# Practice GMAT Data Sufficiency Question

If x and y are integers, what is the ratio of 2x to y?
1. 8x3 = 27y3
2. 4x2 = 9y2
 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. Take the cube root of both sides:
8x3 = 27y3
2x = 3y
2. Rearrange in order to find a ratio of 2x to y.
2x/y = 3
3. Consequently, 2x is 3 times y.
4. Statement (1) alone is SUFFICIENT.
2. Evaluate Statement (2) alone.
1. Take the square root of both sides:
4x2 = 9y2
2x = 3y
2x/y = 3
2. However, we must also consider that in taking the square root, a negative root is possible. To illustrate this, consider the following example:
Let x = 3 and y = 2 --> 4x2 = 9y2
Let x = -3 and y = 2 --> 4x2 = 9y2
Let x = -3 and y = -2 --> 4x2 = 9y2
Let x = 3 and y = -2 --> 4x2 = 9y2
3. In the four examples above, although 4x2 = 9y2, there is no consistent ratio of 2x to y since the negative numbers cause ratios to be negative. Consequently, Statement (2) is NOT SUFFICIENT.
3. Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.