If d and g are integers, is d + g an even integer? (1) d is an even

Official Explanation

On the GMAT, we can't assume that numbers are integers, but we are told that d and g are integers. The question is whether they sum to an even integer. Well, before looking at the statements, we know that d + g will be an integer: if you add any two positive or negative whole numbers, you'll get a positive or negative whole number (or zero). The question is whether the sum is an even integer. Let's turn to the statements--of course, examining them separately first. We can examine Statement (1) by cases. By the statement, g could be even or odd, allowing two cases. In the former case, d + g is even; in the latter case, it's odd. Therefore, our answer to the question being asked is not consistent in all cases. Statement (1) is insufficient. On to Statement (2), which we can also examine by cases. Statement (2) allows d and g to be anything, as long as they are integers and they are equal to each other. Say d = 1 ; then d + g and is even. Say d = 2; then d + g is even. Examining more cases, we can convince ourselves that d + g will always be even when Statement (2) is true. We note, further, that if d = g, then d + g = 2d, which means that d + g always has two as a factor (since it's 2 times g), which means that d + g must always be even. Statement (2) is sufficient.

The correct answer is (B).