Question
If a number is divided by 6 , 3 is the remainder . What is remainder if the the square of
the number is divided by 6?
Answer: Option C
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Let the number be x
Given that if the number is divided by 6 , 3 is the remainder
=> x ÷ 6 = k, remainder = 3
Hence x = 6k + 3
Square of the number = x2 = (6k + 3)2
=36k2 + 36k + 9 ∵ (a + b)2 = a2 + 2ab + b2
=36k2 + 36k + 6 + 3
= 6(6k2 + 6k + 1) + 3
Hence, when the square of the number is divided by 6, we get 3 as remainder.
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