Find how many positive integers less than 10,000 are there suchthat the sum of the digits of the no. is divisible by 3?
Pick one
A) 1246  B) 2346  C) 5678  D) 3334  E) 4567
If sum of the digits is divisible by 3, the number is divisible by 3.   Therefore, required number of non-negative integers is equal to count of numbers less than 10,000 which are divisible by 3.   Such numbers are (3, 6, 9, ... , 9999) (arithmetic progression with first term=3, last term=9999, common difference=3).   Count of such numbers =   9999   3   =   3333   99993=3333   But zero is also divisible by 3.   This makes our total count 3334   3334
<result>D</result>
Find how many positive integers less than 10,000 are there suchthat the sum of the digits of the no. is divisible by 3?