Anaira Mitch wrote:Sets A and B each consist of three terms selected from the first five prime integers. No term appears more than once within a set, but any integer may be a term in both sets. If the average of the terms in Set A is 4 and the product of the terms in Set B is divisible by 22, how many terms are shared by both sets?

(1) The product of the terms in Set B is not divisible by 5.
(2) The product of the terms in Set B is divisible by 14

Hi Anaira Mitch,

We have the first five primes: 2, 3, 5, 7, and 11.

The average of the terms in Set A is 4. This implies that the sum of the terms is Set A is 4*3 = 12.

Thus set A = {2, 3, 7}

The product of the terms in Set B is divisible by 22. This implies that B = {2, ?, 11}.

If "? = 5," the answer is one (only one term (2) is common; however, if "? = 3 or 7," the answer is two (Two terms (2, and one between 3 and 7) are common)

Let's take each statement one by one.

S1: The product of the terms in Set B is not divisible by 5.

This implies that 5 is not in Set B, thus set B = {2, 11, 3 or 7}. In both cases, A and B share two terms. Sufficient.

S2: The product of the terms in Set B is divisible by 14.

This implies that 7 must be in Set B, thus B = {2, 11, 7}. Therefore, A and B share two terms. Sufficient.

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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