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A number is divided by 12 and gives a remainder of 7. If this number is increase

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Question: A number is divided by 12 and gives a remainder of 7. If this number is increased by 5, what will be the new remainder when divided by 12? (2023)

Options:

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

Correct Answer: 0

Exam Year: 2023

Solution: 

The new number is (original number + 5) = (12k + 7 + 5) = 12k + 12, which gives a remainder of 0.

A number is divided by 12 and gives a remainder of 7. If this number is increase

Practice Questions

Q1
A number is divided by 12 and gives a remainder of 7. If this number is increased by 5, what will be the new remainder when divided by 12? (2023)
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

A number is divided by 12 and gives a remainder of 7. If this number is increased by 5, what will be the new remainder when divided by 12? (2023)
  • Step 1: Understand that when a number is divided by 12 and gives a remainder of 7, it can be written as '12k + 7', where 'k' is some integer.
  • Step 2: Increase the original number by 5. This means we calculate '12k + 7 + 5'.
  • Step 3: Simplify the expression from Step 2: '12k + 7 + 5' becomes '12k + 12'.
  • Step 4: Notice that '12k + 12' can be factored as '12(k + 1)', which means it is a multiple of 12.
  • Step 5: When a number is a multiple of 12, the remainder when divided by 12 is 0.
  • Modular Arithmetic – Understanding how remainders work when dividing numbers.
  • Algebraic Manipulation – Using algebra to express the original number in terms of a variable.
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