Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 Oct 2016, 09:21

# Happening Now:

Live Chat for LBS, INSEAD, & HECParis Applicants | Join ChatRoom1 to Participate.

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If p and q are negative, is p/q > 1

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Director
Joined: 07 Jun 2004
Posts: 612
Location: PA
Followers: 5

Kudos [?]: 657 [8] , given: 22

If p and q are negative, is p/q > 1 [#permalink]

### Show Tags

07 Feb 2011, 07:08
8
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

35% (02:50) correct 65% (01:33) wrong based on 422 sessions

### HideShow timer Statistics

If p and q are negative, is p/q > 1

(1) The positive difference between p and q is 2.
(2) q - p < 1
[Reveal] Spoiler: OA

_________________

If the Q jogged your mind do Kudos me : )

Math Expert
Joined: 02 Sep 2009
Posts: 35286
Followers: 6641

Kudos [?]: 85659 [2] , given: 10242

Re: Algebra DS [#permalink]

### Show Tags

07 Feb 2011, 07:49
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
rxs0005 wrote:
If p and q are negative, is p / q > 1

(1) The positive diff erence between p and q is 2.
(2) q - p < 1

If p and q are negative, is p / q > 1

Given: $$p<0$$ and $$q<0$$. Question: is $$\frac{p}{q}>1$$ --> multiply both sides by $$q$$ and as it's negative flip the sign: is $$p<q$$? or is $$p-q<0$$?

(1) The positive diff erence between p and q is 2 --> $$|p-q|=2$$: either $$p-q>0$$ (answer NO) and $$p-q=2$$ or $$p-q<0$$ (answer YES) and $$p-q=-2$$. Not sufficient.

(2) q - p < 1 ($$p-q>-1$$) --> if $$q=-1$$ and $$p=-1$$ then the answer will be NO but if $$q=-1$$ and $$p=-1.5$$ then the answer will be YES. Not sufficient.

(1)+(2) As from (2) $$p-q>-1$$ then from (1) $$p-q=2$$ so $$p-q>0$$ and we have the answer NO. Sufficient.

_________________
Manager
Joined: 27 Jun 2008
Posts: 85
Location: United States (AL)
Concentration: General Management, Technology
GMAT 1: 660 Q48 V34
WE: Consulting (Computer Software)
Followers: 1

Kudos [?]: 15 [0], given: 22

Re: Algebra DS [#permalink]

### Show Tags

07 Feb 2011, 08:00
Stmt 1: let p=-5, q=-3 Ans : YES, but as its given positive difference is 2 the values can be interchanged Ans : NO insuff

Stmt 2 : q - p < 1 --> q < 1 + p ,, p = -1, q=-2 Ans : NO. p = -3, q = -4, Ans : NO, insuff

Combining,, p = -2, q= -4, NO.. p=-1,q=-3 NO Suff..

very lengthy method.. can anyone pls post easier way to deal with this sort of probs
Current Student
Joined: 30 Apr 2011
Posts: 14
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: Algebra DS [#permalink]

### Show Tags

03 Apr 2012, 20:43
Bunuel wrote:
rxs0005 wrote:
If p and q are negative, is p / q > 1

(1) The positive diff erence between p and q is 2.
(2) q - p < 1

If p and q are negative, is p / q > 1

Given: $$p<0$$ and $$q<0$$. Question: is $$\frac{p}{q}>1$$ --> multiply both sides by $$q$$ and as it's negative flip the sign: is $$p<q$$? or is $$p-q<0$$?

(1) The positive diff erence between p and q is 2 --> $$|p-q|=2$$: either $$p-q>0$$ (answer NO) and $$p-q=2$$ or $$p-q<0$$ (answer YES) and $$p-q=-2$$. Not sufficient.

I'm very confused. First why do you have absolute value? How did you derive p-q>0? p-q<0? p-q=-2? Any way to demonstrate? or explain the concepts? Thank you very much.

rxs0005 wrote:
(2) q - p < 1 ($$p-q>-1$$) --> if $$q=-1$$ and $$p=-1$$ then the answer will be NO but if $$q=-1$$ and $$p=-1.5$$ then the answer will be YES. Not sufficient.

How can q and p both equal -1?

