Manhattan GMAT DS

Why can't you say 0 = (2-p)(2-q) = 4-2p-2q+pq

Yes you can.

Therefore, 4=2p+2q-pq

No, the question now becomes is 2p+2q-pq = 4? You can't say it is.

Now,
(1) pq = -8

say p = -4 and q = 2 then
2p + 2q -pq = 2(p+q) -pq = -4 + 8 = 4 meets the condition

say p = 4 and q = -2 then
2p + 2q -pq = 4 + 8 = 12 does not meet the condition.

INSUFF

(2)
-2 – p = q => p + q = -2.

so, 2p+2q-pq = 2(p+q) -pq = -4 - pq

if p = -4, q = 2 then -4 - pq = -4 + 8 = 4 meets the condition.
if p = -6, q = 4 then -4 - pq = -4 -24 = -28 does not meet the condition.

INSUFF

Together...
pq = -8 and p+q = -2 => p = -4 or p =2 and q = 2 or q=-4. These values do satisfy the condition.

Ans (C).

Ahh..it is not a given...it is the question...how fundamental...I probably should read the sections at the beginning of the study books..THX