A positive integer n when divided by 9 gives 7 as remainder.What will be the remainder when (3n-1) is divided by 9? 

A positive integer n when divided by 9 gives remainder 7.

By using Euclids Division lemma,

n = 9q + 7    where q > 0

 

3n -1  = 3(9q + 7) - 1

3n - 1 = 27 q + 21 - 1

3n - 1 = 27q + 20

3n - 1 = 27q + 18 + 2

3n - 1 = 9(3q + 2) + 2

3n - 1 = 9Q + 2 ......(Where Q = (3q + 2))

 

Remainder is 2.