If the average(arithmetic mean) of four numbers is 10 ,how many of the

Hi AverageGuy123,

This question has some very specific 'restrictions' to it, but if you take the proper notes and TEST VALUES, you can answer this question without too much trouble.

We're told that the average of 4 numbers is 10. We're asked how many (of those 4) are greater than 10.

From the first sentence, we can create an equation:

(W + X + Y + Z)/4 = 10
W + X + Y + Z = 40

Fact 1: Precisely 2 of the numbers equal 10

I'm going to "lock in" the W and the X as 10s....

10 + 10 + Y + Z = 40
Y + Z = 20

Since Fact 1 states that PRECISELY 2 of the numbers equal 10, neither Y nor Z can now be 10s. That means we need 2 numbers that add up to 20 and NEITHER can be a 10...

9 and 11
8 and 12
0 and 20
-1 and 21
Etc.
In EVERY possible example, one number is LESS than 10 and ONE number is GREATER than 10. Thus, the answer to the question is ALWAYS ONE number.
Fact 1 is SUFFICIENT

Fact 2: The largest of the numbers is 10 greater than the smallest of the numbers

IF... the numbers are....
5, 10, 10 and 15.... then the answer to the question is ONE.
4, 10, 12 and 14.... then the answer to the question is TWO.
Fact 2 is INSUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich