Bunuel wrote:
Is x > y?
(1) 1/x < 1/y
(2) 1/x > 1
We need to determine whether x is greater than y.
Statement One Alone:
1/x < 1/y
Statement one alone is not sufficient to answer the question. We see that if x = -2 and y = 4, then x is less than y. On the other hand, if x = 1/2 and y = 1/4, then x is greater than y.
Statement Two Alone:
1/x > 1
Since we don’t know anything about y, statement two is not sufficient to answer the question.
Statements One and Two Together:
Using the information from statement two, we see that x must be positive. Thus, we can reciprocate both sides of the inequality and switch the inequality sign:
1/x > 1
x < 1
Using the information from statement one, we see that y has to be positive if x is positive. Thus, we can reciprocate both sides of the inequality and switch the inequality sign:
1/x < 1/y
x > y
We see that x is indeed greater than y.
Answer: C
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