Practice GMAT Data Sufficiency Question
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If x and y are integers, what is the ratio of 2x to y?
- 8x3 = 27y3
- 4x2 = 9y2
Correct Answer: A
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Evaluate Statement (1) alone.
- Take the cube root of both sides:
8x3 = 27y3
2x = 3y
- Rearrange in order to find a ratio of 2x to y.
2x/y = 3
- Consequently, 2x is 3 times y.
- Statement (1) alone is SUFFICIENT.
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Evaluate Statement (2) alone.
- Take the square root of both sides:
4x2 = 9y2
2x = 3y
2x/y = 3
- 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
- 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.
- Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
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