[/quote]
Math Expert
Joined: 02 Sep 2009
Posts: 35286
Followers: 6641

Kudos [?]: 85659 [0], given: 10242

Re: Algebra DS [#permalink]

### Show Tags

04 Apr 2012, 01:35
bohdan01 wrote:
Bunuel wrote:
rxs0005 wrote:
If p and q are negative, is p / q > 1

(1) The positive diff erence between p and q is 2.
(2) q - p < 1

If p and q are negative, is p / q > 1

Given: $$p<0$$ and $$q<0$$. Question: is $$\frac{p}{q}>1$$ --> multiply both sides by $$q$$ and as it's negative flip the sign: is $$p<q$$? or is $$p-q<0$$?

(1) The positive diff erence between p and q is 2 --> $$|p-q|=2$$: either $$p-q>0$$ (answer NO) and $$p-q=2$$ or $$p-q<0$$ (answer YES) and $$p-q=-2$$. Not sufficient.

I'm very confused. First why do you have absolute value? How did you derive p-q>0? p-q<0? p-q=-2? Any way to demonstrate? or explain the concepts? Thank you very much.

rxs0005 wrote:
(2) q - p < 1 ($$p-q>-1$$) --> if $$q=-1$$ and $$p=-1$$ then the answer will be NO but if $$q=-1$$ and $$p=-1.5$$ then the answer will be YES. Not sufficient.

How can q and p both equal -1?

"The positive difference between p and q is 2" means that the distance between p and q is 2, which can be expressed as $$|p-q|=2$$. For example positive difference between -5 and -3 is 2: |-5-(-3)|=2.

Next:
Absolute value properties:
When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|={-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|={some \ expression}$$. For example: $$|5|=5$$;

So, for $$|p-q|=2$$:
If $$p-q>0$$ then $$|p-q|=p-q=2$$ (example: $$p=-3$$ and $$q=-5$$);
If $$p-q<0$$ then $$|p-q|=-(p-q)=q-p=2$$ (example: $$p=-5$$ and $$q=-3$$);

Check Absolute Value chapter of Math Book for more: math-absolute-value-modulus-86462.html

As for $$p=q=-1$$: unless it is explicitly stated otherwise, different variables can represent the same number.

Hope it's clear.
_________________
Manager
Joined: 28 Jul 2011
Posts: 240
Followers: 3

Kudos [?]: 108 [0], given: 16

Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]

### Show Tags

04 Apr 2012, 06:21
C

bookmarking

given p<0 & q<0

find
p/q>1 or p < q

(A) The positive diff erence between p and q is 2.

there |p-q| = 2
so we have

if (p-q) = 2 then p > q

(p-q) = -2 then q > p

datanot sufficient

(B) q - p < 1 or p-q > -1 (multiply both sides by -ve and flip the sign)

if(p>q)
p = -0.5
q = -1

then p-q > -1

if(p<q)
p = -1
q = -0.5

then p-q > -1

datanot sufficient

(C)

only possibility
if(p>q)
p = -0.5 / -3
q = -1 / -5
then p-q > -1
also if (p-q) = 2 then p > q

opposite not true
if(p<q)
p = -5
q = -3

(p-q) = -2 then q > p but p-q not > -1

then p-q > -1 [not possible]
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6971
Location: Pune, India
Followers: 2028

Kudos [?]: 12755 [1] , given: 221

Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]

### Show Tags

05 Apr 2012, 00:06
1
KUDOS
Expert's post
rxs0005 wrote:
If p and q are negative, is p / q > 1

(1) The positive diff erence between p and q is 2.
(2) q - p < 1

It is a good question and you can solve it logically too.

Given p and q are negative so p/q must be positive (negative/negative). Whether p/q is greater than 1 depends on whether p < q. If p < q, then yes, p/q > 1 (if p is more negative, it has higher absolute value). Else p/q is not greater than 1.

So we have to find out whether p is less than q.

(1) The positive diff erence between p and q is 2.

This only tells us that the difference between them is 2. It doesn't tell us which one is greater so not sufficient.

