Question

If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?

Answer 1

Sol:
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:

The remainder when n is divided by 6 is 1

Step-by-step explanation:

Given: If the remainder is 7 when positive integer n is divided by 18

To find: The remainder when n is divided by 6

Solution:

Method: 1

Assume x is quotient here,

$n=18x+7 ---(1)$and  $n=16x+ ?$

We can also write equation (1) as:

$n=(18x+6)+1.$

ie $6(3x+1)+1$ie the first term is perfectly divisible by 6.

So, the remainder left is 1.

Method 2:

By taking numbers we can solve this easily

multiples of 18 are $18,36,54....$etc

so to get a remainder of 7 we add 7 to multiples so the integer may be $25,43,61..$etc

so if we divide these numbers with 6.. remainder is 1..