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a, b, and c are positive integers. If a, b, and c are assembled into t

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a, b, and c are positive integers. If a, b, and c are assembled into t [#permalink]

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New post 27 Oct 2014, 07:22
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Tough and Tricky questions: Factors.



a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc?

(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above
Spoiler: OA

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a, b, and c are positive integers. If a, b, and c are assembled into t [#permalink]

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New post 27 Oct 2014, 20:41
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Bunuel wrote:

Tough and Tricky questions: Factors.



a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc?

(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above


Option A, C & E can be safely ignored as we can pick up some numbers which contradict the divisibility

247247 >> Cannot be divided by 16, 5 & 3

To check for 13, better to go the algebraic way:

\(abcabc = a * 10^5 + b * 10^4 + c * 10^3 + a * 10^2 + b * 10^1 + c * 10^0\)

\(= a10^2(1000+1) + b10(1000+1) + c(1000+1)\)

Check divisibility of 1001 by 13

\(\frac{1001}{13} = 77\)

Answer = B = 13
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Re: a, b, and c are positive integers. If a, b, and c are assembled into t [#permalink]

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New post 09 Apr 2016, 04:31
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Bunuel wrote:

Tough and Tricky questions: Factors.



a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc?

(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above



Here the BEST approach would be dividing by abc..
we can be sure that abcabcwill get div by abc..
abcabc/abc = 1001..
what are factors of 1001 = 7*11*13..
Thus in given choices 13 is correct
ans B
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Re: a, b, and c are positive integers. If a, b, and c are assembled into t [#permalink]

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New post 12 Aug 2017, 07:55
Bunuel wrote:

Tough and Tricky questions: Factors.



a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc?

(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above


abcabc = 10^5*a + 10^4*b + 10^3*c + 10^2 *a + 10 * b + c
= 1001 (100a + 10b + c)

Now 1001 = 13*7*11

So, 13 must be a factor of abcabc

Answer B
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Re: a, b, and c are positive integers. If a, b, and c are assembled into t   [#permalink] 12 Aug 2017, 07:55
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