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# If p/q > 5, is q < 2?

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If p/q > 5, is q < 2? [#permalink]

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27 Feb 2010, 14:26
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55% (hard)

Question Stats:

66% (02:09) correct 34% (01:35) wrong based on 48 sessions

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If p/q > 5, is q < 2?

(1) q > 1
(2) -2p > 20
[Reveal] Spoiler: OA

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Last edited by Bunuel on 15 Oct 2013, 09:04, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Pr 1012 - If p/q > 5 [#permalink]

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27 Feb 2010, 21:42
If p/q > 5, is q<2?

1. q>1
Not sufficient. No infor about p
2. -2p>20
-p>10
p<-10 and p/q>5, so q is negative for p/q to be positive.
Sufficient

B
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Re: Pr 1012 - If p/q > 5 [#permalink]

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01 Mar 2010, 10:12
IMO B

given that
p/q >5
=> q < p/5

stmt 1 => 1 < q < p/5
Not sufficient since we dont know the value of p

stmt 2 => -2p > 20
=> -p > 10
=> p < -10
from Q. stem q > p/5
=> q < -10/5
=> q < -2 < 2 ----- Sufficient
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Re: Pr 1012 - If p/q > 5 [#permalink]

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01 Mar 2010, 11:40
Well, as per ur feedback, stmt 2 tells q<-2 while stmt 1 says q >1. I think its contradictory!! In GMAT its not possible.

Any thoughts??

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Re: Pr 1012 - If p/q > 5 [#permalink]

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03 Mar 2010, 12:20
It is true that the two statements will never contradict each other. However in this case you must also consider that 'q' can have multiple ranges of values

i.e.: q>1 and q<-2. If q>1, then q=1.5, 2, 3, 4,5, etc., thus statement 1 is INSUFFICENT
but when q<-2, you have a clear and decisive answer to this yes/no DS question.
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Re: If p/q > 5, is q<2? 1. q>1 2. -2p>20 SOURCE - PR [#permalink]

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15 Oct 2013, 06:41
jeeteshsingh wrote:
If p/q > 5, is q<2?

1. q>1
2. -2p>20

SOURCE - PR 1021

Hi all, I'll give this one a shot. So here we go.

If p/q > 5, is q<2?

Statement 1- Clearly Insuff
Statament 2 - Now couple of things on inequalities

First of all, p/q > 5, We can multiply both sides by 'q' only because we know that p/q is positive (since it is >5) so then p and q will both have the same sign.
So we have that p>5q
Second, we have -2p>20. Note that in this case since we are dividing both sides by -2, we MUST switch the inequality sign. So p<-10.
Now we need to combine both statements

-10>p>5q
So we have that -10>5q, Hence q<2.

Happy to discuss this nice inequalities problem further
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Re: If p/q > 5, is q < 2? [#permalink]

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15 Oct 2013, 09:14
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Expert's post
If p/q > 5, is q < 2?

Notice that from p/q > 5 it follows that p and q have the same sign

(1) q > 1. If q = 2 and p = 100, then the answer is NO but if q = 1.5 and p = 100, then the answer is YES. Not sufficient.

(2) -2p > 20. Reduce by -2 and flip the sign: p < -10. So, we have that p is negative, thus q is negative too --> q = negative < 2. Sufficient.

Technically answer should be B, as statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

But even though formal answer to the question is B, this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. But the statements above contradict each other:
From (1) we have that q is positive and from (2) we have that q is negative. The statements clearly contradict each other.

So, the question is flawed. You won't see such a question on the test.
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Re: If p/q > 5, is q < 2?   [#permalink] 15 Oct 2013, 09:14
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