(2) q - p < 1
This tells us that if q is greater than p, it is less than 1 greater than p. q can be equal to p or less than p but if it is greater than p, it is certainly less than 1 greater than p. This means (q = -1.2, p = -1.9), (q = -23, p = -23.4), (q = -3, p = -3), (q = -4, p = -2) are possible pairs (and many more). Again, we don't know whether p is greater or q so not sufficient.

Using both together, we know that the difference between p and q is 2 and if q is greater than p, it is less than 1 greater than p. Since the difference between them is 2, q cannot be greater than p so p must be greater than q. We can say that "No. p is not less than q."
Hence sufficient. Answer (C)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 02 Jun 2011 Posts: 159 Followers: 1 Kudos [?]: 69 [0], given: 11 Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink] ### Show Tags 06 Apr 2012, 23:26 rxs0005 wrote: If p and q are negative, is p / q > 1 (1) The positive diff erence between p and q is 2. (2) q - p < 1 st. (1) the +ve difference = |p-q| = 2 implies p-q > 0 or p-q < 0 if p-q > 0 then p>q then p/q> 1 But if p-q < 0 then p<q or p/q cannot be greater than 1 anyway st. (1) gives two options which leads "insufficient" st. (2) q-p<1 (this could be p-q < -1 which mean p-q> -1 ) implies q-p = 0 or q-p is -ve if q-p=0then p/q > 1 is not possible But if q-p is -ve then it gives different values of p and q which says both - p/q>1 or p/q<1 however st.(2) insufficient Combining together st. (1) and st. (2) p-q > -1 and p-q =2 implies p>q or we can say p/q>1 Sufficient hope i got it correct frm bunnel and karishma Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6971 Location: Pune, India Followers: 2028 Kudos [?]: 12755 [0], given: 221 Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink] ### Show Tags 07 Apr 2012, 04:36 rxs0005 wrote: If p and q are negative, is p / q > 1 (1) The positive diff erence between p and q is 2. (2) q - p < 1 st. (1) the +ve difference = |p-q| = 2 implies p-q > 0 or p-q < 0 if p-q > 0 then p>q then p/q> 1 But if p-q < 0 then p<q or p/q cannot be greater than 1 anyway st. (1) gives two options which leads "insufficient" |p-q| = 2 gives you two cases: Either p-q = 2 or q-p = 2 We do not know whether p is smaller than q. st. (2) q-p<1 (this could be p-q < -1 which mean p-q> -1 ) q-p < 1 is the same as p-q > -1 (when you multiply both sides by -1) implies q-p = 0 or q-p is -ve if q-p=0then p/q > 1 is not possible But if q-p is -ve then it gives different values of p and q which says both - p/q>1 or p/q<1 however st.(2) insufficient If q-p<1, q could be greater or p could be greater. So we again cannot figure whether p is smaller than q Combining together st. (1) and st. (2) p-q > -1 and p-q =2 implies p>q or we can say p/q>1 Sufficient Combining, stmnt 1 tells us that either p-q = 2 or q-p = 2. Stmnt 2 tells us that q-p<1. Hence q-p cannot be 2. Therefore, p-q must be 2. p must be greater than q. We know that p is greater so p/q is not greater than 1 (since p and q are both negative) Answer (C). _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Intern
Joined: 01 Mar 2012
Posts: 32
Concentration: Operations, Finance
GMAT 1: 740 Q49 V41
GPA: 3.3
WE: Engineering (Manufacturing)
Followers: 1

Kudos [?]: 4 [0], given: 46

Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]

### Show Tags

23 Apr 2012, 21:40
Guess this is a 700+ level problem.
Anyway, excellent explanation Karishma
Senior Manager
Joined: 30 Jun 2011
Posts: 274
Followers: 0

Kudos [?]: 57 [0], given: 20

Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]

### Show Tags

22 May 2012, 18:26
i was able to solve but within 3 minutes.... how to solve this question in less than 2 min.
Intern
Joined: 07 May 2011
Posts: 42
GMAT 1: Q V
GMAT 2: Q V
Followers: 0

Kudos [?]: 18 [0], given: 11

Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]

### Show Tags

27 Nov 2012, 18:56
Luckily I went for the diagram and was able to do it in under 2 minutes.

Draw a line with 0 in the middle. p and q are both to the left of 0. We only know this much. We don't know their position with respect to 0, i. e we don't know whether q or p is closer to 0 or even whether p and q are the same number, both negative. Question asks whether p/q>1 meaning is p more negative than q? This suggests that the question is about the position of p and q with respect to each other and 0.

