Question

How many natural numbers between 1 and 500 are not divisible by 7 and leave a remainder of 3 when divided by 4?

Answer 1

The numbers which leaves 3 as reminder when divided by 4 =

1∠4n + 3 = 500  

1∠4n = 497

n = 124

Therefore, the number of values of n is given range =124 = 0 +1 = 125

4n + 3 is divisible by 7 and n= 7K + 1

1 ∠ 4(7k +1) + 3 ∠500

1 ∠ 4(7k +1) = ∠497

1 ∠7k + 1 ∠ 124

1∠7k = 123

k = 123/7 = 17

Therefore, the number of values of n is given range =17 = 0 +1 = 18

So 125 - 18 = 107 numbers are there.