It is currently 18 Jan 2018, 20:02

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 May 2008
Posts: 28

Kudos [?]: 26 [1], given: 4

Is pq = 1? (1) pqp = p (2) qpq = q [#permalink]

### Show Tags

16 May 2009, 20:17
1
KUDOS
8
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

41% (00:56) correct 59% (00:42) wrong based on 500 sessions

### HideShow timer Statistics

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.

Kudos [?]: 26 [1], given: 4

Manager
Joined: 27 Sep 2008
Posts: 76

Kudos [?]: 13 [0], given: 0

### Show Tags

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

Kudos [?]: 13 [0], given: 0

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1347

Kudos [?]: 2082 [4], given: 6

### Show Tags

17 May 2009, 18:05
4
KUDOS
Expert's post
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

Kudos [?]: 2082 [4], given: 6

Intern
Joined: 06 May 2008
Posts: 28

Kudos [?]: 26 [1], given: 4

### Show Tags

17 May 2009, 18:32
1
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

Since we don't know whether p=0 or q=0, we can't divide the ecuations by these variables.

Kudos [?]: 26 [1], given: 4

Manager
Joined: 13 May 2009
Posts: 191

Kudos [?]: 52 [1], given: 1

### Show Tags

25 May 2009, 23:17
1
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

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.
_________________

Kudos [?]: 52 [1], given: 1

Senior Manager
Joined: 24 Aug 2009
Posts: 492

Kudos [?]: 904 [6], given: 276

Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: Is pq = 1? [#permalink]

### Show Tags

28 Jul 2013, 19:50
6
KUDOS
1
This post was
BOOKMARKED
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
_________________

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

Kudos [?]: 904 [6], given: 276

Intern
Joined: 02 Feb 2013
Posts: 41

Kudos [?]: 11 [0], given: 20

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, 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 ?

Kudos [?]: 11 [0], given: 20

Senior Manager
Joined: 24 Aug 2009
Posts: 492

Kudos [?]: 904 [0], given: 276

Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: Is pq = 1? [#permalink]

### Show Tags

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

Kudos [?]: 904 [0], given: 276

Intern
Joined: 31 Mar 2013
Posts: 2

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

GMAT Date: 10-23-2013
Re: Is pq = 1? [#permalink]

### Show Tags

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 !

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

Math Expert
Joined: 02 Sep 2009
Posts: 43322

Kudos [?]: 139442 [6], given: 12790

Re: Is pq = 1? [#permalink]

### Show Tags

01 Oct 2013, 03:37
6
KUDOS
Expert's post
4
This post was
BOOKMARKED
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.

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.
_________________

Kudos [?]: 139442 [6], given: 12790

Manager
Joined: 29 Sep 2013
Posts: 51

Kudos [?]: 42 [0], given: 48

Re: Is pq = 1? (1) pqp = p (2) qpq = q [#permalink]

### Show Tags

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.

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

Kudos [?]: 42 [0], given: 48

Math Expert
Joined: 02 Sep 2009
Posts: 43322

Kudos [?]: 139442 [0], given: 12790

Re: Is pq = 1? (1) pqp = p (2) qpq = q [#permalink]

### Show Tags

04 Oct 2013, 00:18
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.

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

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.
_________________

Kudos [?]: 139442 [0], given: 12790

Manager
Joined: 29 Sep 2013
Posts: 51

Kudos [?]: 42 [0], given: 48

Re: Is pq = 1? (1) pqp = p (2) qpq = q [#permalink]

### Show Tags

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.

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

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.

Kudos [?]: 42 [0], given: 48

Manager
Joined: 18 Dec 2012
Posts: 96

Kudos [?]: 63 [0], given: 34

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, 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?

Kudos [?]: 63 [0], given: 34

Non-Human User
Joined: 09 Sep 2013
Posts: 14241

Kudos [?]: 291 [0], given: 0

Re: Is pq = 1? (1) pqp = p (2) qpq = q [#permalink]

### Show Tags

13 Aug 2017, 10:20
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.
_________________

Kudos [?]: 291 [0], given: 0

Re: Is pq = 1? (1) pqp = p (2) qpq = q   [#permalink] 13 Aug 2017, 10:20
Display posts from previous: Sort by