Is m not = n?

[jenniferdpitts]

Is m not = n?

1) m + n < 0
2) mn < 0

I thought the answer was D, but GMAT says it is B.

[rchitta]

a) m + n < 0

=> m < -n (INSUFFICIENT)

which does not reveal much because
if m and n are both equal to -1 then m + n < 0 and m == n
but if m and n are -2 and -1 then m + n < 0 and m != n (not equal to)

So, this is a MAYBE case.

b) mn < 0 (SUFFICIENT)
=> (m != 0 and n !=0 and either m < 0 OR n < 0 BUT NOT both)
which means m != n (A +ve number cannot be equal to a -ve number)

So the answer is B

[RonPurewal]

hi - please call the statements (1) and (2), not (a) and (b), since that's what they're called on the exam. thanks. (this is important - i'm not just nit-picking - since (a) and (b) refer to answer choices, not statements.)

m + n < 0

it's pretty easy to find a YES and a NO here.
if m and n are the same negative number (such as -1 and -1), then that's a NO.
if m and n are different (such as -1 and -2), then that's a YES.
insufficient.

mn < 0
=> (m != 0 and n !=0 and either m < 0 OR n < 0 BUT NOT both)

this is a correct analysis, but you should just realize (by memorization, most likely) that "mn < 0" means "m and n have OPPOSITE SIGNS".
one of them is positive; the other is negative.
this is not the kind of thing on which you should have to think through a complex statement filled with logical operators, such as the one above.

if m and n have opposite signs, then they aren't equal, so this is sufficient.