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rss GMAT Practice Question (One of Hundreds)
If x and y are integers, what is the ratio of 2x to y?
  1. 8x3 = 27y3
  2. 4x2 = 9y2
Correct Answer: A
Try to find a ratio of x to y. Be aware that taking the square root results in both a positive and a negative solution.
  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.