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]Answer
There are 3!, or 6, different three-digit numbers that can be constructed using the digits a, b, and c:
The value of any one of these numbers can be represented using place values. For example, the value of abc is 100a + 10b + c.
Therefore, you can represent the sum of the 6 numbers as:
x is equal to 222(a + b + c). Therefore, x must be divisible by 222.
The correct answer is E.[/spoiler]
(A) 3
(B) 6
(C) 11
(D) 22
(E) 222
[spoiler]Answer
There are 3!, or 6, different three-digit numbers that can be constructed using the digits a, b, and c:
The value of any one of these numbers can be represented using place values. For example, the value of abc is 100a + 10b + c.
Therefore, you can represent the sum of the 6 numbers as:
x is equal to 222(a + b + c). Therefore, x must be divisible by 222.
The correct answer is E.[/spoiler]
Regards,
Sunit
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Kill all my demons..And my angels might die too!
Sunit
________________________________
Kill all my demons..And my angels might die too!
