Question

A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13 ?

(a) 0 (b) 1 (c) 3 (d) 5

Answer 1

The number can be expessed by 143n+31 (euclid division lemma, a = bq+r) where n is any natural number.

Now as 143 is divisible by 13, 143n leaves no remainer or zero as remainder when divided by 13.

So we only need to focus on 31 now.

31 divided by 13 leaves remainder 5

Hence the answer is 5.