Bunuel wrote:
Is x = y?
(1) x² = xy
(2) x² = y²
Target question: Is x = y? Statement 1: x² = xy NOTE: Although it would be nice to divide both sides of the equation by x (to get x = y), we can't do that because it COULD be the case that x = 0, which means we're dividing by 0 (a big No-No)
Instead, we can subtract xy from both sides to get: x² - xy = 0
Factor: x(x - y)
So, EITHER x = 0 OR x - y = 0
So, it COULD be the case that x = 0 and y = 1, in which case the answer to the target question is
NO, x does not equal yOr, it COULD be the case that x = 1 and y = 1, in which case the answer to the target question is
YES, x equals ySince we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x² = y²Subtract y² from both sides to get: x² - y² = (x + y)(x - y) = 0
So, EITHER x + y = 0 OR x - y = 0
So, it COULD be the case that x = -1 and y = 1, in which case the answer to the target question is
NO, x does not equal yOr, it COULD be the case that x = 1 and y = 1, in which case the answer to the target question is
YES, x equals ySince we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that EITHER x = 0 OR x - y = 0
Statement 2 tells us that EITHER x + y = 0 OR x - y = 0
Since both statements must be true, it MUST be the case that x - y = 0, which means the answer to the target question is
YES, x equals ySince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent