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 8x^{3} = 27y^{3}
 4x^{2} = 9y^{2}

Evaluate Statement (1) alone.
 Take the cube root of both sides:
8x^{3} = 27y^{3}
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.
 Take the cube root of both sides:

Evaluate Statement (2) alone.
 Take the square root of both sides:
4x^{2} = 9y^{2}
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 > 4x^{2} = 9y^{2}
Let x = 3 and y = 2 > 4x^{2} = 9y^{2}
Let x = 3 and y = 2 > 4x^{2} = 9y^{2}
Let x = 3 and y = 2 > 4x^{2} = 9y^{2}  In the four examples above, although 4x^{2} = 9y^{2}, there is no consistent ratio of 2x to y since the negative numbers cause ratios to be negative. Consequently, Statement (2) is NOT SUFFICIENT.
 Take the square root of both sides:
 Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
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