Practice GMAT Data Sufficiency Question
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If x is not zero, is x2 + 2x > x2 + x?
- xodd integer > xeven integer
- x2 + x - 12 = 0
Correct Answer: A
- Simplify the original question by factoring:
x2 + 2x > x2 + x
2x > x
x > 0
Simplified question: is x > 0?
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Evaluate Statement (1) alone.
- When dealing with a number that is raised to an even exponent, it is important to remember that the sign of the base number can be either positive or negative (i.e., if x2 = 16, x = -4 and 4). Moreover, it is important to remember that raising a fraction to a larger exponent makes the resulting number smaller:
(1/2)2 > (1/2)3 > (1/2)4
- There are three possible cases:
Case (1): x < 0
If x were negative, xodd would be negative while xeven would be positive. This would make xodd {=negative} < xeven {=positive}, which is an explicit contradiction of Statement (1). As a result, we know x cannot be negative. Statement (1) is SUFFICIENT. At this point, you should not keep evaluating since you know that Statement (1) provides enough information to answer the question "is x > 0?"
Case (2): 0 < x < 1
In this case, based upon what was shown above, for xodd integer > xeven integer to hold true, odd integer must be less than even integer.
Case (3): x > 1
This case is the opposite of Case (2). In other words, for xodd integer > xeven integer, the odd integer must be greater than the even integer.
- Since Statement (1) eliminates the possibility of x being a negative number, we can definitively answer the question: is x > 0?
- Statement (1) alone is SUFFICIENT.
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Evaluate Statement (2) alone.
- Factor x2 + x - 12 = 0
(x - 3)(x + 4) = 0
x = 3, -4
- Since x can be either positive or negative, Statement (2) is not sufficient.
- Statement (2) alone is NOT SUFFICIENT.
- Since Statement (1) alone is SUFFICIENT but Statement (2) alone is NOT SUFFICIENT, answer A is correct.
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