Question

A number when divided by 195 leaves a remainder 47. If the same number is divided by 15, the remainder will be:

• A. 4
• B. 3
• C. 2
• D. 1

Hint:

When working with remainders, simplify the division by considering only the remainder part of the number. This can help reduce complex calculations.

Answer 1

The Correct Option is C

Let the number be \( N \). When divided by 195, the remainder is 47, so we can write: \[ N = 195k + 47 \] for some integer \( k \). Now, divide \( N \) by 15: \[ N = 195k + 47 \] Dividing by 15: \[ 195k + 47 \quad \Rightarrow \quad \left( \frac{195k}{15} + \frac{47}{15} \right) \] Since \( \frac{195k}{15} \) is divisible by 15, we are left with the remainder from \( \frac{47}{15} \). \[ 47 \div 15 = 3 \text{ remainder } 2 \] Thus, the remainder is \( \boxed{2} \).