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by which x must be divisible

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by abhi332 » Thu Feb 25, 2010 1:28 pm
If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct
nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?
(A) 3
(B) 6
(C) 11
(D) 22
(E) 222

[spoiler]OA:E[/spoiler]
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by harsh.champ » Thu Feb 25, 2010 1:36 pm
abhi332 wrote:If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct
nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?
(A) 3
(B) 6
(C) 11
(D) 22
(E) 222

[spoiler]OA:E[/spoiler]
abc
acb
bca
bac
cba
cab
Each no. occurs exactly twice at units ,tens and hundreds place.
2a + 2(10a) + 2(100a)
Similarly for b and c
Hence, x = 2 x 111 (a+b+c)
= 222(a+b+c)

Hence,the answer is E
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