Data Sufficiency

Vincen wrote: ↑

Fri Sep 03, 2021 9:35 am

If there are 13 boys in club X, what is the average age of these boys?

(1) The oldest boy is 13 years old and the youngest boy is 9 years old.
(2) Eleven of the boys are either 10 years old or 11 years old.

Answer: E

Source: GMAT Prep

Target question: What is the average age of the 13 boys?

When I SCAN the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……

Statements 1 and 2 combined
There are several scenarios that satisfy BOTH statements. Here are two:
Case a: The ages are {9, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 13}.
Case b: The ages are {9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 13}
Since the two sets have DIFFERENT sums, we know that the averages will be DIFFERENT
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent