Odd - even

If n is odd, is x +1 odd.

1) x=n+1
2) n=13

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.

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.

gmatutor wrote:

If n is odd, is x +1 odd.

1) x=n+1
2) n=13

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.

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.

You're 100% correct, but you made things far more complicated than necessary.

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."

Thnx. Even I chose A for the reason that n is odd so n+1 is even so n+1+1 will be odd but OA says B so i just wanted to clarify. I guess the OA is incorrect.