mindful wrote:Is x < y ?

(1) y = x^-3

(2) x < 0

Since Statement 2 is clearly insufficient on its own -- it offers no information about y -- consider how Statement 2 might affect Statement 1.

Statement 1: y = x˘³
Case 1: x=-1, implying that y = (-1)˘³ = -1.
In this case, x=y, so the answer to the question stem is NO.
Case 2: x=-2, implying that y = (-2)˘³ = -1/8.
In this case, x<y, so the answer to the question stem is YES.

Case 1 satisfies BOTH statements.
In Case 1, the answer to the question stem is NO.
Case 2 satisfies BOTH statements.
In Case 2, the answer to the question stem is YES.
Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.

Thank you v. much. I will appreciate any comments from anyone on the best way to plug numbers in these situations. Personally it seems so cumbersome. In my head I think I need something positive, then something negative. I also start to think what if they are fractions. Then I have to think of a scenario for each. Before I know it I have spent a good deal of time. Any advice?

mindful, plugging in numbers is fine, especially to help understand how a problem works, but it's also good to have a conceptual solution, as you've said. (It helps you feel sure of an answer, and teaches you some math in the process, which is great.)

I'd approach the question like this.

S1 lets us rewrite the question as

Is x < x�³ ?

If x is POSITIVE, the question becomes

Is x� < 1 ?

If x is NEGATIVE, the question becomes

Is x� > 1 ?

So S1 allows us to clarify the question, but we still don't know what we're asking, or what x is.

S2 tells us that x is negative. On its own, who cares?

Taking the two together, we know that we must write the question as "Is x� > 1?" But we still don't know what x is! So we can't solve, and our answer is E.