Question

When an integer 'n' is divided by 'k', the remainder is on When another integer 'm' is divided by 'k', the remainder is 2. What is the remainder when 'n x m' is divided by 'k'?

• A. 1
• B. 2
• C. с. 3
• D. n-1
• E. n/2

Answer 1

The Correct Option is B

Step 1: Understand the problem.
We are given that when an integer \( n \) is divided by \( k \), the remainder is 1. That is:
\( n \equiv 1 \, (\text{mod} \, k) \)
When another integer \( m \) is divided by \( k \), the remainder is 2. That is:
\( m \equiv 2 \, (\text{mod} \, k) \)
We are asked to find the remainder when \( n \times m \) is divided by \( k \).

Step 2: Use the properties of remainders.
From modular arithmetic, we know that:
If \( n \equiv 1 \, (\text{mod} \, k) \) and \( m \equiv 2 \, (\text{mod} \, k) \), then:
\( n \times m \equiv 1 \times 2 = 2 \, (\text{mod} \, k) \)
Therefore, the remainder when \( n \times m \) is divided by \( k \) is 2.

Step 3: Conclusion.
The remainder when \( n \times m \) is divided by \( k \) is 2.

Final Answer:
The correct option is (B): 2.