REINE wrote:Solve

Hi REINE,

While posting a question you should write the prompt or some meaningful reference in the subject line. Also it is advisable that you write the source of the question and the correct answer.

Anyway, let's come to the question.

Question: Is x < y?

Statement 1: y = x^(-3)

=> y = 1/x^3

Case 1: Say x = -2 => y = 1/(-2)^3 = -1/8

We see that -2 < -1/8 or x < y. The answer is Yes.

Case 2: Say x = -1/2 => y = 1/(-1/2)^3 = -8

We see that -1/2 > -8 or x > y. The answer is No. No unique answer.

Statement 2: x < 0

Clearly insufficient. We do not have any information on y.

Statement 1 & 2 together:

For both the cases discussed above, we have x < 0, and they do not render a unique answer. Insufficient.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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Hi REINE,

One of the interesting aspects of DS questions is that you don't have to deal with the two Facts in the order that they're provided (meaning that you can 'jump' to Fact 2 first if you choose). By working with the information in a different 'order', you can sometimes save time on the overall amount of work that you have to do to answer the question.

Here, we're asked if X is less than Y. This is a YES/NO question. Clearly, to answer this question, we need information on BOTH variables (either individually or how they relate to one another).

2) X < 0

This tells us nothing about the value of Y, so it's clearly INSUFFICIENT. However, it gets me thinking that we might need to focus on NEGATIVE values of X to get to the solution....

1) Y = X^(-3)

IF....
X = -1, then Y = (-1)^(-3) = 1/(-1)^3) = 1/-1 = -1
Here, X and Y are EQUAL, so the answer to the question is NO.

X = -2, then Y = (-2)^(-3) = 1/(-2)^3) = 1/-8 = -1/8
-2 IS less than -1/8, so the answer to the question is YES.
Fact 1 is INSUFFICIENT

Since we know that the answer to the question changes depending on the relative NEGATIVE value of X, there's no more work to be done. We already have two TESTs that 'fit' both Facts.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich