# Practice GMAT Data Sufficiency Question

If x and y are positive integers, is the following cube root an integer?
1. x = y2(y-1)
2. x = 2
 A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
1. Evaluate Statement (1) alone.
1. Substitute the value of x from Statement (1) into the equation and manipulate it algebraically.

2. Since the question says that y is a positive integer, you know that the cube root of y3, which equals y, will also be a positive integer. Statement (1) is SUFFICIENT.
2. Evaluate Statement (1) alone (Alternative Method).
1. 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 + y2 equal to an integer cubed?"
2. Statement (1) can be re-arranged as follows:
x = y3 - y2
y3 = x + y2
Since y is an integer, the cube root of y3, which equals y, will also be an integer.
3. Since y3 = x + y2, the cube root of x + y2 will also be an integer. Therefore, the following will always be an integer:
4. Statement (1) alone is SUFFICIENT.
3. Evaluate Statement (2) alone.
1. Statement (2) provides minimal information. The question can be written as: "is the following cube root an integer?"
2. If y = 4, x + y2 = 2 + 42 = 18 and the cube root of 18 is not an integer. However, if y = 5, x + y2 = 2 + 52 = 27 and the cube root of 27 is an integer. Statement (2) is NOT SUFFICIENT.
4. Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.