What is the average of numbers a and b?

(1) The median of a+2, a-3 and a+5 is 14.
(2) The only mode of a, b and 14 is 14.

The OA is the option C.

I can't see how to use the second statement to get the answer. Can anyone clarify this for me? I'd be thankful for your help.

Hello M7MBA.

On this question, we need to find $$\frac{a+b}{2}=?$$

(1) The median of a+2, a-3 and a+5 is 14.

This statement tells us the following $$a-3\ \ \ <\ \ a+2\ \ \ <\ a+5\ \Rightarrow\ \ a+2=14\ \Rightarrow\ \ a=12.$$ Since we don't know anything about "b", this statement is NOT SUFFICIENT.

(2) The only mode of a, b and 14 is 14.

This statement tells us that the only mode of the set {a, b, 14} is 14. That implies that "a" or "b" or "both" are equal to 14. Since we can know what is exactly the value of "a" and "b", this statement is NOT SUFFICIENT.

Now, using both statements together

We have that a=12 and therefore b=14. This implies that $$\frac{a+b}{2}=\frac{12+14}{2}=13.$$ Therefore, this case is SUFFICICIENT.

In conclusion, the correct answer is the option C