On dividing a positive integer n by 9, we get 7 as a remainder. What w

1.	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» (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.

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»

(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.