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If x and y are positive integers, is x^2*y^2 even ?

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If x and y are positive integers, is x^2*y^2 even ?

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If x and y are positive integers, is x^2*y^2 even ?

(1) x + 5 is a prime number

(2) y + 1 is a prime number

OA A

Source: Magoosh

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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

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