Do you need an explanation, or are you just sharing the problem?

If you'd like help with the question, please let us know what about it is causing you trouble -- what answer you thought it was and why. That'll help us know what you need to know.

hello Laura, Thanks for your reply. I needed an explanation for this. I thought it was E. I found c could be both even or odd combining both 1 & 2. Can you help?

Laura GMAT Tutor wrote:Do you need an explanation, or are you just sharing the problem?

If you'd like help with the question, please let us know what about it is causing you trouble -- what answer you thought it was and why. That'll help us know what you need to know.

The answer is C.

Let us assume c=1 and d+1 =1.

I have marked y where the expression satisfies the statement


1) The last 3 rows produce the result c(d+1) even

c could be odd or even.

2) the first and the last 2 rows produce (c+2)(d+4) even. c could odd or even.Insufficient

Combining 1 and 2.

Only last 2 rows satisfy and in each case c is even.Hence sufficient

If c and d are integers, is c even?

1. c(d+1) is even
2. (c+2)(d+4) is even

Focus on what must be true and can be deduced. Keep in mind that (even)(any integer) = even, and (odd)(odd) = odd.

From statement (1), if c(d+1) is even, then it must be true that either c = even or (d+1)=even, or possibly both.
d+1=even means that d would be odd.

So from statement 1, there are two possibilities, which aren't mutually exclusive (meaning they could both be happening at the same time):
either c= even (and it doesn't matter what d is) or d=odd (and it doesn't matter what c is).

It's possible that c is even. It's possible that c is odd. That's insufficient to answer the original question.

From statement (2), it must be true that (c+2) is even or (d+4) is even.
If (c+2) = even, then c= even. If (d+4) = even, then d= even.
From statement (2), either c=even (with d being even or odd), or d=even (with c being even or odd), or both. It's possible that c is even, it's possible that c=odd. That's insufficient to answer the original question.

Together, it may be a big confusing to think through all of this. Let's organize it this way.

Either d=odd or d=even. That's for sure.
If d=odd, then according to statement (2), c would HAVE to be even. That's because according to statement (2), at least one of the two variables HAS to be even. [Note that d=odd and c=even also satisfies statement (1).]

If d=even, the according to statement (1), c would HAVE to be even. That's because according to statement (1), if d=even, then c would have be even in order for statement (1) to hold true. [Note that d=even and c=even also satisfies statement (2).]

Therefore in both scenarios, c has to be even.

Hope that helps.