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# If x represents the sum of all the positive three-digit

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Intern
Joined: 10 Jan 2006
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If x represents the sum of all the positive three-digit [#permalink]

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18 May 2006, 08:38
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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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Manager
Joined: 28 Mar 2006
Posts: 157

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18 May 2006, 09:43
E it is...I solved b taking numbers..1 2 3 ...
cross checked again by taking 1 2 n 4

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Senior Manager
Joined: 15 Mar 2005
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18 May 2006, 10:33
For a, b and c, sum of possible 3! = 6 numbers is
abc + acb + bac + bca + cab + cba
= 100a + 10b+ c + 100a + 10c + b + 100b + 10a + c + 100b + 10c + a + 100c + 10a + b + 100c + 10b +a
= 222(a+b+c).

Hence E.
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Who says elephants can't dance?

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CEO
Joined: 20 Nov 2005
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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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18 May 2006, 11:03
Number is 2*(a+b+c) + 2*10 (a+b+c) + 2*100 (a+b+c) = (2+20+200) (a+b+c) = 222 (a+b+c) Hence E is the answer.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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Director
Joined: 16 Aug 2005
Posts: 937

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18 May 2006, 11:04
yes E it is. Question can confuse a lot of people if they are not confident (like me). I had no clue and started writing some stuff...then watched it getting easy...

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Director
Joined: 24 Oct 2005
Posts: 659

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19 May 2006, 03:16
I prefer using nos for this.

Take nos 1, 2, 3

The diff 3 digit nos that can be formed are
123, 132, 213, 231, 213, 321
Sum = 1332.

222 is divisible.

Hence E

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19 May 2006, 03:16
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