How many 3 digit numbers are such that when divided by 7, leave a remainder 3 in each case.

The first and last numbers between 100 and 999 which on divisibility by 7 leaves the remainder 3 are 101 and 997 respectively.

Since, all the numbers between 100 and 999 which are divisible by 7 and leaves the remainder 3 are in AP, where, a = 101, l = 997 and d = 7.

Now, l = a + (n – 1)d

Hence, there are 129 numbers between 100 and 999 which are exactly divisible by 7 and leaves the remainder 3.