Nice Question..

The first five prime integers are 2, 3, 5, 7, and 11.

Set A: The average of the terms in Set A is 4, so the sum of the terms is (4)(3) = 12. There is only one

way for three of the first five primes to sum to 12: 2 + 3 + 7. Set A is {2, 3, 7}.

Set B: The product of the terms in Set B is divisible by 22, so 2 and 11 are terms in Set B. Set B is

{2, 11, x}, where x can be 3, 5, or 7.

We know that Sets A and B share one term: the 2. If x is either 3 or 7, the sets will share two terms. If

x is 5, the sets will only share one term.

Thus, we can rephrase the question as “Is x = 5?” A definite Yes or No answer leads to a definite

value answer for the number of shared terms (that is, Yes = 1, No = 2).

(1) SUFFICIENT: If the product of the terms in Set B is not divisible by 5, x ≠ 5 and the answer to

our rephrased question is a definite No.

(2) SUFFICIENT: If the product of the terms in Set B is divisible by 14, then 2 and 7 are terms in B.

Therefore, x = 7 and the answer to our rephrased question is a definite No.

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