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

It is currently 27 Aug 2014, 17:38

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is pq = 1? (1) pqp = p (2) qpq = q

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 06 May 2008
Posts: 28
Followers: 0

Kudos [?]: 13 [1] , given: 4

Is pq = 1? (1) pqp = p (2) qpq = q [#permalink] New post 16 May 2009, 20:17
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

39% (01:53) correct 61% (00:37) wrong based on 162 sessions
Is pq = 1?

(1) pqp = p

(2) qpq = q
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Oct 2013, 02:21, edited 2 times in total.
Added the OA.
Manager
Manager
avatar
Joined: 27 Sep 2008
Posts: 77
Followers: 1

Kudos [?]: 7 [0], given: 0

Re: A One product [#permalink] New post 16 May 2009, 23:29
Statement 1

pqp = p
Dividing both sides in p
pq = 1

sufficient

Statement 2

qpq = q
Dividing both sides in q
qp = 1

sufficient

So the answer is (D)
2 KUDOS received
GMAT Instructor
avatar
Joined: 24 Jun 2008
Posts: 967
Location: Toronto
Followers: 253

Kudos [?]: 658 [2] , given: 3

GMAT Tests User
Re: A One product [#permalink] New post 17 May 2009, 18:05
2
This post received
KUDOS
DFG5150 wrote:
Is pq = 1?

(1) pqp = p

(2) qpq = q


It's certainly possible, using either or both statements, that p = q = pq = 1. It's also possible that p = q = pq = 0. So the answer is E.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

1 KUDOS received
Intern
Intern
avatar
Joined: 06 May 2008
Posts: 28
Followers: 0

Kudos [?]: 13 [1] , given: 4

Re: A One product [#permalink] New post 17 May 2009, 18:32
1
This post received
KUDOS
Greenberg wrote:
Statement 1

pqp = p
Dividing both sides in p
pq = 1

sufficient

Statement 2

qpq = q
Dividing both sides in q
qp = 1

sufficient

So the answer is (D)


Since we don't know whether p=0 or q=0, we can't divide the ecuations by these variables.
1 KUDOS received
Manager
Manager
User avatar
Joined: 13 May 2009
Posts: 195
Schools: Stanford, Harvard, Berkeley, INSEAD
Followers: 4

Kudos [?]: 27 [1] , given: 1

GMAT Tests User
Re: A One product [#permalink] New post 25 May 2009, 23:17
1
This post received
KUDOS
Greenberg wrote:
Statement 1

pqp = p
Dividing both sides in p
pq = 1

sufficient

Statement 2

qpq = q
Dividing both sides in q
qp = 1

sufficient

So the answer is (D)


You forgot to consider whether p or q are 0, in which case you'd be dividing by 0 (which is undefined). If it's not stated that the variable can't be 0, move the variables to one side and factor.
_________________

Hades

Intern
Intern
avatar
Joined: 02 Feb 2013
Posts: 28
Location: India
Concentration: Operations, Strategy
GMAT 1: 690 Q47 V38
GMAT 2: 720 Q48 V41
GPA: 3.2
WE: Programming (Computer Software)
Followers: 1

Kudos [?]: 6 [0], given: 18

Re: Is pq = 1? (1) pqp = p (2) qpq = q [#permalink] New post 28 Jul 2013, 19:35
since statement gives us PQ=1 as an option, and statement 2 also gives us PQ=1, as an option, shudnt we have C as the answer ?
5 KUDOS received
Director
Director
avatar
Joined: 24 Aug 2009
Posts: 509
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 9

Kudos [?]: 362 [5] , given: 241

Re: Is pq = 1? [#permalink] New post 28 Jul 2013, 19:50
5
This post received
KUDOS
abilash10 wrote:
Is pq = 1?
(1) pqp = p
(2) qpq = q


