If x is a positive integer greater than 1, is x! + x + 1 a prime number?
(1) x < 10
(2) x is odd
OAB
(1) x < 10
(2) x is odd
OAB
HI j_shreyans,
This question is perfect for TESTing VALUES.
We're told that X is a POSITIVE INTEGER greater than 1. We're asked if X! + X + 1 is prime. This is YES/NO question.
Fact 1: X < 10
If X = 2, then 2! + 2 + 1 = 5 and the answer to the question is YES.
If X = 3, then 3! + 3 + 1 = 10 and the answer to the question is NO.
Fact 1 is INSUFFICIENT
Fact 2: X is odd
If X =3, then 3! + 3 + 1 = 10 and the answer to the question is NO.
If X = 5, then 5! + 5 + 1 = 126 and the answer to the question is NO.
From here, it's worthwhile to discuss a Number Property that applies....
Since X is Odd AND greater than1, X! will be EVEN (since the product includes at least 1 even number). Adding X (which is odd) + 1 (which is also odd), the sum MUST BE EVEN. The sum will be divisible by 2, so it will NOT be prime and the answer to the question will ALWAYS BE NO.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
