Last visit was: 16 Jul 2025, 17:02 It is currently 16 Jul 2025, 17:02
Close
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
Your Progress

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.
Close
Request Expert Reply
Confirm Cancel
User avatar
rxs0005
Joined: 07 Jun 2004
Last visit: 21 Jun 2017
Posts: 436
Own Kudos:
3,120
 [45]
Given Kudos: 22
Location: PA
Posts: 436
Kudos: 3,120
 [45]
11
Kudos
Add Kudos
34
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 16 Jul 2025
Posts: 102,594
Own Kudos:
741,981
 [7]
Given Kudos: 98,202
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 741,981
 [7]
3
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
General Discussion
User avatar
kanhaiya
Joined: 27 Jun 2008
Last visit: 15 Jun 2016
Posts: 33
Own Kudos:
Given Kudos: 22
Location: United States (AL)
Concentration: General Management, Technology
GMAT 1: 660 Q48 V34
WE:Consulting (Computer Software)
GMAT 1: 660 Q48 V34
Posts: 33
Kudos: 28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
bicu17
Joined: 30 Apr 2011
Last visit: 09 Jan 2017
Posts: 11
Own Kudos:
Products:
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
rxs0005
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
(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]
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 16 Jul 2025
Posts: 102,594
Own Kudos:
Given Kudos: 98,202
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 741,981
Kudos
Add Kudos
Bookmarks
Bookmark this Post
bohdan01
Bunuel
rxs0005
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
(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.
User avatar
kuttingchai
Joined: 28 Jul 2011
Last visit: 17 Oct 2016
Posts: 126
Own Kudos:
Given Kudos: 16
Posts: 126
Kudos: 443
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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]
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 16 Jul 2025
Posts: 16,111
Own Kudos:
74,359
 [1]
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,111
Kudos: 74,359
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rxs0005
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)
User avatar
kashishh
Joined: 02 Jun 2011
Last visit: 15 Oct 2019
Posts: 89
Own Kudos:
Given Kudos: 11
Posts: 89
Kudos: 421
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rxs0005
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
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 16 Jul 2025
Posts: 16,111
Own Kudos:
74,359
 [1]
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,111
Kudos: 74,359
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
rxs0005
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).
avatar
grumpytesttaker
Joined: 07 May 2011
Last visit: 01 Apr 2013
Posts: 14
Own Kudos:
Given Kudos: 11
Posts: 14
Kudos: 50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
i was able to solve but within 3 minutes.... how to solve this question in less than 2 min.
avatar
damamikus
Joined: 10 Jan 2014
Last visit: 12 Oct 2017
Posts: 16
Own Kudos:
Given Kudos: 6
Posts: 16
Kudos: 36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
rxs0005
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 ..

Answer: C.

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 ..
avatar
prasun9
Joined: 14 Feb 2013
Last visit: 06 May 2016
Posts: 62
Own Kudos:
Given Kudos: 18
Status:Oh GMAT ! I give you one more shot :)
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)
GMAT 2: 690 Q49 V34
Posts: 62
Kudos: 503
Kudos
Add Kudos
Bookmarks
Bookmark this Post
damamikus
Bunuel
rxs0005
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 ..

Answer: C.

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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 16 Jul 2025
Posts: 102,594
Own Kudos:
Given Kudos: 98,202
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 741,981
Kudos
Add Kudos
Bookmarks
Bookmark this Post
damamikus
Bunuel
rxs0005
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 ..

Answer: C.

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?
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,422
Own Kudos:
Posts: 37,422
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderator:
Math Expert
102594 posts