Question

If a number is divided by 6, the remainder is 3 then what will be the remainder when the square of the same number is divided by 6 again

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is D 3

We know
a = bq + r where 0 ≤ r < b
Let the number be N
N = 6m + 3, where m is the quotient
Now,
$N^2=(6m+3{)}^2$
$=36m^2+9+36m$
$=6(6m^2+6m+1)+3$
= 6k + 3, where $k=6m^2+6m+1$
So, when $N^2$ is divided by 6, it leaves 3 as remainder.
Hence, correct option is D