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A number is divided by 8 and gives a remainder of 3. If this number is increased

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Question: A number is divided by 8 and gives a remainder of 3. If this number is increased by 5, what will be the new remainder when divided by 8? (2023)

Options:

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

Correct Answer: 1

Exam Year: 2023

Solution: 

The new number is (original number + 5) = (8k + 3 + 5) = 8k + 8, which gives a remainder of 0.

A number is divided by 8 and gives a remainder of 3. If this number is increased

Practice Questions

Q1
A number is divided by 8 and gives a remainder of 3. If this number is increased by 5, what will be the new remainder when divided by 8? (2023)
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

A number is divided by 8 and gives a remainder of 3. If this number is increased by 5, what will be the new remainder when divided by 8? (2023)
  • Step 1: Understand that when a number is divided by 8 and gives a remainder of 3, it can be expressed as '8k + 3', where 'k' is any whole number.
  • Step 2: Increase the original number by 5. This means we take '8k + 3' and add 5 to it.
  • Step 3: Calculate the new number: (8k + 3) + 5 = 8k + 8.
  • Step 4: Now, we need to divide this new number (8k + 8) by 8.
  • Step 5: When we divide '8k + 8' by 8, it simplifies to 'k + 1' with a remainder of 0, because 8k is perfectly divisible by 8 and 8 is also perfectly divisible by 8.
  • Step 6: Therefore, the new remainder when the increased number is divided by 8 is 0.
  • Modular Arithmetic – Understanding how remainders work when dividing numbers.
  • Algebraic Manipulation – Ability to manipulate expressions to find new values based on given conditions.
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