Odd - even
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Statement one must be sufficient. Any odd integer can be expressed as 2k+1 where k is an integer. Thus x which is equal to an odd +1 can be expressed as 2k+2. The definition of an even integer is an integer that is divisible by 2. 2k+2 must be divisible by 2, since you could divide both terms by 2 or factor a 2 out of both terms. Since x is even, x+1 must be odd. Which is enough information to answer the question.If n is odd, is x +1 odd.
1) x=n+1
2) n=13
Statement 2 tells us that n=13 but tells us nothing about x or a relationships between x and n. Statement 2 is not sufficient.
The answer is A - statement 1 alone is sufficient.
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You're 100% correct, but you made things far more complicated than necessary.gmatutor wrote:Statement one must be sufficient. Any odd integer can be expressed as 2k+1 where k is an integer. Thus x which is equal to an odd +1 can be expressed as 2k+2. The definition of an even integer is an integer that is divisible by 2. 2k+2 must be divisible by 2, since you could divide both terms by 2 or factor a 2 out of both terms. Since x is even, x+1 must be odd. Which is enough information to answer the question.If n is odd, is x +1 odd.
1) x=n+1
2) n=13
Statement 2 tells us that n=13 but tells us nothing about x or a relationships between x and n. Statement 2 is not sufficient.
The answer is A - statement 1 alone is sufficient.
1) x=n+1
or
x + 1 = n + 2
So, x + 1 = odd + 2, which will always be odd: sufficient.
We could have also just reasoned it out:
"I know that n is odd, and I know exactly how far away from n x is on the number line - therefore I can definitely figure out if x is odd or even: sufficient."
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