Bunuel wrote:
Is x < y?
(1) 1/x < 1/y
(2) x/y < 0
Target question: Is x < y? Statement 1: 1/x < 1/y Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = -1 and y = 1. In this case, the answer to the target question is
YES, x is less than yCase b: x = 2 and y = 1. In this case, the answer to the target question is
NO, x is not less than ySince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x/y < 0 This tells us that x and y have OPPOSITE signs, but we don't have any information about which variable is positive and which variable is negative.
So, there's no way to tell whether
x < ySince we can't answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 2 tells us that x and y have OPPOSITE signs
Statement 1 tells us that 1/x < 1/y. If x and y have OPPOSITE signs, then we can be certain that x is NEGATIVE and y is POSITIVE.
Take: 1/x < 1/y
Multiply both sides by x to get: 1 > x/y
[since we multiplied both sides by a NEGATIVE value, we REVERSED the direction of the inequality symbol] Multiply both sides by y to get:
y > xPerfect! The answer to the target question is
YES, x is less than ySince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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