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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

Expert replies
by M7MBA » Sat Jul 25, 2020 3:01 pm

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E

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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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Source: — Problem Solving |

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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