Question

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?

Answer 1

The options are
A. 1112
B. 2213
C. 2223
D. 3334

Answer 2

Hint: If a number is divisible by 3, the sum of its digits are divisible by 3 and the other way round works too.

Answer 3

i know that
but how will i find the sum?

Answer 4

I was hoping you'd figure it out yourself. Solve 3k<=10,000 for k, with k a natural number.

Answer 5

Ah
i have to solve 3k=10,000?

Answer 6

Yep

Answer 7

3333.3333

Answer 8

but how u figured?

Answer 9

Yeah that's why I put the inferior sign, round it to the inferior natural number.

Answer 10

well sum of the digits divisible by 3 means the number itself divisible by 3

Answer 11

does it includes 0

Answer 12

@ikram002p please explain

Answer 13

so
3,6,9,.......,9,999
all are divisible by 3 and there sum of digits is divisible by 3 as well

Answer 14

yep

Answer 15

Here's an example 18 is divisible by 3 : 1+8 = 9 is divisible by 3.

Answer 16

:) so u can count them now ?

Answer 17

read the divisiblity for 3 here https://en.wikipedia.org/wiki/Divisibility_rule

Answer 18

here is a trick
3,6,9,.......,9,999 = 3*(1,2,3,......,1111)

Answer 19

ps:- dont forget the zero ;)

Answer 20

actually that equals 3333 from \(3,6,\cdots\ 9999\)

Answer 21

oh sorry i made a typo :P

Answer 22

so it would be 3333+(Zero count 1)=3334

Answer 23

it says sum of digits divisible by 3 not equal 3
3|0

Answer 24

:/

Answer 25

ikky i get ur explanation
3(1,2...)
3k

Answer 26

so now u can count them ?

Answer 27

i made a typo first here

3,6,9,.......,9,999 = 3*(1,2,3,......,3333)

Answer 28

and dont forget to add the zero :D

Answer 29

yay
got it :*

Answer 30

good :D

Answer 31

Thank you so much to @ikram002p @Loser66 @mathmath333 @math&ing001 and that unknown user(i know who is it)

Answer 32

you are the most welcome ;)