rvc
  • rvc
Hom many non-negative integers less than 10,000 are there such that the sum of the digits of the number is divisible by 3?
Mathematics
jamiebookeater
  • jamiebookeater
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rvc
  • rvc
The options are A. 1112 B. 2213 C. 2223 D. 3334
math&ing001
  • math&ing001
Hint: If a number is divisible by 3, the sum of its digits are divisible by 3 and the other way round works too.
rvc
  • rvc
i know that but how will i find the sum?

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math&ing001
  • math&ing001
I was hoping you'd figure it out yourself. Solve 3k<=10,000 for k, with k a natural number.
rvc
  • rvc
Ah i have to solve 3k=10,000?
math&ing001
  • math&ing001
Yep
rvc
  • rvc
3333.3333
rvc
  • rvc
but how u figured?
math&ing001
  • math&ing001
Yeah that's why I put the inferior sign, round it to the inferior natural number.
ikram002p
  • ikram002p
well sum of the digits divisible by 3 means the number itself divisible by 3
mathmath333
  • mathmath333
does it includes 0
rvc
  • rvc
@ikram002p please explain
ikram002p
  • ikram002p
so 3,6,9,.......,9,999 all are divisible by 3 and there sum of digits is divisible by 3 as well
rvc
  • rvc
yep
math&ing001
  • math&ing001
Here's an example 18 is divisible by 3 : 1+8 = 9 is divisible by 3.
ikram002p
  • ikram002p
:) so u can count them now ?
mathmath333
  • mathmath333
read the divisiblity for 3 here https://en.wikipedia.org/wiki/Divisibility_rule
ikram002p
  • ikram002p
here is a trick 3,6,9,.......,9,999 = 3*(1,2,3,......,1111)
ikram002p
  • ikram002p
ps:- dont forget the zero ;)
mathmath333
  • mathmath333
actually that equals 3333 from \(3,6,\cdots\ 9999\)
ikram002p
  • ikram002p
oh sorry i made a typo :P
ikram002p
  • ikram002p
so it would be 3333+(Zero count 1)=3334
ikram002p
  • ikram002p
it says sum of digits divisible by 3 not equal 3 3|0
rvc
  • rvc
:/
rvc
  • rvc
ikky i get ur explanation 3(1,2...) 3k
ikram002p
  • ikram002p
so now u can count them ?
ikram002p
  • ikram002p
i made a typo first here 3,6,9,.......,9,999 = 3*(1,2,3,......,3333)
ikram002p
  • ikram002p
and dont forget to add the zero :D
rvc
  • rvc
yay got it :*
ikram002p
  • ikram002p
good :D
rvc
  • rvc
Thank you so much to @ikram002p @Loser66 @mathmath333 @math&ing001 and that unknown user(i know who is it)
ikram002p
  • ikram002p
you are the most welcome ;)

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