Practice GMAT Data Sufficiency Question
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If the product of X and Y is a positive number, is the sum of X and Y a negative number?
 X > Y^{5}
 X > Y^{6}
Correct Answer: B
 There are two possible cases (or conditions) under which the product of X and Y could be positive:
Case (1): Positive(Positive) = Positive
Case (2): Negative(Negative) = Positive 
Evaluate Statement (1) alone.
 Since Y is raised to an odd exponent, the sign of the base (i.e., the sign of Y) is the same as the sign of the entire expression (i.e., the sign of Y^{5}).
 There is no way of distinguishing whether we are in Case (1) or (2) and the answer to the resulting question of whether X + Y is negative can be different depending on the chosen values of X and Y. Consider two examples, one from each case.
 Case (1):
X = 100
Y = 2
XY = (100)(2) = 200 = Positive
X > Y^{5}
X + Y = 100 + 2 = 102 = Positive  Case (2):
X = 10
Y = 2
XY = (10)(2) = 20 = Positive
X > Y^{5}
X + Y = (10) + (2) = 12 = Negative  Since there is no way to determine whether X + Y is positive, Statement (1) is not sufficient.
 Statement (1) is NOT SUFFICIENT.

Evaluate Statement (2) alone.
 Y^{6} must be a positive number since, even if Y were negative, raising it to an even exponent would make the entire quantity positive.
 Substituting this into the information given in Statement (2):
X > Y^{6}
X > (positive number)
X must be positive since any number that is larger than a positive number is itself positive.  Since X is positive, in order for XY to be positive, Y must also be positive (i.e., we are dealing with Case (1) from above). Consequently, a positive number (i.e., X) plus a positive number (i.e., Y) must itself be positive.
X + Y = ?
Positive + Positive = Positive
We can definitively answer "no" to the original question.  Statement (2) is SUFFICIENT.
 Since Statement (1) alone is NOT SUFFICIENT but Statement (2) alone is SUFFICIENT, answer B is correct.
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