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
Solution:
(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
$\Rightarrow 3 n-1=9 \times 3 q+9 \times 2+2$
$\Rightarrow 3 n-1=9 \times(3 q+2)+2$
So, when (3n − 1) is divided by 9, we get the remainder 2.