BTGmoderatorDC wrote:If x and y are positive integers, is x²y² even ?
(1) x + 5 is a prime number
(2) y + 1 is a prime number
OA A
Source: Magoosh
Target question: Is x²y² even ?
Statement 1: x + 5 is a prime number
So, x+5 is a prime number greater than 5, which means x+5 must be ODD (since 2 is only even prime)
If x+5 is ODD, then
x must be EVEN
If x is EVEN, then x²y² must be even
The answer to the target question is
YES, x²y² IS even
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: y + 1 is a prime number
There are several scenarios that satisfy statement 2. Here are two:
Case a: x = 0 and y = 1. Notice that y+1 = 1+1 = 2, which is prime. In this case, x²y² = 0²1² = 0. So, the answer to the target question is
YES, x²y² IS even
Case b: x = 1 and y = 1. Notice that y+1 = 1+1 = 2, which is prime. In this case, x²y² = 1²1² = 1. So, the answer to the target question is
NO, x²y² is NOT even
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
