Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 10:27 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If p,q,r are non-zero numbers, is pq/r>0?

Author Message
TAGS:

### Hide Tags  G
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]

### Show Tags

3 00:00

Difficulty:   15% (low)

Question Stats: 86% (01:10) correct 14% (01:28) wrong based on 41 sessions

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

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

### Show Tags

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  G
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]

### Show Tags

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 P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937
Re: If p,q,r are non-zero numbers, is pq/r>0?  [#permalink]

### Show Tags

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.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net Re: If p,q,r are non-zero numbers, is pq/r>0?   [#permalink] 06 Jan 2019, 07:21
Display posts from previous: Sort by

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