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?
Given: A positive integer n is divided by 9 gives 7 as the remainder.
Let a be quotient
n=9a+7
Now, 3n−1=3(9a+7)−1=27a+21−1=27a+20=27a+18+2=9(3a+6)+2
⇒3n−1=9(3a+6)+2
So, when 3n−1 is divided by 9
Remainder =2.
Hence, if (3n−1) is divided by 9 then the remainder will be 2