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A number is divided by 11 and gives a remainder of 4. If this number is multipli

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Question: A number is divided by 11 and gives a remainder of 4. If this number is multiplied by 3, what will be the remainder when the result is divided by 11?

Options:

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

Correct Answer: 2

Solution: 

The new number is 3*(11k + 4) = 33k + 12, and 12 mod 11 = 1.

A number is divided by 11 and gives a remainder of 4. If this number is multipli

Practice Questions

Q1
A number is divided by 11 and gives a remainder of 4. If this number is multiplied by 3, what will be the remainder when the result is divided by 11?
  1. 1
  2. 2
  3. 3
  4. 4

Questions & Step-by-Step Solutions

A number is divided by 11 and gives a remainder of 4. If this number is multiplied by 3, what will be the remainder when the result is divided by 11?
  • Step 1: Understand that when a number is divided by 11 and gives a remainder of 4, we can express this number as 11k + 4, where k is some integer.
  • Step 2: Multiply the entire expression (11k + 4) by 3. This gives us 3 * (11k + 4) = 33k + 12.
  • Step 3: Now, we need to find the remainder when 33k + 12 is divided by 11.
  • Step 4: Notice that 33k is a multiple of 11, so it will leave a remainder of 0 when divided by 11.
  • Step 5: Now, focus on the 12. We need to find 12 mod 11, which means we want to find the remainder when 12 is divided by 11.
  • Step 6: When we divide 12 by 11, the quotient is 1 and the remainder is 1 (since 12 - 11 = 1).
  • Step 7: Therefore, the remainder when 33k + 12 is divided by 11 is the same as the remainder when 12 is divided by 11, which is 1.
  • Modular Arithmetic – Understanding how remainders work when dividing numbers, particularly in the context of multiplication and addition.
  • Properties of Remainders – Applying properties of remainders when performing operations like multiplication.
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