Practice GMAT Data Sufficiency Question
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If x and y are positive integers, is the following cube root an integer?
 x = y^{2}(y1)
 x = 2
Correct Answer: A

Evaluate Statement (1) alone.
 Substitute the value of x from Statement (1) into the equation and manipulate it algebraically.
 Since the question says that y is a positive integer, you know that the cube root of y^{3}, which equals y, will also be a positive integer. Statement (1) is SUFFICIENT.
 Substitute the value of x from Statement (1) into the equation and manipulate it algebraically.

Evaluate Statement (1) alone (Alternative Method).
 For the cube root of a number to be an integer, that number must be an integer cubed. Consequently, the simplified version of this question is: "is x + y^{2} equal to an integer cubed?"
 Statement (1) can be rearranged as follows:
x = y^{3}  y^{2}
y^{3} = x + y^{2}
Since y is an integer, the cube root of y^{3}, which equals y, will also be an integer.  Since y^{3} = x + y^{2}, the cube root of x + y^{2} will also be an integer. Therefore, the following will always be an integer:
 Statement (1) alone is SUFFICIENT.

Evaluate Statement (2) alone.
 Statement (2) provides minimal information. The question can be written as: "is the following cube root an integer?"
 If y = 4, x + y^{2} = 2 + 4^{2} = 18 and the cube root of 18 is not an integer. However, if y = 5, x + y^{2} = 2 + 5^{2} = 27 and the cube root of 27 is an integer. Statement (2) is NOT SUFFICIENT.
 Statement (2) provides minimal information. The question can be written as: "is the following cube root an integer?"
 Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
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