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Largest Integer

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Largest Integer

by beat_gmat_09 » Sun Nov 28, 2010 4:04 am
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
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by vamsi_567 » Sun Nov 28, 2010 4:28 am
beat_gmat_09 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
Is the answer E?

the possibe combination wud be ...abc+acb+bac+bca+cab+cba
Since abc = 100a+10b+c...if we add all the above nos...

=> (100a+10b+c) +(100a+10c+b) +(100b+10a+c) +(100b+10c+a) +(100c+10a+b) +(100c+10b+a)

=> 222a+222b+222c

=> 222 (a+b+c)...hence divisible by 222

wats the OA?
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by beat_gmat_09 » Sun Nov 28, 2010 7:42 am
You're right. OA: E
Thanks.
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