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# Hard problem?

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Let \(S(n)\) equal the sum of the digits of positive integer \(n\). For example, \(S(1507)=13\) . For a particular positive integer \(n\)\(S(n)=1274\). Which of the following could be the value of \(S(n+1)\)?

I'm getting 1239 as an answer.

Please help!

Mar 14, 2018

### 5+0 Answers

#1
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n is an integer..... n+1 is the NEXT sequential integer.....obtained by adding '1' to the n integer....so the sum of the digits COULD be '1' greater.  Is this a multiple choice question?   What are your choices?

1275

Mar 14, 2018
edited by ElectricPavlov  Mar 14, 2018
#3
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The question asks what   'could'  the next one be.....and we weren't given any multiple choices...

ElectricPavlov  Mar 14, 2018
edited by ElectricPavlov  Mar 14, 2018
#4
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We are looking for an integer whose sum of its digits  = 1274

Here's a possibility :

S(n)  = 1274  = S ( 7777....7)   where we have 7 repeated 182 times

Note that    7 * 182  =   1274

So....  S ( n + 1) = S( [7777....7] + 1 )  = S(1275)    =  S (555.....5)   where we have 5 repeated 255 times

Note that  255 * 5  =  1275   Mar 14, 2018
#5
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We are talking about a VERY large number here....there are thousands of possibilities....without knowing the starting a1  and the  r of the series and where in the series you are, it could be almost anything.....were you given any more information...or multiple choices?

Mar 15, 2018