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# Does pqr equal r?

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Manager
Joined: 16 Jan 2011
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12 Aug 2012, 13:34
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45% (medium)

Question Stats:

52% (00:43) correct 48% (00:43) wrong based on 166 sessions

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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
[Reveal] Spoiler: OA

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Re: Does pqr equal r? [#permalink]

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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.

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Re: Does pqr equal r? [#permalink]

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

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Manager
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Re: Does pqr equal r? [#permalink]

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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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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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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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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!

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Re: Does pqr equal r? [#permalink]

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

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