A number when divided by 11, it leaves remainder 3. We get remainder 5, when the quotient obtained is divided by 9. What will be the remainder when this number is divided by 3?

A number when divided by 11, it leaves remainder 3. We get remainder 5, when the quotient obtained is divided by 9. What will be the remainder when this number is divided by 3? Correct Answer 1

Given:

A number is divided by 11 and remainder = 3.

The quotient is divided by 9, the remainder = 5

Concept Used:

Dividend = Divisor × Quotient + Remainder

x = q₁ × a + r₁

q₁ = q₂ × b + r₂

We assume q₂ = 1

where, x, a and b are natural numbers.

q₁ and q₂ are quotients for x and q₁ respectively.

r₁ and r₂ are remainders obtained from dividing x and q₁ by a and b respectively.

Calculations:

Let the required number be N.

Let the quotients obtained after dividing N and its quotient be q₁ and q₂.

Let divisors and remainders for N and q₁ be d₁, d₂ and r₁, r₂ respectively.

Assume q₂ = 1

q₁ = q₂ × d₂ + r₂

⇒ q₁ = 1 × 9 + 5

⇒ q₁ = 14

N = q₁ × d₁ + r₁

⇒ N = 14 × 11 + 3

⇒ N = 157

On dividing N by 3, we get

⇒ 157/3 = (156 + 1)/3

⇒ Remainder = 1

∴ The remainder when the number 157 is divided by 3 is 1.