Anichka wrote:
If N = 1000x + 100y + 10z, where x, y, and z are different positive integers less than 4, the remainder when N is divided by 9 is
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
Since x, y, and z are distinct positive integers less than 4, they can be 1, 2, or 3, doesn't matter which one is what.
Then N = 10(100x + 10y + z) = xyz0 is 10 times a three digit number formed by any of the permutations of the digits 1, 2, and 3.
For example 1230, 3210, 3120,...in fact, is quite a short list, only 3! = 6 numbers.
The divisibility rule by 9 says that the sum of the digits of the number and the number itself, leave the same remainder when divided by 9.
For example, when the remainder is 0, the number and the sum of its digit, are both divisible by 9.
Since the sum of the digits of N is 1 + 2 + 3 = 6, the remainder when N is divided by 9, is 6.
Answer C.
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