A certain number when successively divided by 3, 5 and 8

Home » Aptitude » Number System » Question

A certain number when successively divided by 3, 5 and 8 leaves remainder 1, 2, 3
respectively. Find the remainders when the same number is divided by reversing the divisors.

1. 3, 2, 1
2. 4, 1, 1
3. 4, 2, 2
4. 1, 4, 1

Correct Option: B

This problem can be solved by determining true or complete remainder and dividing it by reversing the order of divisors.
True remainder = d₁d₂r₃ + d1r₂ + r₁
Here, d₁ = 3, d₂ = 5, r₁ = 1, r₂= 2, r₃ = 3
∴ True remainder = 3 × 5 × 3 + 3 × 2 + 1= 45 + 6 + 1 = 52
Now, we divide 52 by 8, 5 and 3

Hence, the remainders are 4, 1 and 1.