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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
A) pq > -10
B) pq < -10
C) -p < 2q
D) -p > 2q
E) pq > 10
04 Jan 2018, 01:41
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Rocky1304
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
A) pq > -10
B) pq < -10
C) -p < 2q
D) -p > 2q
E) pq > 10
If p > 5 and q > -2, then which of the following is always true?
A) pq > -10. If p = 100 and q = -1, then pq = -100 < -10. So, this option is not always true.
B) pq < -10. If p = 100 and q = 0, then pq = 0 > -10. So, this option is not always true.
C) -p < 2q. This is the same as p + 2q > 0.
We have p > 5 and 2q > -4 (multiplied by 2)
Add: p + 2q > 1. So, p + 2q is greater than 0.
So, this option is always true.
D) -p > 2q. Above we got that -p < 2q, so this is not true.
E) pq > 10. If p = 100 and q = 0, then pq = 0 < 10. So, this option is not always true.
Answer: C.
04 Jan 2018, 11:39
Kudos
Bookmarks
Rocky1304
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
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.
