Vincen wrote:A set consists of 20 different numbers whose average is 10. Which of the following pairs, when added to the set of numbers, must reduce its standard deviation?

A. 0, 0
B. 0, 20
C. 10, 10
D. -10, 10
E. 5, 15

The OA is C.

I don't know how can I solve this PS question. I don't understand what is standard deviation. Experts could you explain this to me please?

I am not an "expert" but standard deviation is just the dispersion of numbers or variance in regards to the mean. So for example, a set of 2,2,2 would have a standard deviation of 0, since there is no variance. The GMAT doesn't really test your knowledge of how to calculate SD, you just need to understand the principle.
As to the question, since you have a group of 20 random numbers, whose mean is 10 , the closer the numbers to the mean will reduce the standard deviation. In this problem, you are adding two numbers whose deviation is 0.

Hope that made sense. Maybe an expert can opine and explain it better.