Question

On dividing a positive integer n by 9, we get 7 as a 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 × 3q + 9 × 2 + 2

⇒ 3n – 1 = 9 × (3q + 2) + 2 

So, when (3n-1) is divided by 9, we get the remainder 2.