Question

c) What is the sum of the remainders on
dividing the numbers from 1to 100 by 3?

Answer 1

Answer:

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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