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A number leaves a remainder of 7 when divided by 11. If we subtract 3 from this

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Question: A number leaves a remainder of 7 when divided by 11. If we subtract 3 from this number, what will be the new remainder when divided by 11? (2023)

Options:

  1. 3
  2. 4
  3. 5
  4. 6

Correct Answer: 3

Exam Year: 2023

Solution: 

The new number is (original number - 3), which gives a remainder of (7 - 3) = 4.

A number leaves a remainder of 7 when divided by 11. If we subtract 3 from this

Practice Questions

Q1
A number leaves a remainder of 7 when divided by 11. If we subtract 3 from this number, what will be the new remainder when divided by 11? (2023)
  1. 3
  2. 4
  3. 5
  4. 6

Questions & Step-by-Step Solutions

A number leaves a remainder of 7 when divided by 11. If we subtract 3 from this number, what will be the new remainder when divided by 11? (2023)
  • Step 1: Understand that the original number leaves a remainder of 7 when divided by 11.
  • Step 2: Write the original number in a form that shows the remainder: original number = 11k + 7, where k is some integer.
  • Step 3: Subtract 3 from the original number: new number = (11k + 7) - 3.
  • Step 4: Simplify the new number: new number = 11k + 4.
  • Step 5: Now, find the remainder when the new number (11k + 4) is divided by 11.
  • Step 6: Since 11k is divisible by 11, the remainder comes from the 4.
  • Step 7: Therefore, the new remainder when the new number is divided by 11 is 4.
  • Remainders and Modular Arithmetic – Understanding how remainders work when performing arithmetic operations on numbers in modular systems.
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