1. the positive difference between them is 2 suggests that the distance between p and q is 2 units. this only tells us the distance and not which one is more negative than the other. Not Sufficient.
2. q-p<1 suggests that the difference between the two is less than 1. but their degree of negativity is not clear. by itself, this statement points to the possibility that q and p may be the same number; -2-(-2)=0<1, or one of them could be slightly more negative and still have satisfy q-p<1. so Not Sufficient.

when you take 1 and 2 together, the possibility that the two are the same number is eliminated because 1 says that the two numbers are 2 units apart. so now, the number line will have p and q standing at 2 units apart and based on statement 2, q has to be more negative than p. Hence C.

vikram4689 wrote:
i was able to solve but within 3 minutes.... how to solve this question in less than 2 min.
Intern
Joined: 10 Jan 2014
Posts: 22
Followers: 0

Kudos [?]: 3 [0], given: 6

Re: Algebra DS [#permalink]

### Show Tags

17 Feb 2014, 12:35
Bunuel wrote:
rxs0005 wrote:
If p and q are negative, is p / q > 1

(1) The positive diff erence between p and q is 2.
(2) q - p < 1

If p and q are negative, is p / q > 1

Given: $$p<0$$ and $$q<0$$. Question: is $$\frac{p}{q}>1$$ --> multiply both sides by $$q$$ and as it's negative flip the sign: is $$p<q$$? or is $$p-q<0$$?

(1) The positive diff erence between p and q is 2 --> $$|p-q|=2$$: either $$p-q>0$$ (answer NO) and $$p-q=2$$ or $$p-q<0$$ (answer YES) and $$p-q=-2$$. Not sufficient.

(2) q - p < 1 ($$p-q>-1$$) --> if $$q=-1$$ and $$p=-1$$ then the answer will be NO but if $$q=-1$$ and $$p=-1.5$$ then the answer will be YES. Not sufficient.

(1)+(2) As from (2) $$p-q>-1$$ then from (1) $$p-q=2$$ so $$p-q>0$$ and we have the answer NO. Sufficient.

Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that p-q>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because p-q>-1 (from I) could mean that p-q<0 or p-q>0 ..

Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that p-q>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because p-q>-1 (from I) could mean that p-q<0 or p-q>0 ..
Manager
Status: Oh GMAT ! I give you one more shot :)
Joined: 14 Feb 2013
Posts: 96
Location: United States (MI)
Concentration: General Management, Technology
GMAT 1: 580 Q44 V28
GMAT 2: 690 Q49 V34
GPA: 3.5
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 94 [0], given: 18

Re: Algebra DS [#permalink]

### Show Tags

17 Feb 2014, 14:16
damamikus wrote:
Bunuel wrote:
rxs0005 wrote:
If p and q are negative, is p / q > 1

(1) The positive diff erence between p and q is 2.
(2) q - p < 1

If p and q are negative, is p / q > 1

Given: $$p<0$$ and $$q<0$$. Question: is $$\frac{p}{q}>1$$ --> multiply both sides by $$q$$ and as it's negative flip the sign: is $$p<q$$? or is $$p-q<0$$?

(1) The positive diff erence between p and q is 2 --> $$|p-q|=2$$: either $$p-q>0$$ (answer NO) and $$p-q=2$$ or $$p-q<0$$ (answer YES) and $$p-q=-2$$. Not sufficient.

(2) q - p < 1 ($$p-q>-1$$) --> if $$q=-1$$ and $$p=-1$$ then the answer will be NO but if $$q=-1$$ and $$p=-1.5$$ then the answer will be YES. Not sufficient.

(1)+(2) As from (2) $$p-q>-1$$ then from (1) $$p-q=2$$ so $$p-q>0$$ and we have the answer NO. Sufficient.

Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that p-q>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because p-q>-1 (from I) could mean that p-q<0 or p-q>0 ..

Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that p-q>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because p-q>-1 (from I) could mean that p-q<0 or p-q>0 ..

