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Does pqr equal r?

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Does pqr equal r? [#permalink]

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New post 12 Aug 2012, 13:34
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Does pqr equal r?

(1) pqs = s where s is some unknown number
(2) mpq = m where m is some unknown number
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Re: Does pqr equal r? [#permalink]

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New post 12 Aug 2012, 13:47
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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]

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New post 13 Aug 2012, 10:52
Cant combining equal PQ=1 ?

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Re: Does pqr equal r? [#permalink]

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New post 13 Aug 2012, 12:28
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]

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New post 14 Aug 2012, 01:04
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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]

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New post 14 Aug 2012, 08:59
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]

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New post 10 Dec 2012, 06:06
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]

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Re: Does pqr equal r?   [#permalink] 16 Nov 2017, 08:38
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