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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

(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.

(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.

(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 \(q=-3\));

Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]
04 Apr 2012, 23:06

1

This post received 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) _________________

Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]
07 Apr 2012, 03:36

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

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).

Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]
27 Nov 2012, 17:56

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.

(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 ..

(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 _________________

(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 \(p-q=2>0\).

Re: If p and q are negative, is p/q > 1 [#permalink]
27 May 2015, 10:28

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. _________________

My last interview took place at the Johnson School of Management at Cornell University. Since it was my final interview, I had my answers to the general interview questions...