What is the sum of the remainders on dividing the numbers from 1to 100 by 3?
Answers
Given : Divide numbers from 1 to 100 by 3
To find : sum of the remainders
Solution:
1 to 100 numbers lets divide into 3 groups
remainder 1 , remainder 2 , remainder = 0
1 , 4 7 , 10 , ...................... , 100
Remainder = 1 in each case
total numbers 100 = 1 + (n-1)3 => n = 34
sum of remainder = 34 * 1 = 34
2 , 5 , 8 , ..................................., 98
remainder = 2 in each case
total numbers 98 = 2 + (n - 1) 3 => n = 33
sum of remainder = 33 * 2 = 66
3 , 6 , 9 .........................,.,. ,99
remainder = 0
sum of the remainders on dividing the numbers from 1to 100 by 3 = 34 + 66
= 100
sum of the remainders on dividing the numbers from 1to 100 by 3 = 100
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