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27 Oct 2014, 07:22
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
43% (01:58) correct
57%
(01:40)
wrong
based on 404
sessions
History
Date
Time
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Not Attempted Yet
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
27 Oct 2014, 20:41
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Bunuel
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
09 Apr 2016, 04:31
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Bunuel
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
