A number when divided by 7 leaves remainder of 4. If the square of the same number is divided by 7, then what is the remainder?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 3)

Answer 1

Given:

A number when divided by 7 leaves a remainder of 4.

Concept used:

Dividend = Divisor × Quotient + Remainder

Calculation:

Let the number and quotient be N and D respectively.

According to the question,

N = 7D + 4

⇒ N² = (7D + 4)²

⇒ N² = 49D² + 56D + 16

⇒ N² = 7(7D² + 8D + 2) + 2

So, 7(7D2 + 8D + 2) is completely divisible by 7.

Now, the remainder is 2.

∴ The remainder is 2.