Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 06 May 2008
Posts: 21

Is pq = 1? (1) pqp = p (2) qpq = q
[#permalink]
Show Tags
Updated on: 01 Oct 2013, 03:21
Question Stats:
47% (01:25) correct 53% (01:17) wrong based on 386 sessions
HideShow timer Statistics
Is pq = 1? (1) pqp = p (2) qpq = q
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by DFG5150 on 16 May 2009, 21:17.
Last edited by Bunuel on 01 Oct 2013, 03:21, edited 2 times in total.
Added the OA.




Math Expert
Joined: 02 Sep 2009
Posts: 58427

Re: Is pq = 1?
[#permalink]
Show Tags
01 Oct 2013, 04:37
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(pq1)=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(pq1)=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.
_________________




Senior Manager
Joined: 24 Aug 2009
Posts: 445
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: Is pq = 1?
[#permalink]
Show Tags
28 Jul 2013, 20:50
abilash10 wrote: Is pq = 1? (1) pqp = p (2) qpq = q Statement 1pqp = p p (pq1)=0 It means p=0 or pq=1 Not sufficient Statement 2qpq = q q (pq1)=0 It means q=0 or pq=1 Not sufficient Statement 1 & 2Combining both statements we get \(p^3q^2\)  p = 0 p(\(p^2q^2\)  1) = 0 p (pq1)(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




Manager
Joined: 27 Sep 2008
Posts: 54

Re: A One product
[#permalink]
Show Tags
17 May 2009, 00:29
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)



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1803

Re: A One product
[#permalink]
Show Tags
17 May 2009, 19:05
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.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Intern
Joined: 06 May 2008
Posts: 21

Re: A One product
[#permalink]
Show Tags
17 May 2009, 19:32
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.



Manager
Joined: 14 May 2009
Posts: 170
Schools: Stanford, Harvard, Berkeley, INSEAD

Re: A One product
[#permalink]
Show Tags
26 May 2009, 00:17
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.
_________________



Intern
Joined: 02 Feb 2013
Posts: 41
Location: India
Concentration: Operations, Technology
GMAT 1: 690 Q47 V38 GMAT 2: 720 Q48 V41
GPA: 3.2
WE: Programming (Computer Software)

Re: Is pq = 1?
[#permalink]
Show Tags
28 Jul 2013, 21:21
yes but if (1) gives us PQ= 1 as a possible conclusion, and so does (2), then cant we conclude that PQ=1 ?



Senior Manager
Joined: 24 Aug 2009
Posts: 445
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: Is pq = 1?
[#permalink]
Show Tags
28 Jul 2013, 21:29
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
Joined: 31 Mar 2013
Posts: 2
GMAT Date: 10232013

Re: Is pq = 1?
[#permalink]
Show Tags
01 Oct 2013, 03:05
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 !



Intern
Joined: 29 Sep 2013
Posts: 45

Re: Is pq = 1? (1) pqp = p (2) qpq = q
[#permalink]
Show Tags
03 Oct 2013, 10:53
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/pMeaning are p and q reciprocal?. Yes/No Statement 1pqp=p p^2q=p q=p/p^2 q=1/p so Sufficient Statement 2qpq=q q^2p=q p=q/q^2 p=1/q so Sufficient Therefore the answer is C



Math Expert
Joined: 02 Sep 2009
Posts: 58427

Re: Is pq = 1? (1) pqp = p (2) qpq = q
[#permalink]
Show Tags
04 Oct 2013, 01:18
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/pMeaning are p and q reciprocal?. Yes/No Statement 1pqp=p p^2q=p q=p/p^2 q=1/p so SufficientStatement 2qpq=q q^2p=q p=q/q^2 p=1/q so SufficientTherefore the answer is CIf 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.
_________________



Intern
Joined: 29 Sep 2013
Posts: 45

Re: Is pq = 1? (1) pqp = p (2) qpq = q
[#permalink]
Show Tags
04 Oct 2013, 01:36
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/pMeaning are p and q reciprocal?. Yes/No Statement 1pqp=p p^2q=p q=p/p^2 q=1/p so SufficientStatement 2qpq=q q^2p=q p=q/q^2 p=1/q so SufficientTherefore the answer is CIf 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.



Manager
Joined: 18 Dec 2012
Posts: 94
Location: India
Concentration: General Management, Strategy
GMAT 1: 660 Q49 V32 GMAT 2: 530 Q37 V25
GPA: 3.32
WE: Manufacturing and Production (Manufacturing)

Re: Is pq = 1? (1) pqp = p (2) qpq = q
[#permalink]
Show Tags
04 Oct 2013, 02:02
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?



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: Is pq = 1? (1) pqp = p (2) qpq = q
[#permalink]
Show Tags
30 Sep 2018, 15:00
DFG5150 wrote: Is pq = 1? (1) pqp = p (2) qpq = q
\(pq\,\,\mathop = \limits^? \,\,1\) Let´s go straight to bifurcate (1+2), to guarantee the right answer is (E), indeed. \(\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {p,q} \right) = \left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {p,q} \right) = \left( {0,0} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



NonHuman User
Joined: 09 Sep 2013
Posts: 13411

Re: Is pq = 1? (1) pqp = p (2) qpq = q
[#permalink]
Show Tags
08 Oct 2019, 13:35
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: Is pq = 1? (1) pqp = p (2) qpq = q
[#permalink]
08 Oct 2019, 13:35






