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

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Math Expert
Joined: 02 Sep 2009
Posts: 46319
a, b, and c are positive integers. If a, b, and c are assembled into t [#permalink]

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27 Oct 2014, 07:22
1
8
00:00

Difficulty:

85% (hard)

Question Stats:

43% (01:14) correct 57% (01:17) wrong based on 143 sessions

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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

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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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27 Oct 2014, 20:41
7
2
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

$$\frac{1001}{13} = 77$$

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Joined: 02 Aug 2009
Posts: 5938
Re: a, b, and c are positive integers. If a, b, and c are assembled into t [#permalink]

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09 Apr 2016, 04:31
1
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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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

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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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