As @grumpytesttaker said the best way to solve such problems is to use the number line.

The question stem says that p and q are negative so we can have 2 scenarios (p to the left of q or p to the right of q)

Now to definitively say whether p/q>1 we need to find if |p| > |q| as both are negative so there is no question of signs. Since both are negative nos |p| > |q| only if p is to the left of q on the Number Line. So we just need to find if p is to the left or right of q.

(1) |p - q| = 2, this means p and q have a separation of 2. But this is possible if p is to the left of q or p is to the right of q. So this statement doesn't help us. Not Sufficient.

(2) q - p < 1, Since both nos are negative we can rewrite this statement as |p| - |q| < 1. Now if p is to the left of q (|p| > |q|) then the separation between p and q have to be less than 1.
But if p is to the right of q (|p| < |q|) then the separation can be anything. Since this statement doesn't say if p is to the left or right of q, it is Not Sufficient.

(1) & (2) Now if we combine the 2 statements we can see that p cannot be to the left of q because (1) -- |p| - |q| = 2 and (2) -- |p| - |q| < 1 together is not possible.
So the only possibility is p is to the right of q, which answers the question, since |p| < |q| hence p/q < 1

So (1) & (2) put together answers the question. Sufficient. Answer C
_________________

Life is a highway
I wanna ride it all night long

Math Expert
Joined: 02 Sep 2009
Posts: 35286
Followers: 6641

Kudos [?]: 85659 [0], given: 10242

Re: Algebra DS [#permalink]

### Show Tags

18 Feb 2014, 01:28
damamikus wrote:
Bunuel wrote:
rxs0005 wrote:
If p and q are negative, is p / q > 1

(1) The positive diff erence between p and q is 2.
(2) q - p < 1

If p and q are negative, is p / q > 1

Given: $$p<0$$ and $$q<0$$. Question: is $$\frac{p}{q}>1$$ --> multiply both sides by $$q$$ and as it's negative flip the sign: is $$p<q$$? or is $$p-q<0$$?

(1) The positive difference between p and q is 2 --> $$|p-q|=2$$: either $$p-q>0$$ (answer NO) and $$p-q=2$$ or $$p-q<0$$ (answer YES) and $$p-q=-2$$. Not sufficient.

(2) q - p < 1 ($$p-q>-1$$) --> if $$q=-1$$ and $$p=-1$$ then the answer will be NO but if $$q=-1$$ and $$p=-1.5$$ then the answer will be YES. Not sufficient.

(1)+(2) As from (2) $$p-q>-1$$ then from (1) $$p-q=2$$ so $$p-q>0$$ and we have the answer NO. Sufficient.

Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that p-q>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because p-q>-1 (from I) could mean that p-q<0 or p-q>0 ..

Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that p-q>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because p-q>-1 (from I) could mean that p-q<0 or p-q>0 ..

Sure. From (1) we have two possible cases: $$p-q=2$$ or $$p-q=-2$$. Since from (1) we have that $$p-q>-1$$, then $$p-q\neq{-2}$$, thus $$p-q=2>0$$.

Does this make sense?
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12221
Followers: 542

Kudos [?]: 151 [0], given: 0

Re: If p and q are negative, is p/q > 1 [#permalink]

### Show Tags

27 May 2015, 11:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12221
Followers: 542

Kudos [?]: 151 [0], given: 0

Re: If p and q are negative, is p/q > 1 [#permalink]

### Show Tags

30 Jun 2016, 02:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If p and q are negative, is p/q > 1   [#permalink] 30 Jun 2016, 02:59
Similar topics Replies Last post
Similar
Topics:
3 If P & Q are integers such that |P|Q=4 , is P negative? (1) |P|+|Q| 1 28 Feb 2016, 00:22
1 If P And Q Are Non Negative,Is P+Q >Pq 1 20 Feb 2015, 01:41
2 p>q, Is q negative? 5 08 Feb 2015, 01:16
8 If 2p not equal to -q, is (2p-q)/(2p+q)>1? 15 05 Nov 2012, 13:24
2 If p/q > 5, is q < 2? 6 27 Feb 2010, 14:26
Display posts from previous: Sort by

# If p and q are negative, is p/q > 1

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.