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Does pqr equal r?

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Does pqr equal r? [#permalink] New post 12 Aug 2012, 12:34
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

61% (01:25) correct 39% (00:30) wrong based on 31 sessions
Does pqr equal r?

(1) pqs = s where s is some unknown number
(2) mpq = m where m is some unknown number
[Reveal] Spoiler: OA
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Re: Does pqr equal r? [#permalink] New post 12 Aug 2012, 12:47
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Does pqr equal r?

Does pqr=r? --> does pqr-r=0? --> does r(pq-1)=0? --> does r=0 or pq=1?

(1) pqs = s where s is some unknown number --> pqs=s --> pqs-s=0 --> s(pq-1)=0 --> s=0 or pq=1. Not sufficient.

(2) mpq = m where m is some unknown number --> mpq=m --> mpq-m=0 --> m(pq-1)=0 --> m=0 or pq=1. Not sufficient.

(1)+(2) If s=m=0 then pq can take any value, so it may or may not equal to 1. Not sufficient.

Answer: E.
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Re: Does pqr equal r? [#permalink] New post 13 Aug 2012, 09:52
Cant combining equal PQ=1 ?
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Re: Does pqr equal r? [#permalink] New post 13 Aug 2012, 11:28
why cant i come to pq=1 from pqs=s? for the 1st statement and pq=q from mpq=m?
may be its too stupid even to ask such a question, but im stuck!
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Re: Does pqr equal r? [#permalink] New post 14 Aug 2012, 00:04
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Galiya wrote:
why cant i come to pq=1 from pqs=s? for the 1st statement and pq=q from mpq=m?
may be its too stupid even to ask such a question, but im stuck!


That's not a stupid question at all.

The point is that from pqs = s it's not necessary pq to be 1: pqs=s --> pqs-s=0 --> s(pq-1)=0 --> s=0 OR pq=1. So, as you see, if s=0, then pq can take ANY value: 1, 10, -9, 0, ... Therefore we cannot say from the first statement whether pq=1.

The same for (2).

Hope it's clear.
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Re: Does pqr equal r? [#permalink] New post 14 Aug 2012, 07:59
my carelessness will ruin my score

thank you for your explanation, Bunuel! you are the best!
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Re: Does pqr equal r? [#permalink] New post 10 Dec 2012, 05:06
Is pqr = r?

pqr - r = 0
r ( pq - 1) = 0
r = 0 OR pq = 1

For the equation to hold, either:
(1) r=0 and pq could be anything, OR
(2) pq=1 and r could be any number

If we prove (1) or (2) then the answer to the question is YES!

Statement 1: pqs = s tells us either s=0 or pq=1. If s=0 then pq could be any number. it tells nothing about r also. INSUFFICIENT!
Statement 2: pqm = m is the same as Statement 1. INSUFFICIENT!

Answer: E
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Re: Does pqr equal r?   [#permalink] 10 Dec 2012, 05:06
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