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

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Joined: 25 Dec 2018
Posts: 148
Location: India
GMAT 1: 490 Q47 V13
GPA: 2.86
If p,q,r are non-zero numbers, is pq/r>0?  [#permalink]

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05 Jan 2019, 11:06
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86% (01:10) correct 14% (01:28) wrong based on 41 sessions

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

1. p+q>0
2. rq>0
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Joined: 01 May 2017
Posts: 82
Location: India
Re: If p,q,r are non-zero numbers, is pq/r>0?  [#permalink]

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05 Jan 2019, 18:05
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
Joined: 25 Dec 2018
Posts: 148
Location: India
GMAT 1: 490 Q47 V13
GPA: 2.86
Re: If p,q,r are non-zero numbers, is pq/r>0?  [#permalink]

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06 Jan 2019, 04:38
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.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937
Re: If p,q,r are non-zero numbers, is pq/r>0?  [#permalink]

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06 Jan 2019, 07:21
1
1
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?   [#permalink] 06 Jan 2019, 07:21
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