A number when divided by 5 leaves a remainder 3. What is the remainder when the square of the same number is divided by 5?
1). 1
2). 2
3). 3
4). 4
Let the number be x
From given data-
Number when divided by 5 leaves a remainder 3
∴ x = 5q + 3 → dividend= divisor× quotient+ remainder
When square of number is divided by 5
∴ (5q+3)2 ÷ 5
⇒ (25q2 + 30q + 9) ÷ 5 → (a + b)2 = a2 + 2ab + b2
⇒ [5(5q2 + 6q + 1) + 4] ÷ 5
Here we can notice that when divided by 5 square of that number leaves 4 as a remainder