Question

How can I find that how many 3 digit numbers are there which leave a remainder 3 on division by 7?

Answer 1

3 digit numbers are between 100 and 999. First 3 digit number to leave a remainder of 3 when divided by 7 is 100.

Last 3 digit number to leave a remainder of 3 when divided by 7 is 996. it is an AP with
a=100,d=7,

tn=996
a=100,
d=7,
tn=997
tn=997=100+7(n−1)

tn=997=100+7(n−1)
897=7(n−1)

897=7(n−1)


128=n−1
n=129.