rishianand7 wrote:If x and y are positive, is x^3 > y?
(1) x^(1/2) > y
(2) x > y

Target question: Is x^3 > y?

Statement 1: x^(1/2) > y
Aside: x^(1/2) = √x
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1/4 and y = 1/5 (since 1/4^(1/2) = 1/2, and 1/2 is greater than 1/5). In this case x^3 is less than y
Case b: x = 4 and y = 1 (since 4^(1/2) = 2, and 2 is greater than 1). In this case x^3 is greater than y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1/4 and y = 1/5. In this case x^3 is less than y
Case b: x = 4 and y = 1. In this case x^3 is greater than y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Notice that I used the same values for x and y for both statements. So, if those values yielded NOT SUFFICIENT conclusions for each statement alone, they will yield a NOT SUFFICIENT conclusion for the statement combined.

Answer = E

Cheers,
Brent

Hi rishianand7,

Brent's explanation is spot-on (and it's exactly how I would have explained it).

As you continue to practice DS questions, make sure to think about the "possibilities" implied by the question. This prompt tells us that x and y are POSITIVE, but DOESN'T say that they're integers. This gets me thinking that I should consider BOTH integers and non-integers when attempting to solve. One of the reasons why DS questions appear on the GMAT is because they inherently test the thoroughness of your thinking. If you're not thorough, then you'll miss something. Top B-Schools aren't interested in applicants who "miss" things.

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