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

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Director
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Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

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New post 26 Oct 2018, 16:47
bigdady wrote:
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.
Director
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Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

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New post 27 Dec 2018, 20:51
bigdady wrote:
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.
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Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

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New post 30 Jan 2020, 02:05
I took n=1
so equation became:
25*10^1 + k * 10^2(1) = 0
=250 + 100k = 0
= 50 (5 + 2k) = 0
now plug in values and check for answers
= 5 + 2(47)
=5+94
=99

is my approach correct?
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Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

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New post 05 Feb 2020, 11:38
25*10^n+K*10^2n ---> assuming n=1 as it will have least impact when adding digits (10(25+10K))
substitute k values from option (10(25+470))--> 4950 ___ adding digits 18 hence e
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A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

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New post 17 Feb 2020, 11:01
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A positive integer is divisible by 9 if and only if the sum of its   [#permalink] 17 Feb 2020, 11:01

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