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# A positive integer is divisible by 9 if and only if the sum of its

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Director
Joined: 19 Oct 2013
Posts: 509
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

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26 Oct 2018, 16:47
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 $$25*10^n + k*10^{2n}$$ divisible by 9?

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

In this question regardless of the value of n we will have units digit of 0

So we are concerned with how 2+5+k adds up to a number divisible by 9

if we take 2+5+4+7 = 18 a number divisible by 9.

E is the answer choice.
Senior Manager
Joined: 29 Jun 2017
Posts: 457
Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

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27 Dec 2018, 20:51
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 $$25*10^n + k*10^{2n}$$ divisible by 9?

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

is this from official source.
this is hard. many person do it wrongly

because k*10^2n has at least 1 number more than 25*10^n, we know that the sume of the two number will be
K25*10^x
for exam ple if k=52
the sume will be
5225*10^n

ONLY THIS CASE HAPPEN, we can add the digit, and find the answer is E.
Re: A positive integer is divisible by 9 if and only if the sum of its &nbs [#permalink] 27 Dec 2018, 20:51

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# A positive integer is divisible by 9 if and only if the sum of its

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