Mechmeera wrote:source Kaplan
x is a positive integer and (x − 1) is prime. Is x a prime number?
(1) x + 2 is prime.
(2) x + 1 is not prime.
List options for x-1:
x-1 = 2, 3, 5, 7, 11, 13, 15, 17...
Adding 1 to each value in the list, we get the following options for x:
x = 3, 4, 6, 8, 12, 14, 16, 18...
Notice that x=3 is the only ODD option for x.
Statement 1: x+2 is prime
Of the options for x, only x=3 satisfies the constraint that x+2 is prime:
3+2 = 5.
Since the remaining options for x are even, each will yield an EVEN -- and thus, NONPRIME -- value for x+2.
Thus, x=3.
SUFFICIENT.
Statement 2: x+1 is not prime
It's possible that x=3, since 3+1 = 4, which is not prime.
It's possible that x=5, since 5+1 = 6, which is not prime.
Since x can be different values, INSUFFICIENT.
The correct answer is
A.
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