k is a positive integer. Is k prime?

Question

(1) At least one number in the set {1, k, k + 7} is prime.
(2) k is odd.

Bunuel · Answer

k is a positive integer. Is k prime?

Notice that we are told that k is a  positive  integer.

(1) At least one number in the set {1, k, k + 7} is prime. Clearly insufficient.
(2) k is odd. Clearly insufficient.

(1)+(2) The set is {1, k=odd, k+7=even>2}. Since at least on number in this set is a prime, then it must be k. Sufficient.

Answer: C.

fireinbelly · Answer

you made it look so simple...thanks a ton Bunuel.

unceldolan · Answer

I thought it was A because I thought that in a set, the numbers are organized by size. So I assumed that k is prime because any prime + 7 = no prime. But obviously a set is not sorted. I get the rest of the reasoning. Am I right assuming that sets don't need to be sorted? Please verify!

Thanks!

Bunuel · Answer

A set is not necessarily ordered but this has nothing to do with the first statement.

The question asks whether k is a prime number. (1) says that at least one number in the set {1, k, k + 7} is prime. Sure k can be prime but k can as well be for example 4, so not a prime and in this case k+7=11 is a prime.

Hope it's clear.

EMPOWERgmatRichC · Answer

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:  C

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

Anurag06 · Answer

Hi Bunuel

Probably it might sound dumb but an odd number like 15 also came to my mind. In that case my choice moves to "E". Can you please help?

Bunuel · Answer

(1) says: at least one number in the set {1, k, k + 7} is prime.

If k = 15, then the set is {1, k = 15, k + 7 = 22}, non of which is prime. So, k cannot be 15.

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k is a positive integer. Is k prime?

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k is a positive integer. Is k prime?

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