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(1) √x > y
If x = 4, y = 1, then 2 > 1 and x^3 = 4^3 = 64 > 1. Here x^3 > y.
If x = 1/4, y = 1/3, then 1/2 > 1/3 and x^3 = 1/64. Here x^3 < y.
No definite answer; NOT sufficient.

(2) x > y
If x = 4, y = 1, then 4 > 1 and x^3 = 4^3 = 64 > 1. Here x^3 > y.
If x = 1/2, y = 1/3, then 1/2 > 1/3 and x^3 = 1/8. Here x^3 < y.
No definite answer; NOT sufficient.

Combining (1) and (2), If x = 4, y = 1, then √x > y and x > y. Here x^3 > y.
If x = 9/16, y = 1/2, then √x = 3/4. Here √x > y and x > y. Here x^3 < y.
No definite answer; NOT sufficient.

The correct answer is E.

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Anurag Mairal, Ph.D., MBA
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For a solution to a similar problem, check here:

http://www.beatthegmat.com/ds-inequalities-strategy-help-please-t102609.html

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