Statement 1-
pqp = p
p (pq-1)=0
It means p=0 or pq=1
Not sufficient

Statement 2-
qpq = q
q (pq-1)=0
It means q=0 or pq=1
Not sufficient

Statement 1 & 2-
Combining both statements we get p^3q^2 - p = 0
p(p^2q^2 - 1) = 0
p (pq-1)(pq+1) = 0
p=0 or pq=1 or pq=-1
Not sufficient
Answer E
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Intern
Intern
avatar
Joined: 02 Feb 2013
Posts: 28
Location: India
Concentration: Operations, Strategy
GMAT 1: 690 Q47 V38
GMAT 2: 720 Q48 V41
GPA: 3.2
WE: Programming (Computer Software)
Followers: 1

Kudos [?]: 6 [0], given: 18

Re: Is pq = 1? [#permalink] New post 28 Jul 2013, 20:21
yes but if (1) gives us PQ= 1 as a possible conclusion, and so does (2), then cant we conclude that PQ=1 ?
Director
Director
avatar
Joined: 24 Aug 2009
Posts: 509
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 9

Kudos [?]: 362 [0], given: 241

Re: Is pq = 1? [#permalink] New post 28 Jul 2013, 20:29
abilash10 wrote:
yes but if (1) gives us PQ= 1 as a possible conclusion, and so does (2), then cant we conclude that PQ=1 ?


That's not correct always and for the same reason i combined both the statements.
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Intern
Intern
avatar
Joined: 31 Mar 2013
Posts: 2
GMAT Date: 10-23-2013
Followers: 0

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

Re: Is pq = 1? [#permalink] New post 01 Oct 2013, 02:05
fameatop wrote:
abilash10 wrote:
yes but if (1) gives us PQ= 1 as a possible conclusion, and so does (2), then cant we conclude that PQ=1 ?


That's not correct always and for the same reason i combined both the statements.


Hey can you please explain when to combine the statements and when not to ?
I was under the impression that for such questions, one needs to look at the common solution from both the qquestions to arrive at the answer.
If you could explain when to use these two approaches, it would help.

Thanks !
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22141
Followers: 3405

Kudos [?]: 24884 [2] , given: 2697

Re: Is pq = 1? [#permalink] New post 01 Oct 2013, 03:37
2
This post received
KUDOS
Expert's post
warabull wrote:
fameatop wrote:
abilash10 wrote:
yes but if (1) gives us PQ= 1 as a possible conclusion, and so does (2), then cant we conclude that PQ=1 ?


That's not correct always and for the same reason i combined both the statements.


Hey can you please explain when to combine the statements and when not to ?
I was under the impression that for such questions, one needs to look at the common solution from both the qquestions to arrive at the answer.
If you could explain when to use these two approaches, it would help.

Thanks !


Notice that p=0 from the first statement does not exclude q being 0 too and similarly q=0 from the second statement does not exclude p being 0 too.

Is pq = 1?

(1) pqp = p --> p(pq-1)=0 --> either p=0 and q=(any number), including 0 so in this case pq=0 not 1 or pq=1. Not sufficient.

(2) qpq = q --> q(pq-1)=0 --> either q=0 and p=(any number), including 0 so in this case pq=0 not 1 or pq=1. Not sufficient.

(1)+(2) When combined we have that either p=q=0 or pq=1. Not sufficient.

Answer: E.

When we consider two statements together we should take the values which satisfy both statements. For this question pq=1 satisfies both statement, but p=q=0 also satisfies both statements. So what you call "common solution" for this question is: pq=1 OR pq=0\neq{1}.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 29 Sep 2013
Posts: 48
Followers: 0

Kudos [?]: 12 [0], given: 40

CAT Tests
Re: Is pq = 1? (1) pqp = p (2) qpq = q [#permalink] New post 03 Oct 2013, 09:53
DFG5150 wrote:
Is pq = 1?

(1) pqp = p

(2) qpq = q


This is how I approached the question; if anyone can kindly point out my flaw.
The question is asking pq=1

or p=1/q or q=1/p

Meaning are p and q reciprocal?. Yes/No

Statement 1
pqp=p
p^2q=p
q=p/p^2
q=1/p so Sufficient

Statement 2

qpq=q
q^2p=q
p=q/q^2
p=1/q so Sufficient

Therefore the answer is C
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22141
Followers: 3405

Kudos [?]: 24884 [0], given: 2697

Re: Is pq = 1? (1) pqp = p (2) qpq = q [#permalink] New post 04 Oct 2013, 00:18
Expert's post
suk1234 wrote:
DFG5150 wrote:
Is pq = 1?

