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If a positive integer 'n' is divided by 15, the remainder is 4. What is the remainder if 'n2' is divided by 15?
1. 1
2. 0
3. 2
4. 3

1 Answer

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Correct Answer - Option 1 : 1

Given:

If a positive integer 'n' is divided by 15, the remainder is 4.

Concept used:

Dividend = (Divisor × Quotient) + Remainder

Calculation:

Let the quotient be ‘a’

According to the question,

⇒ n = (15 × a) + 4

Square both sides 

⇒ n2 = [(15 × a) + 4]2

⇒ n2 = (15a + 4)2

⇒ n2 = 225a2 + 120a + 16 

⇒ n2 = 225a + 120a + 16 

⇒ n2 = 15(15a + 8) + 16

On comparing with (Dividend = (Divisor × Quotient) + Remainder)

⇒ Remainder = 1

 1 is the remainder when n2 is divided by 15.

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