Question : A number, when divided by 6, leaves a remainder of 3. When the square of the same number is divided by 6, the remainder is:
Option 1: 0
Option 2: 2
Option 3: 1
Option 4: 3
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Correct Answer: 3
Solution :
Let the number be $x$.
Dividend = Quotient × Divisor + Remainder
When divided by 6, $x$ leaves a remainder of 3.
Let the quotient be $q$.
Then, $x=6q+3$
Now, squaring both sides we get,
$x^2=(6q+3)^2$
⇒ $x^2=36q^2+36q+9$
⇒ $x^2=6(6q^2+6q+1)+3$
Thus, $x^2$ divided by 6 leaves 3 as a remainder.
Hence, the correct answer is 3.
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