Problem Solving

[GMAT math practice question]

The average of a, b, c, and d is 5 and their standard deviation is 4. What is the sum of the average and the standard deviation of 2a-5, 2b-5, 2c-5 and 2d-5?

A. 7
B. 9
C. 11
D. 13
E. 15

=>

Remember the property E(aX+b) = aE(X) + b, where E(X) is the average of a set X.
Remember the property S(aX+b) = |a|S(X), where S(X) is the standard deviation of a set X.

E(2X-5) = 2E(X) – 5 = 2*5 – 5 = 10 – 5 = 5.
S(2X-5) = 2*S(X) = 2*4 = 8.

Then, the sum of their average and standard deviation is 5 + 8 = 13.

Therefore, the answer is D.
Answer: D