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# If positive integer P is a multiple of 22 and positive integer Q is a

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Intern
Joined: 10 Jul 2016
Posts: 45
If positive integer P is a multiple of 22 and positive integer Q is a  [#permalink]

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18 Jan 2017, 16:19
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If positive integer P is a multiple of 22 and positive integer Q is a multiple of 55, is PQ a multiple of 70??

(1) Q is a multiple of 49

(2) P is a multiple of 4
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: If positive integer P is a multiple of 22 and positive integer Q is a  [#permalink]

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18 Jan 2017, 18:09
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1
siddharthsinha123 wrote:
If positive integer P is a multiple of 22 and positive integer Q is a multiple of 55, is PQ a multiple of 70??

(1) Q is a multiple of 49

(2) P is a multiple of 4

P is a multiple of 22 and Q is a multiple of 55..
So PQ will be multiple of 22*55=11*11*2*5...
We are looking if PQ is multiple of 70 or 2*5*7..

PQ is surely a multiple of 2*5, we have to find if any of the two , P and Q, is multiple of 7...

Let's see the statements
1) Q is a multiple of 49
So Q is multiple of 7*7...
Ans is YES
Suff

2) P is multiple of 4
We still do not know if any of the two P or Q is multiple of 7..
Insufficient

A
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Joined: 19 Oct 2015
Posts: 26
Re: If positive integer P is a multiple of 22 and positive integer Q is a  [#permalink]

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05 Jul 2017, 09:25
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If positive integer P is a multiple of 22 and positive integer Q is a multiple of 55, is PQ a multiple of 70??

(1) Q is a multiple of 49

(2) P is a multiple of 4

------
Factors of P= 2 and 11
Factors of Q= 5 and 11

so Common factors are 2,5,11

Here it says that is PQ multiple of 70 ?
No factors of 70 are= 2*5*7

for PQ so asto be multiple of 70, there should be multiple of 7 greater than 7
and option A clearly say that Q is multiple of 49.

Answer A
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Re: If positive integer P is a multiple of 22 and positive integer Q is a  [#permalink]

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16 Jul 2018, 07:18
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Re: If positive integer P is a multiple of 22 and positive integer Q is a   [#permalink] 16 Jul 2018, 07:18
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# If positive integer P is a multiple of 22 and positive integer Q is a

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