Question

On dividing a positive integer n by 9, we get 7 as remainder. What will be the remainder if (3n − 1) is divided by 9?

(a) 1
(b) 2
(c) 3
(d) 4

Answer 1

(b) 2

Let q be the quotient.
It is given that:
remainder = 7
On applying Euclid's algorithm, i.e. dividing n by 9, we have
n = 9q + 7
⇒ 3n = 27q + 21
⇒ 3n − 1 = 27q + 20
⇒ 3n − 1 = 9 $\times$ 3q + 9 $\times$ 2 + 2
⇒ 3n − 1 = 9 $\times$ (3q + 2) + 2
So, when (3n − 1) is divided by 9, we get the remainder 2.