from vw = 16, we can understand that v and w are of same sign. (i.e both can be positive or negative). so we can`t answer using this alone.

from v + w = -10. we can understand that one of them or both should be negative for the sum to be -ve. so we can`t answer using this alone.

when we combine both the options, form the 1st option we can understand that both should be of same sign. From 2nd option we can get that they are negative. which means v < 0. so we can answer the question v > 0? with no.

hence it is c

vk_vinayak wrote:If v ≠ 0, is v > 0 ?

(1) vw = 16

(2) v + w = -10

[spoiler]OA: C[/spoiler]

Anurag's is the preferred method here (fast and accurate).

However, if you didn't see that fast/logical approach, here's the longer/algebraic approach.

Target question: Is v > 0 ?

Statement 1: vw = 16
Lots of possible values for v and w. Here are two.
case a: v = 1, w = 16, which means v is greater than zero
case b: v = -1, w = -16, which means v is not greater than zero
So, statement 1 is NOT SUFFICIENT

Statement 2: v + w = -10
Lots of possible values for v and w. Here are two.
case a: v = 1, w = -11, which means v is greater than zero
case b: v = -1, w = -9, which means v is not greater than zero
So, statement 2 is NOT SUFFICIENT

Statements 1 + 2:
Take v + w = -10 and solve for w to get: w = -10 - v
Take vw = 16 and replace w with -10 - v to get: v(-10 - v) = 16
Solve for v...
v(-10 - v) = 16
-10v - v^2 = 16
v^2 + 10v + 16 = 0
(v+2)(v+8) = 0
v = -2 or -8
Here, we can see that v is definitely not greater than zero

Answer = C

Cheers,
Brent