topmbaseeker wrote:
Is x² – y² a positive number?
(1) x – y is a positive number.
(2) x + y is a positive number.
The key to answering this question is the first recognize that x² – y² = (x + y)(x - y)
This allows us to rephrase our
target question as follows:
Target question: Is (x + y)(x - y) a positive number? Statement 1: x – y is a positive numberHere we know that (x - y) is positive, but we know nothing about (x + y)
To see what I mean, consider these two possible cases that satisfy statement 1:
Case a: x = 2 and y = 1. In this case, (x + y)(x - y) = (2 + 1)(2 - 1) = 3. So, the answer to the target question is
YES, (x + y)(x - y) IS a positive numberCase b: x = 1 and y = -2. In this case, (x + y)(x - y) = (1 + (-2))(1 - (-2)) = -3. So, the answer to the target question is
NO, (x + y)(x - y) is NOT a positive numberSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x + y is a positive number.Here we know that (x + y) is positive, but we know nothing about (x - y)
Consider these two possible cases that satisfy statement 2:
Case a: x = 2 and y = 1. In this case, (x + y)(x - y) = (2 + 1)(2 - 1) = 3. So, the answer to the target question is
YES, x² – y² IS a positive numberCase b: x = -1 and y = 2. In this case, (x + y)(x - y) = ((-1) + 2)((-1) - 2) = -3. So, the answer to the target question is
NO, x² – y² is NOT a positive numberSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that (x - y) is POSITIVE
Statement 2 tells us that (x + y) is POSITIVE
So, (x + y)(x - y) = (POSITIVE)(POSITIVE) = POSITIVE
The answer to the target question is
YES, x² – y² IS a positive numberSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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