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# p, q, and r are positive integers. If p, q, and r are assembled into t

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Joined: 27 Dec 2012
Posts: 1825
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Concentration: General Management, Technology
WE: Information Technology (Computer Software)
p, q, and r are positive integers. If p, q, and r are assembled into t  [#permalink]

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27 Oct 2014, 19:51
5
13
00:00

Difficulty:

55% (hard)

Question Stats:

61% (01:53) correct 39% (01:38) wrong based on 151 sessions

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p, q, and r are positive integers. If p, q, and r are assembled into the six-digit number pqrpqr, which one of the following must be a factor of pqrpqr?

(A) 23
(B) 19
(C) 17
(D) 7
(E) none of the above

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Joined: 16 Oct 2014
Posts: 9
Re: p, q, and r are positive integers. If p, q, and r are assembled into t  [#permalink]

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28 Oct 2014, 01:28
4
2
One short way -
pqrpqr = 1000pqr + pqr = (1000+1)pqr = 1001pqr

Therefore any factor of 1001 is a factor of pqrpqr
7 is a factor of 1001

So D
##### General Discussion
Intern
Joined: 23 Oct 2012
Posts: 44
Re: p, q, and r are positive integers. If p, q, and r are assembled into t  [#permalink]

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28 Oct 2014, 01:09
Nice question. i was wondering what would be the shortest way to solve this problem.

Bunuel, your help is required ?
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Joined: 08 Aug 2017
Posts: 3
WE: Analyst (Investment Banking)
Re: p, q, and r are positive integers. If p, q, and r are assembled into t  [#permalink]

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13 Oct 2017, 06:42
JohanH wrote:
One short way -
pqrpqr = 1000pqr + pqr = (1000+1)pqr = 1001pqr

Therefore any factor of 1001 is a factor of pqrpqr
7 is a factor of 1001

So D

How to know that 7 is a factor of 1,001?:
1. Take the last digit of 1,001 and multiply it by 2: 1x2 = 2
2. Calculate the difference between the other digits and the last result: 100 - 2 = 98, is 98 a factor of 7? Yes (98 : 7 = 14). Then, answer D is correct.
Manager
Joined: 19 Aug 2016
Posts: 84
Re: p, q, and r are positive integers. If p, q, and r are assembled into t  [#permalink]

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19 Oct 2017, 21:37
JohanH wrote:
One short way -
pqrpqr = 1000pqr + pqr = (1000+1)pqr = 1001pqr

Therefore any factor of 1001 is a factor of pqrpqr
7 is a factor of 1001

So D

Why are we doing 1000 pqr???
just wondering what the logic is

Thanks
Manager
Joined: 06 Aug 2017
Posts: 86
GMAT 1: 570 Q50 V18
GMAT 2: 610 Q49 V24
GMAT 3: 640 Q48 V29
p, q, and r are positive integers. If p, q, and r are assembled into t  [#permalink]

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21 Oct 2017, 04:36
1
PareshGmat wrote:
p, q, and r are positive integers. If p, q, and r are assembled into the six-digit number pqrpqr, which one of the following must be a factor of pqrpqr?

(A) 23
(B) 19
(C) 17
(D) 7
(E) none of the above

Another, more clear method of doing this.

pqrpqr => 100000p+10000q+1000r+100p+10q+r =>(100000+100)p +(10000+10)q+(1000+1)r =>100100p + 10010q +1001r => 1001 (100p+10q+r)

So pqrpqr = 1001 (100p+10q+r) = 1001 (pqr)

1001 is always divisible by 7.

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Re: p, q, and r are positive integers. If p, q, and r are assembled into t  [#permalink]

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21 Oct 2017, 04:40
zanaik89 wrote:
JohanH wrote:
One short way -
pqrpqr = 1000pqr + pqr = (1000+1)pqr = 1001pqr

Therefore any factor of 1001 is a factor of pqrpqr
7 is a factor of 1001

So D

Why are we doing 1000 pqr???
just wondering what the logic is

Thanks

Hi Zanaik,

Here, is how it is derived.

pqrpqr => 100000p+10000q+1000r+100p+10q+r =>(100000+100)p +(10000+10)q+(1000+1)r =>100100p + 10010q +1001r => 1001 (100p+10q+r)

So pqrpqr = 1001 (100p+10q+r) = 1001 (pqr)
_________________

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GMAT PREP 1: Q50 V34 - 700

Veritas Test 1: Q43 V34 - 630
Veritas Test 2: Q46 V30 - 620
Veritas Test 3: Q45 V29 - 610
Veritas Test 4: Q49 V30 - 650

GMAT PREP 2: Q50 V34 - 700

Veritas Test 5: Q47 V33 - 650
Veritas Test 5: Q46 V33 - 650

Manager
Joined: 19 Aug 2016
Posts: 84
Re: p, q, and r are positive integers. If p, q, and r are assembled into t  [#permalink]

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21 Oct 2017, 23:51
Jabjagotabhisavera wrote:
zanaik89 wrote:
JohanH wrote:
One short way -
pqrpqr = 1000pqr + pqr = (1000+1)pqr = 1001pqr

Therefore any factor of 1001 is a factor of pqrpqr
7 is a factor of 1001

So D

Why are we doing 1000 pqr???
just wondering what the logic is

Thanks

Hi Zanaik,

Here, is how it is derived.

pqrpqr => 100000p+10000q+1000r+100p+10q+r =>(100000+100)p +(10000+10)q+(1000+1)r =>100100p + 10010q +1001r => 1001 (100p+10q+r)

So pqrpqr = 1001 (100p+10q+r) = 1001 (pqr)

Excellent explanation!!

Thank u very much for the reply...Really appreciate it!!
Re: p, q, and r are positive integers. If p, q, and r are assembled into t &nbs [#permalink] 21 Oct 2017, 23:51
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