Sackmann, originally published at GMAT Hacks. Jeff has created several valuable GMAT-preparation resources, including Total GMAT Math and Total GMAT Verbal.