November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat. November 20, 2018 November 20, 2018 06:00 PM EST 07:00 PM EST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Director
Joined: 07 Jun 2004
Posts: 600
Location: PA

If p and q are negative, is p/q > 1
[#permalink]
Show Tags
07 Feb 2011, 06:08
Question Stats:
39% (02:13) correct 61% (02:06) wrong based on 515 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
If the Q jogged your mind do Kudos me : )




Math Expert
Joined: 02 Sep 2009
Posts: 50627

Re: Algebra DS
[#permalink]
Show Tags
07 Feb 2011, 06:49
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 \(pq<0\)? (1) The positive diff erence between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. (2) q  p < 1 (\(pq>1\)) > 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) \(pq>1\) then from (1) \(pq=2\) so \(pq>0\) and we have the answer NO. Sufficient. Answer: C.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 27 Jun 2008
Posts: 53
Location: United States (AL)
Concentration: General Management, Technology
WE: Consulting (Computer Software)

Re: Algebra DS
[#permalink]
Show Tags
07 Feb 2011, 07:00
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



Intern
Joined: 30 Apr 2011
Posts: 12

Re: Algebra DS
[#permalink]
Show Tags
03 Apr 2012, 19:43
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 \(pq<0\)? (1) The positive diff erence between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. I'm very confused. First why do you have absolute value? How did you derive pq>0? pq<0? pq=2? Any way to demonstrate? or explain the concepts? Thank you very much. rxs0005 wrote: (2) q  p < 1 (\(pq>1\)) > 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: 50627

Re: Algebra DS
[#permalink]
Show Tags
04 Apr 2012, 00:35
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 \(pq<0\)? (1) The positive diff erence between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. I'm very confused. First why do you have absolute value? How did you derive pq>0? pq<0? pq=2? Any way to demonstrate? or explain the concepts? Thank you very much. rxs0005 wrote: (2) q  p < 1 (\(pq>1\)) > 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 \(pq=2\). 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 \(pq=2\): If \(pq>0\) then \(pq=pq=2\) (example: \(p=3\) and \(q=5\)); If \(pq<0\) then \(pq=(pq)=qp=2\) (example: \(p=5\) and \(q=3\)); Check Absolute Value chapter of Math Book for more: mathabsolutevaluemodulus86462.htmlAs for \(p=q=1\): unless it is explicitly stated otherwise, different variables can represent the same number. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 28 Jul 2011
Posts: 186

Re: If p and q are negative, is p / q > 1 (1) The positive
[#permalink]
Show Tags
04 Apr 2012, 05:21
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 pq = 2 so we have
if (pq) = 2 then p > q
(pq) = 2 then q > p
datanot sufficient
(B) q  p < 1 or pq > 1 (multiply both sides by ve and flip the sign)
if(p>q) p = 0.5 q = 1
then pq > 1
if(p<q) p = 1 q = 0.5
then pq > 1
datanot sufficient
(C)
only possibility if(p>q) p = 0.5 / 3 q = 1 / 5 then pq > 1 also if (pq) = 2 then p > q
opposite not true if(p<q) p = 5 q = 3
(pq) = 2 then q > p but pq not > 1
then pq > 1 [not possible]



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8550
Location: Pune, India

Re: If p and q are negative, is p / q > 1 (1) The positive
[#permalink]
Show Tags
04 Apr 2012, 23:06
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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Joined: 02 Jun 2011
Posts: 130

Re: If p and q are negative, is p / q > 1 (1) The positive
[#permalink]
Show Tags
06 Apr 2012, 22:26
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 = pq = 2 implies pq > 0 or pq < 0 if pq > 0 then p>q then p/q> 1 But if pq < 0 then p<q or p/q cannot be greater than 1 anyway st. (1) gives two options which leads "insufficient" st. (2) qp<1 (this could be pq < 1 which mean pq> 1 ) implies qp = 0 or qp is ve if qp=0then p/q > 1 is not possible But if qp 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) pq > 1 and pq =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: 8550
Location: Pune, India

Re: If p and q are negative, is p / q > 1 (1) The positive
[#permalink]
Show Tags
07 Apr 2012, 03:36
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 = pq = 2 implies pq > 0 or pq < 0 if pq > 0 then p>q then p/q> 1 But if pq < 0 then p<q or p/q cannot be greater than 1 anyway st. (1) gives two options which leads "insufficient" pq = 2 gives you two cases: Either pq = 2 or qp = 2 We do not know whether p is smaller than q.st. (2) qp<1 (this could be pq < 1 which mean pq> 1 ) qp < 1 is the same as pq > 1 (when you multiply both sides by 1) implies qp = 0 or qp is ve if qp=0then p/q > 1 is not possible But if qp 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 qp<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) pq > 1 and pq =2 implies p>q or we can say p/q>1 Sufficient Combining, stmnt 1 tells us that either pq = 2 or qp = 2. Stmnt 2 tells us that qp<1. Hence qp cannot be 2. Therefore, pq 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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 07 May 2011
Posts: 31

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

Re: Algebra DS
[#permalink]
Show Tags
17 Feb 2014, 11:35
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 \(pq<0\)? (1) The positive diff erence between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. (2) q  p < 1 (\(pq>1\)) > 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) \(pq>1\) then from (1) \(pq=2\) so \(pq>0\) and we have the answer NO. Sufficient. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>0 .. Answer: C. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>0 ..



Manager
Status: Oh GMAT ! I give you one more shot :)
Joined: 14 Feb 2013
Posts: 79
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)

Re: Algebra DS
[#permalink]
Show Tags
17 Feb 2014, 13:16
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 \(pq<0\)? (1) The positive diff erence between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. (2) q  p < 1 (\(pq>1\)) > 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) \(pq>1\) then from (1) \(pq=2\) so \(pq>0\) and we have the answer NO. Sufficient. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>0 .. Answer: C. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>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: 50627

Re: Algebra DS
[#permalink]
Show Tags
18 Feb 2014, 00:28
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 \(pq<0\)? (1) The positive difference between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. (2) q  p < 1 (\(pq>1\)) > 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) \(pq>1\) then from (1) \(pq=2\) so \(pq>0\) and we have the answer NO. Sufficient. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>0 .. Answer: C. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>0 .. Sure. From (1) we have two possible cases: \(pq=2\) or \(pq=2\). Since from (1) we have that \(pq>1\), then \(pq\neq{2}\), thus \(pq=2>0\). Does this make sense?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



NonHuman User
Joined: 09 Sep 2013
Posts: 8818

Re: If p and q are negative, is p/q > 1
[#permalink]
Show Tags
07 Sep 2018, 06:56
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If p and q are negative, is p/q > 1 &nbs
[#permalink]
07 Sep 2018, 06:56






