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.
If s is a positive integer, is s prime?
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- Brent@GMATPrepNow
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Target question: Is s prime?VJesus12 wrote:If s is a positive integer, is s prime?
(1) 21/s is an integer
(2) 47/s is an integer
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
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Statement One Alone:VJesus12 wrote:If s is a positive integer, is s prime?
(1) 21/s is an integer
(2) 47/s is an integer
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
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