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If x is not zero, is x^{2} + 2x > x^{2} + x?
 x^{odd integer} > x^{even integer}
 x^{2} + x  12 = 0
Correct Answer: A
Simplify the equation and question to: is x > 0?
 Simplify the original question by factoring:
x^{2} + 2x > x^{2} + x
2x > x
x > 0
Simplified question: is x > 0? 
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 x^{2} = 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, x^{odd} would be negative while x^{even} would be positive. This would make x^{odd} {=negative} < x^{even} {=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 x^{odd integer} > x^{even 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 x^{odd integer} > x^{even 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.
 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 x^{2} = 16, x = 4 and 4). Moreover, it is important to remember that raising a fraction to a larger exponent makes the resulting number smaller:

Evaluate Statement (2) alone.
 Factor x^{2} + 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.
 Factor x^{2} + x  12 = 0
 Since Statement (1) alone is SUFFICIENT but Statement (2) alone is NOT SUFFICIENT, answer A is correct.