Question

When a number is divided by 3 it leaves remainder as 5. What will be the remainder when 3n + 3 are divided by 3?

(a) 0

(b) 3

(c) 9

(d) 6

This question was posed to me during an interview for a job.

The above asked question is from Euclid’s Division Lemma in chapter Real Numbers of Mathematics – Class 10

Answer 1

Right answer is (a) 0

Explanation: Let the number be n.

If the number is divided by 3 it leaves 5 as remainder.

By Euclid’s division lemma,

n = 3q + 5 where q is quotient

3n = 3(3q+5)

3n = 9q + 15

3n + 3 = 9q + 18 = 3 × 3q + 3 × 6 = 3 (3q + 6)

Hence, the remainder is 0.