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positive int

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by Ozlemg » Thu Aug 04, 2011 1:40 am
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

OA : B
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by Anurag@Gurome » Thu Aug 04, 2011 3:30 am
Ozlemg wrote: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

OA : B
The sin-digit integer abcabc can be written as 100000a + 10000b + 1000c + 100a + 10b + c = 100100a + 10010b + 1001c = 1001(100a + 10b + c)
Now from the given answer choices, check 1001 is divisible by which integer.
It can be seen that 1001 is divisible only by 13.

The correct answer is B.
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by Frankenstein » Thu Aug 04, 2011 3:30 am
Hi,
abcabc = (1001)*abc
1001 = 13*11*7

Hence, B
Cheers!

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