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?​

Answer 1

Answer:

2

Step-by-step explanation:

⇒n=9q+7.

⇒3n=3(9q+7)=27q+21.

⇒3n−1=27q+21−1=27q+20=9(3q+2)+2.

⇒ Dividing 3n−1 by 9 is equivalent to dividing 9(3q+2)+2 by 9.

Since 9 is a factor of 9(3q+2) and 2<9, the remainder when 9(3q+2)+2 is divided by 9 is 2.

⇒ The remainder when 3n−1 is divided by 9 is 2.