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
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,
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
; then
and is even. Say
; then
is even.
Examining more cases, we can convince ourselves that
will always
be even when Statement (2) is true. We note, further, that if
, then
, which means that
always has
two as a factor (since it's 2 times g),
which means that
must always
be even. Statement (2) is sufficient.
The correct answer is (B).
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