Rocky1304 wrote:

If p > 5 and q > -2, then which of the following is always true?

A) pq > -10

B) pq < -10

C) -p < 2q

D) -p > 2q

E) pq > 10

p > 5

p = 6, 7, 8, 9, 10, 11, 12, ...

q > -2

q = -1, 0, 1, 2, 3, 4, 5, ...

A) pq > -10

If p = 11, q = -1, then pq = -11. Not always true.

B) pq < -10

If p = 6, q = -1, then pq = -6. Not always true.

E) pq > 10

If p = 6, q = 0, then pq = 0. Not always true.

C) -p < 2q

p is positive. Divide both sides by 2p to get -1/2 < q/p

Looks like it might be true based on some values of p and q we have taken above. Let's hold on to it and check the leftover option.

D) -p > 2q

Divide both sides by 2p to get -1/2 > q/p

If q = -1 and p = 6, we get -1/2 > -1/6 which is not true.

So (C) must always be true. We don't need to worry about non-integer values of p and q.

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