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

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Question: A number is divided by 12 and gives a remainder of 7. If this number is multiplied by 2, what will be the remainder when the new number is divided by 12? (2023)

Options:

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

Correct Answer: 2

Exam Year: 2023

Solution: 

The new number is (original number * 2) = (12k + 7) * 2 = 24k + 14, which gives a remainder of 2.

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

Practice Questions

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

Questions & Step-by-Step Solutions

A number is divided by 12 and gives a remainder of 7. If this number is multiplied by 2, what will be the remainder when the new number is divided by 12? (2023)
  • Step 1: Understand that when a number is divided by 12 and gives a remainder of 7, it can be expressed as 'original number = 12k + 7', where k is some integer.
  • Step 2: Multiply the original number by 2. This gives us 'new number = 2 * (12k + 7)'.
  • Step 3: Distribute the 2 in the equation: 'new number = 2 * 12k + 2 * 7'.
  • Step 4: Simplify the equation: 'new number = 24k + 14'.
  • Step 5: Now, we need to find the remainder when 'new number' is divided by 12. We can rewrite 14 as '12 + 2'.
  • Step 6: When we divide '24k + 14' by 12, the '24k' part is divisible by 12, leaving us with the remainder from '14'.
  • Step 7: Since '14' can be expressed as '12 + 2', the remainder when dividing by 12 is simply 2.
  • 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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