Question

a positive integer n when divided by 9,gives 7 as remainder.what will be the remainder when (3n-1) divided by 9?

Answer 1

Answer:

Step-by-step explanation:Given A positive integer n is divided by 9 gives 7 as the remainder.

Let a be quotient

n = 9a+7

3n-1 is divided by 9

now, 3n-1= 3(9a+7)-1

=27a + 21-1

=27a +20 = 27 a + 18 + 2

= 9( 3a + 6) + 2 when divided by 9

Remainder = 2.

Answer 2

Answer:

Step-by-step explanation:

Given :-

A positive integer n when divided by 9.

Gives 7 as remainder.

To Find :-

Remainder when (3n - 1) is divided by 9.

Solution :-

We have, n = 9q + 7, where g is the quotient.

= 3n = 27q + 21 (Multiply by 3)

= 3n - 1 = 27q + 20 = 9(39 + 2) + 2

Hence, remainder is 2, when (3n - 1) is divided by 9.

Important Information :-

Euclid's Division Lemma -

Dividend = Divisor × quotient + Remainder

This holds for every pair of positive integers as proved in the following lemma.