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

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

16 May 2009, 21:17

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Is pq = 1?

(1) pqp = p

(2) qpq = q

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Re: A One product [#permalink]

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)

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Re: A One product [#permalink]

17 May 2009, 19:05

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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.
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Re: A One product [#permalink]

17 May 2009, 19:32

IanStewart wrote:

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.

That's right... OA is E.

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Re: A One product [#permalink]

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.

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Re: A One product [#permalink]

18 May 2009, 00:11

Great IanStewart!!!
IMO E
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Re: A One product [#permalink]

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

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

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

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