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A number leaves a remainder of 4 when divided by 6. If this number is multiplied

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Question: A number leaves a remainder of 4 when divided by 6. If this number is multiplied by 3, what will be the remainder when the result is divided by 6? (2023)

Options:

  1. 0
  2. 1
  3. 2
  4. 3

Correct Answer: 0

Exam Year: 2023

Solution: 

If the number is 6k + 4, then 3(6k + 4) = 18k + 12, which leaves a remainder of 0 when divided by 6.

A number leaves a remainder of 4 when divided by 6. If this number is multiplied

Practice Questions

Q1
A number leaves a remainder of 4 when divided by 6. If this number is multiplied by 3, what will be the remainder when the result is divided by 6? (2023)
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

A number leaves a remainder of 4 when divided by 6. If this number is multiplied by 3, what will be the remainder when the result is divided by 6? (2023)
  • Step 1: Understand that the number leaves a remainder of 4 when divided by 6. This means the number can be expressed as 6k + 4, where k is any whole number.
  • Step 2: Multiply the number (6k + 4) by 3. This gives us 3(6k + 4).
  • Step 3: Distribute the 3 in the expression: 3(6k) + 3(4) = 18k + 12.
  • Step 4: Now, we need to find the remainder when 18k + 12 is divided by 6.
  • Step 5: Notice that 18k is a multiple of 6, so it leaves a remainder of 0 when divided by 6.
  • Step 6: Next, divide 12 by 6. The result is 2 with a remainder of 0.
  • Step 7: Combine the remainders: 0 (from 18k) + 0 (from 12) = 0.
  • Step 8: Therefore, the final remainder when the result is divided by 6 is 0.
  • Modular Arithmetic – Understanding how remainders work when dividing numbers.
  • Algebraic Manipulation – Using algebra to express numbers in terms of their divisors and remainders.
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