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A number leaves a remainder of 7 when divided by 10. If this number is decreased

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Question: A number leaves a remainder of 7 when divided by 10. If this number is decreased by 3, what will be the new remainder when divided by 10? (2023)

Options:

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

Correct Answer: 0

Exam Year: 2023

Solution: 

The new number is (original number - 3) = (10k + 7 - 3) = 10k + 4, which gives a remainder of 4.

A number leaves a remainder of 7 when divided by 10. If this number is decreased

Practice Questions

Q1
A number leaves a remainder of 7 when divided by 10. If this number is decreased by 3, what will be the new remainder when divided by 10? (2023)
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

A number leaves a remainder of 7 when divided by 10. If this number is decreased by 3, what will be the new remainder when divided by 10? (2023)
  • Step 1: Understand that the original number leaves a remainder of 7 when divided by 10. This means it can be written as 10k + 7, where k is some integer.
  • Step 2: Decrease the original number by 3. So, we calculate (10k + 7) - 3.
  • Step 3: Simplify the expression: (10k + 7) - 3 = 10k + 4.
  • Step 4: Now, we need to find the remainder when 10k + 4 is divided by 10.
  • Step 5: When dividing 10k + 4 by 10, the 10k part gives a remainder of 0, and the 4 gives a remainder of 4.
  • Step 6: Therefore, the new remainder when the decreased number is divided by 10 is 4.
  • Remainders – Understanding how remainders work when dividing numbers.
  • Algebraic Manipulation – Using algebra to express the original number in terms of a variable.
  • Modular Arithmetic – Applying the concept of modular arithmetic to find new remainders after modifications.
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