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

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Joined: 23 Mar 2014
Posts: 16
If p>5 and q>-2, then which of the following is always true?  [#permalink]

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Updated on: 04 Jan 2018, 18:27
1
4
00:00

Difficulty:

65% (hard)

Question Stats:

52% (01:47) correct 48% (01:27) wrong based on 107 sessions

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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

Originally posted by Rocky1304 on 03 Jan 2018, 22:53.
Last edited by Bunuel on 04 Jan 2018, 18:27, edited 1 time in total.
Edited the question.
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Joined: 02 Sep 2009
Posts: 52296
If p>5 and q>-2, then which of the following is always true?  [#permalink]

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04 Jan 2018, 00:41
2
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

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.

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Re: If p>5 and q>-2, then which of the following is always true?  [#permalink]

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04 Jan 2018, 10:39
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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Re: If p>5 and q>-2, then which of the following is always true?  [#permalink]

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16 Apr 2018, 00:50
+1 for option C.
In addition to solutions above , one could also arrive at C in the following way:
-p<-5; -2q<4
-p-2q<-1 --> -p<2q-1 which means , -p<2q.
Hence option C
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Re: If p>5 and q>-2, then which of the following is always true? &nbs [#permalink] 16 Apr 2018, 00:50
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