Is x y? (1) 1/x 1

Question

Is x > y?

(1) 1/x < 1/y
 
(2) 1/x > 1

kk47 · Answer

(1) is not sufficient as we cannot decide from the inequality whether x and y are positive or not.

(2) gives x to be positive and less than 1. But is insufficient to answer the question.

(1,2) gives 0<x<1. Let's take x to be 1/2
=> 1/y > 2
=> y has to be positive, and y < 1/2, or y < x.
Therefore together they are sufficient.

Answer is C.

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sjavvadi · Answer

Statement (1) would be sufficient when we know if x and y are positive or negative.

Statement (2) gives 0<x<1 but nothing about y.

Together we can get the soultion

BillyZ · Answer

Official solution from Veritas Prep. This inequality problem fairly clearly includes the concept of reciprocals, but less conspicuously invokes the concept of positive/negative number properties. With statement 1, the "obvious" cases seem to support that x>y. If you take the statement that \frac{1}{x}<\frac{1}{y} and plug in x=3 and y=2 , that holds with the statement \frac{1}{3}<\frac{1}{2} and means that x>y . And if both variables are negative, the same can hold. For \frac{1}{x} <\frac{1}{y} to hold where x and y are negative, then \frac{1}{x} has to be farther from zero. So that might look like x=−2 and y=−3 , where x is still greater than y. But think of a case where the x term will always be smaller than the y term: where x is negative and y is positive. Then the process of taking reciprocals doesn't matter: \frac{1}{x} is going to still be negative, and \frac{1}{y} is still going to be positive. So in this case, you get the answer "no," that x is not greater than y. So statement 1 is not sufficient, and that is because of the fact that x could be negative while y is positive. Statement 2 alone is certainly not sufficient, as it does not provide enough information about y. You know from this statement that 0

natesalzman · Answer

Is x>y?

(1)  \frac{1}{x} < \frac{1}{y} 
(2)  \frac{1}{x} > 1

Having a problem with the OA. The answer provided is  C 
But they don't consider the possibility of y being a non-integer... I feel like I am probably missing something obvious but it has always been my understanding that one could not assume anything with DS questions.

Bunuel · Answer

To answer your question, please check alternative solution below. Is x>y? (1) \frac{1}{x} < \frac{1}{y} . If x and y have the same sign, then when cross-multiplying we'll get y < x but if x and y have the opposite signs, when cross-multiplying we'll get y > x. Not sufficient. (2) \frac{1}{x} > 1 . Clearly insufficient because we know nothing about y. Though from this statement we can get that x must be positive. (1)+(2) Since from (2) x is positive, then from (1) we'll get that (positive) < 1/y, which would mean that y must also be positive. Therefore, when cross-multiplying \frac{1}{x} < \frac{1}{y} , we'll get y < x. Sufficient. Answer: C.

ScottTargetTestPrep · Answer

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

bumpbot · Answer

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Is x > y? (1) 1/x < 1/y (2) 1/x > 1

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