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If a, b, and c are all integers, is ab + bc + ca + a^2 odd?
(1) a + 2b + c is even.
(2) abc is odd.
Okay. So upfront I'm bummed about the question. Not a lot of simplification to be done here. There are too many iterations to consider. So I just know I'm dealing with even/odd, and I'm going into the statements.
In statement 1, I know 2b is even, so I know a + c is even, which means a and b are either both even or both odd.
If both are even, every integer in that question will be even (since each is multiplied by either a or c). So the sum will be even.
If both A,C are odd. AC + A^2 will be even (since each individually will be odd). Then AB + BC will match parity (even/odd) as well. So the sum will be even.
Statement 1 is sufficient.
Statement 2 tells us every integer is odd, so each part of the sum will be odd. The sum of 4 odd numbers is even. So statement 2 is sufficient.
The answer is D.
Some lessons:
--Know you're basic even and odd rules cold. odd*odd = odd, even*integer = even; odd + odd = even, even + even = even, even + odd = odd.
--TEST EACH CASE FULLY. It would be too quick in statement 1 to say 'well I know either a and c are both even or both odd, but I don't know which, and I don't know anything about b, so insufficient.' This question, and many like it, are very cleverly designed so that different possibilities up front actually trickle down to the same answer to the question.
--The trickiest part of statement 1 was the recognition that ab + bc must be even if a and c are both odd. This is because either b is even, and each is even, or b is odd, and it's odd + odd. You could also factor out b to get b(a+c), and a+c will be even.
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REED ARNOLDManhattan Prep GMAT InstructorVideo: The 24 Things Every GMAT Studier Needs to DoThe Studying Verbal Starter Kit (...That's much more than a 'starter kit')The PERFECT data sufficiency question:On a three person bench, George sits in the middle of Alice and Darryl. If Alice is married, is an unmarried person sitting next to a married person?
1). George is married.
2). Darryl is not married.
Answer: