Question

what are the 3 digit number between 100 and 999 that leaves a remainder 3 when divided by 7​

Answer 1

Answer:

Since, all the numbers between 100 and 999 which are divisible by 7 and leaves the remainder 3 are in AP, where, Hence, there are 129 numbers between 100 and 999 which are exactly divisible by 7 and leaves the remainder

step by step

3 digit numbers are from 100 to 999.

First number 100≡2(mod7)

101≡3(mod7) is the first number having remainder 7

Last number 999≡5(mod7)

Hence 997≡3(mod7) is last number having remainder 7.

So total numbers having remainders 7 between 100 and 999 are

(997−101)÷7+1=128+1=129

(1 added to include 101)