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p, q, and r are positive integers. If p, q, and r are assembled into t
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27 Oct 2014, 20:51
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62% (01:10) correct 38% (01:13) wrong based on 149 sessions
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p, q, and r are positive integers. If p, q, and r are assembled into the sixdigit 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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Re: p, q, and r are positive integers. If p, q, and r are assembled into t
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28 Oct 2014, 02:28
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




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Re: p, q, and r are positive integers. If p, q, and r are assembled into t
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28 Oct 2014, 02:09
Nice question. i was wondering what would be the shortest way to solve this problem. Bunuel, your help is required ?
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Re: p, q, and r are positive integers. If p, q, and r are assembled into t
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13 Oct 2017, 07:42
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 1,00 1 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.



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Re: p, q, and r are positive integers. If p, q, and r are assembled into t
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19 Oct 2017, 22:37
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



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p, q, and r are positive integers. If p, q, and r are assembled into t
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21 Oct 2017, 05:36
PareshGmat wrote: p, q, and r are positive integers. If p, q, and r are assembled into the sixdigit 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. hence answer is D
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Re: p, q, and r are positive integers. If p, q, and r are assembled into t
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21 Oct 2017, 05:40
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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Re: p, q, and r are positive integers. If p, q, and r are assembled into t
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22 Oct 2017, 00:51
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!!




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