If s is a positive integer, is s prime?

[VJesus12]

If s is a positive integer, is s prime?

(1) 21/s is an integer
(2) 47/s is an integer

The OA is the option C.

Is not sufficient each statement alone? Why not? Could someone help me? Please.

[Brent@GMATPrepNow]

If s is a positive integer, is s prime?

(1) 21/s is an integer
(2) 47/s is an integer

Target question: Is s prime?

Given: s is a positive integer

Statement 1: 21/s is an integer
So, s can equal 1, 3, 7 or 21
If s = 1, the answer to the target question is NO, s is NOT prime
If s = 3, the answer to the target question is YES, s IS prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 47/s is an integer
So, s can equal 1 or 47
If s = 1, the answer to the target question is NO, s is NOT prime
If s = 47, the answer to the target question is YES, s IS prime
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that s can equal 1, 3, 7 or 21
Statement 2 tells us that s can equal 1 or 47
Since BOTH statements must be true, it MUST be the case that s = 1
Since s = 1, the answer to the target question must be NO, s is NOT prime
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

[Jeff@TargetTestPrep]

If s is a positive integer, is s prime?

(1) 21/s is an integer
(2) 47/s is an integer

Statement One Alone:

21/s is an integer.

We see that s can be 1, 3, 7, or 21. If s is 3 or 7, then s is a prime. However, if s is 1 or 21, then s is not a prime.

Statement one alone is not sufficient.

Statement One Alone:

47/s is an integer.

We see that s can be 1 or 47. If s is 47, then s is a prime. However, if s is 1, then s is not a prime.

Statement two alone is not sufficient.

Statements One and Two Together:

Using both statements, we see that s must be 1, and 1 is not a prime. Both statements together are sufficient.

Answer: C