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# Discussion

A number when divided by 6 leaves a remainder 3. When the square of the same number is divided by 6, the remainder is:

• A.1
• B.2
• C.3

Let $$x=6q+3$$. Then,
$$x^{2} = (6q+3)^{2} \\= 36q^{2}+36q+9 \\= 6(6q^{2}+6q+1)+3$$
So, when $$2n$$ is divided by $$4$$, remainder $$=3$$