A positive integer is divisible by 9 if and only if the sum of its digits is divisible by 9. If $n$ is a positive inte

A positive integer is divisible by 9 if and only if the sum of its digits is divisible by 9. If $n$ is a positive integer, for which of the following values of $k$ is $25\cdot 10^n+k\cdot 10^{2n}$ divisible by 9?

(A) 9
(B) 16
(C) 23
(D) 35
(E) 47

[spoiler]OA=E[/spoiler]

Source: Official Guide

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Nik13: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Sun Jul 26, 2020 4:57 am

Re: A positive integer is divisible by 9 if and only if the sum of its digits is divisible by 9. If $n$ is a positive

by Nik13 » Sun Jul 26, 2020 5:15 am

Assuming the value of n to be 1, 250+ k × 100 must be a factor of 9

Plugging in the value of k as 47, we get 4950 which is divisible by 9. Thus, the answer is e

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