bibha 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 primeCase 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 primeSince 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 primeLet'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 primeCase 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 primeSince 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 1If 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 = yThis means

the product xy MUST BE PRIMESince we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,

Brent

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