Hi All,

This question can be solved by TESTing VALUES.

We're told that K is a POSITIVE INTEGER. We're asked if K is PRIME. This is a YES/NO question.

Fact 1: At least one number in the set {1, K, K + 7} is prime.

IF....

K = 2, the set is {1, 2, 9} and has at least 1 prime number

The answer to the question is YES.

IF...

K = 4, the set is {1, 4, 11} and has at least 1 prime number

The answer to the question is NO.

Fact 1 is INSUFFICIENT

(2) K is ODD.

IF....

K = 1, then the answer to the question is NO.

K = 3, then the answer to the question is YES.

Fact 2 is INSUFFICIENT

Combined, we know...

At least one number in the set {1, K, K + 7} is prime.

K is ODD

IF...

K = 3, the set is {1, 3, 10} and has at least 1 prime number

The answer to the question is YES.

From the above example, if K is an ODD PRIME, then the answer is ALWAYS YES. We now have to look for possibilities when K is NOT prime....

IF...

K = 9, the set is {1, 9, 16} BUT this does NOT have any primes, so K CANNOT BE 9...

From this example, we can see that if K = an ODD NON-PRIME, then (K+7) will be EVEN (thus, NOT prime). Thus, there are no possible values of K that are odd AND non-prime that will 'fit' these Facts. By extension, that means that K MUST be an ODD PRIME and the answer to the question is ALWAYS YES.

Combined, SUFFICIENT

Final Answer:

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

Rich

_________________

# Rich Cohen

Co-Founder & GMAT Assassin

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