Studying for the GRE can be tough. In the *mean* time, let’s make sure your math score is above *average* by reviewing averages! Consider the following problem:

The average (arithmetic mean) of six numbers is 14. After one of the numbers is removed, the average (arithmetic mean) of the remaining numbers is 16. What number has been removed?

To solve this problem, all you need to remember is the definition of an average:

average = (sum of terms)/(number of terms)

Multiplying both sides by the number of terms, we get:

average(number of terms) = sum of terms

First, let’s figure out the sum of the terms when the average was 14:

14(6) = 84

Next, let’s do the same for the situation in which the average is 16:

16(5) = 80

The difference between the two sums must be the number that was taken out:

84 – 80 = 4

Thus, the answer is 4. That’s all there is to it! Now, try the following problem and post the answer in the comments below:

The average (arithmetic mean) of four numbers is 23. After one of the numbers is removed, the average (arithmetic mean) of the remaining numbers is 15. What number has been removed?

Good luck, and happy studying!

47

Correct!