(1) pqp = p

(2) qpq = q


This is how I approached the question; if anyone can kindly point out my flaw.
The question is asking pq=1

or p=1/q or q=1/p

Meaning are p and q reciprocal?. Yes/No

Statement 1
pqp=p
p^2q=p
q=p/p^2
q=1/p so Sufficient

Statement 2

qpq=q
q^2p=q
p=q/q^2
p=1/q so Sufficient

Therefore the answer is C


If you say that each statement is sufficient, then you mean that the answer should be D, not C, right?

Now, the problem in your solution is that you cannot reduce pqp=p by p to get pq=1. This is because p can be zero and division be zero is not allowed.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

So when you divide by p you assume, with no ground for it, that p does not equal to zero thus exclude a possible solution. Notice that p=0 and pq=1 both satisfy pqp=p.

The same logic applies to the second statement.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 29 Sep 2013
Posts: 48
Followers: 0

Kudos [?]: 12 [0], given: 40

CAT Tests
Re: Is pq = 1? (1) pqp = p (2) qpq = q [#permalink] New post 04 Oct 2013, 00:36
Bunuel wrote:
suk1234 wrote:
DFG5150 wrote:
Is pq = 1?

(1) pqp = p

(2) qpq = q


This is how I approached the question; if anyone can kindly point out my flaw.
The question is asking pq=1

or p=1/q or q=1/p

Meaning are p and q reciprocal?. Yes/No

Statement 1
pqp=p
p^2q=p
q=p/p^2
q=1/p so Sufficient

Statement 2

qpq=q
q^2p=q
p=q/q^2
p=1/q so Sufficient

Therefore the answer is C


If you say that each statement is sufficient, then you mean that the answer should be D, not C, right?

Now, the problem in your solution is that you cannot reduce pqp=p by p to get pq=1. This is because p can be zero and division be zero is not allowed.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

So when you divide by p you assume, with no ground for it, that p does not equal to zero thus exclude a possible solution. Notice that p=0 and pq=1 both satisfy pqp=p.

The same logic applies to the second statement.

Hope it helps.


Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.


Yeaps! got it now. Thanks for the reply, it's very helpful. And thanks for that important bit of information. :thumbup:
Manager
Manager
User avatar
Joined: 18 Dec 2012
Posts: 84
Location: India
Concentration: General Management, Strategy
GMAT 1: 660 Q49 V32
GMAT 2: 530 Q37 V25
GPA: 3.32
WE: Manufacturing and Production (Manufacturing)
Followers: 0

Kudos [?]: 22 [0], given: 20

CAT Tests
Re: Is pq = 1? (1) pqp = p (2) qpq = q [#permalink] New post 04 Oct 2013, 01:02
Bunuel wrote:

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.



This is a very important rule. Thanks bunnel.
_________________

I'm telling this because you don't get it. You think you get it which is not the same as actually getting it. Get it?

Re: Is pq = 1? (1) pqp = p (2) qpq = q   [#permalink] 04 Oct 2013, 01:02
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic If 2p not equal to -q, is (2p-q)/(2p+q)>1? eeakkan 13 05 Nov 2012, 12:24
10 Experts publish their posts in the topic If p and q are negative, is p/q > 1 rxs0005 14 07 Feb 2011, 06:08
Is (p/q) > ( /s) 1) (p/q) > (r/s) 2) r = 1 jimmyjamesdonkey 6 16 Jun 2008, 18:58
Is P + Q > 1/P + 1/Q? 1. P < Q < 1 2. P*Q < 1 bmwhype2 5 17 Oct 2007, 11:06
What is the value of (2^p)*(4^-q)? 1) p=2q 2) p=q getzgetzu 1 06 May 2006, 02:53
Display posts from previous: Sort by

Is pq = 1? (1) pqp = p (2) qpq = q

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.