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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