Find how many positive integers less than 10,000 are there suchthat the sum of the digits of the no. is divisible by 3?  Choose the correct answer: A) 1256 B) 2354 C) 2678 D) 3334 E) 3568
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
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Find how many positive integers less than 10,000 are there suchthat the sum of the digits of the no. is divisible by 3?