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A number leaves a remainder of 6 when divided by 11. If this number is multiplie

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Question: A number leaves a remainder of 6 when divided by 11. If this number is multiplied by 3, what will be the new remainder when divided by 11?

Options:

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

Correct Answer: 3

Solution: 

The new number is 3*(11k + 6) = 33k + 18, which gives a remainder of 7 when divided by 11.

A number leaves a remainder of 6 when divided by 11. If this number is multiplie

Practice Questions

Q1
A number leaves a remainder of 6 when divided by 11. If this number is multiplied by 3, what will be the new remainder when divided by 11?
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

A number leaves a remainder of 6 when divided by 11. If this number is multiplied by 3, what will be the new remainder when divided by 11?
  • Step 1: Understand that the original number can be expressed as '11k + 6', where 'k' is any whole number. This means when you divide this number by 11, you get a remainder of 6.
  • Step 2: Multiply the entire expression '11k + 6' by 3. This gives you '3 * (11k + 6)'.
  • Step 3: Distribute the 3: '3 * 11k + 3 * 6' which simplifies to '33k + 18'.
  • Step 4: Now, we need to find the remainder when '33k + 18' is divided by 11.
  • Step 5: Notice that '33k' is a multiple of 11 (since 33 is 3 times 11), so it will leave a remainder of 0 when divided by 11.
  • Step 6: Now, focus on the '18'. When you divide 18 by 11, you get 1 with a remainder of 7 (because 18 - 11 = 7).
  • Step 7: Combine the results: since '33k' gives a remainder of 0 and '18' gives a remainder of 7, the total remainder when '33k + 18' is divided by 11 is 7.
  • Modular Arithmetic – Understanding how remainders work when dividing numbers.
  • Multiplication and Remainders – Applying multiplication to a number and determining the new remainder.
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