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a, b, and c are positive integers. If a, b, and c are assembled into t
[#permalink]
25 Jul 2022, 03:26
25 Jul 2022, 03:26
Expert Reply
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Question Stats:
77% (02:13) correct
22% (00:59) wrong based on 9 sessions
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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
(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above
Re: a, b, and c are positive integers. If a, b, and c are assembled into t
[#permalink]
27 Jul 2022, 15:22
27 Jul 2022, 15:22
Expert Reply
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
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
gmatclubot
Re: a, b, and c are positive integers. If a, b, and c are assembled into t [#permalink]
27 Jul 2022, 15:22
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