Is the product of x and y a prime number?

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Is the product of x and y a prime number?

(1) x^2 = 1
(2) y is positive and prime; x is positive but not prime

[spoiler]OA=C[/spoiler].

Why is C the correct answer? 1 is a prime number? I am confused. Help.!!!

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by Brent@GMATPrepNow » Mon Apr 23, 2018 5:42 am

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Gmat_mission wrote:Is the product of x and y a prime number?

(1) x² = 1
(2) y is positive and prime; x is positive but not prime
Target question: Is the product xy a prime number?

Statement 1: x² = 1
This tells us that either x = 1 or x = -1, but it provides NO INFORMATION about y.
Consider these two possible cases:
Case a: x = 1 and y = 3. In this case, xy = (1)(3) = 3, which is prime. So, the answer to the target question is YES, the product xy IS prime
Case b: x = 1 and y = 6. In this case, xy = (1)(6) = 6, which is NOT prime. So, the answer to the target question is NO, the product xy is NOT prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is positive and prime; x is positive but not prime
Let's test some possible cases again...
Case a: x = 1 (aside: 1 is NOT prime) and y = 3. In this case, xy = (1)(3) = 3, which is prime. So, the answer to the target question is YES, the product xy IS prime
Case b: x = 4 and y = 3. In this case, xy = (4)(3) = 12, which is NOT prime. So, the answer to the target question is NO, the product xy is NOT 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 either x = 1 or x = -1
Statement 2 tells us that x is POSITIVE, so we now know that x MUST equal 1
If x = 1, then the product xy = (1)(y) = y
Statement 2 also tells us that y is PRIME, and we just concluded that the product xy = y
This means the product xy MUST BE PRIME
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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