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If p,q,r are non-zero numbers, is pq/r>0?

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Manager
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Joined: 25 Dec 2018
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GMAT 1: 490 Q47 V13
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If p,q,r are non-zero numbers, is pq/r>0?  [#permalink]

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New post 05 Jan 2019, 10:06
1
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

89% (00:55) correct 11% (01:41) wrong based on 28 sessions

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If p,q,r are non-zero numbers, is pq/r>0?

1. p+q>0
2. rq>0
Manager
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Posts: 69
Location: India
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Re: If p,q,r are non-zero numbers, is pq/r>0?  [#permalink]

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New post 05 Jan 2019, 17:05
3
If p,q,r are non-zero numbers, is pq/r>0?

For pq/r to be greater than zero any either all should be positive or two of then can be negative (given non-zeros)
We need to know sign of all p,q,r to answer the question

1. p+q>0
We can't predict the sign of p and q,
1) p,q both may be positive
2) p >q and p is positive and q is negative
3) p < q and p - Negative , q - positive
Insufficient

2. \(rq>0\)
q,r have the same sign either positive OR negative, but resulting in a positive values
Still if P is negative,\(pq/r < 0\)
if P is positive, \(pq/r > 0\)
Insufficient

(1) and (2) together,
Still insufficient, as we don't have enough information about the sign of all the variables

Option E is correct
Manager
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Joined: 25 Dec 2018
Posts: 86
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GMAT 1: 490 Q47 V13
GPA: 2.86
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Re: If p,q,r are non-zero numbers, is pq/r>0?  [#permalink]

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New post 06 Jan 2019, 03:38
Dare Devil wrote:
If p,q,r are non-zero numbers, is pq/r>0?

For pq/r to be greater than zero any either all should be positive or two of then can be negative (given non-zeros)
We need to know sign of all p,q,r to answer the question

1. p+q>0
We can't predict the sign of p and q,
1) p,q both may be positive
2) p >q and p is positive and q is negative
3) p < q and p - Negative , q - positive
Insufficient

2. \(rq>0\)
q,r have the same sign either positive OR negative, but resulting in a positive values
Still if P is negative,\(pq/r < 0\)
if P is positive, \(pq/r > 0\)
Insufficient

(1) and (2) together,
Still insufficient, as we don't have enough information about the sign of all the variables

Option E is correct


Thanks for the detailed explanation.
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Re: If p,q,r are non-zero numbers, is pq/r>0?  [#permalink]

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New post 06 Jan 2019, 06:21
akurathi12 wrote:
If p,q,r are non-zero numbers, is pq/r>0?

1. p+q>0
2. rq>0

\(p,q,r\,\, \ne 0\)

\(\frac{{pq}}{r}\,\,\mathop > \limits^? \,\,0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\boxed{\,\,?\,\,:\,\,pq\,\,{\text{and}}\,\,r\,\,{\text{have}}\,\,{\text{same}}\,\,{\text{signs}}\,\,}\)


\(\left( {1 + 2} \right)\,\,\left\{ \matrix{
\,p + q > 0 \hfill \cr
\,r\,\,{\rm{and}}\,\,q\,\,{\rm{same}}\,\,{\rm{signs}} \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {p,q,r} \right) = \left( {1,1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {p,q,r} \right) = \left( { - 1,2,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{E}} \right)\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: If p,q,r are non-zero numbers, is pq/r>0? &nbs [#permalink] 06 Jan 2019, 06:21
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