Knewton GMAT Instructor
Joined: 04 Jan 2011
Posts: 50
Given Kudos: 0
Location: NY, NY
Concentration: Sentence Correction, Critical Reasoning, Reading Comprehension, Problem Solving, Data Sufficiency
Schools:BA New School, PhD Candidate CUNY
Q50 V47
Re: Is 2x + x^2 an integer?
[#permalink]
08 Jan 2011, 17:04
Looking at the prompt:
2x + x^2 can only be an integer if both 2x and x^2 are integers. The only way those can both happen is if x itself is an integer. Certainly, 2x could be an integer with a non-integer value for x (such as 1/2), and x^2 could as well (for values such as sqrt2), but there's no number can do that for both terms. So the question is really asking "Is x an integer?"
Statement (1) should be analyzed in a similar way. Yes, irrational cube-roots could make x^3 an integer, and fractions with a denominator of 3 could make 3x an integer, but the only number that could make BOTH an integer is an integer itself. So, Statement (1) says that "x is an integer," and is therefore Sufficient.
Statement (2), however, only gives us part of this. Sure, x could be an integer, but it could also be a fraction with 2 in the denominator. If x=1/2, the prompt will end up being 1.25, which would be an answer of "No." X might or might not be an integer; this is Insufficient.
Answer: A