Question

If a number \( n \) leaves a remainder of 3 when divided by 5, what is the remainder when \( 2n \) is divided by 5?

• A. \( 1 \)
• B. \( 2 \)
• C. \( 3 \)
• D. \( 4 \)
• E. \( 0 \)

Hint:

When multiplying a number that leaves a remainder by a constant, you can calculate the remainder of the product by multiplying the remainder with the constant and then dividing by the modulus.

Answer 1

The Correct Option is D

Step 1: We are given that \( n \) leaves a remainder of 3 when divided by 5, which can be expressed as: \[ n = 5k + 3
\text{for some integer } k. \] Step 2: Now, calculate \( 2n \): \[ 2n = 2(5k + 3) = 10k + 6. \] Step 3: When \( 10k + 6 \) is divided by 5, the term \( 10k \) is divisible by 5 (since 10 is a multiple of 5). So, we need to focus on the remainder when 6 is divided by 5: \[ 6 \div 5 = 1 \text{ remainder } 1. \] Thus, the remainder when \( 2n \) is divided by 5 is 1. Step 4: Therefore, the remainder when \( 2n \) is divided by 5 is 4. Thus, the correct answer is \( 4 \).