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A number is divided by 15 and gives a remainder of 9. If this number is decrease

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Question: A number is divided by 15 and gives a remainder of 9. If this number is decreased by 4, what will be the new remainder when divided by 15? (2023)

Options:

  1. 0
  2. 1
  3. 2
  4. 5

Correct Answer: 1

Exam Year: 2023

Solution: 

The new number is (original number - 4) = (15k + 9 - 4) = 15k + 5, which gives a remainder of 5.

A number is divided by 15 and gives a remainder of 9. If this number is decrease

Practice Questions

Q1
A number is divided by 15 and gives a remainder of 9. If this number is decreased by 4, what will be the new remainder when divided by 15? (2023)
  1. 0
  2. 1
  3. 2
  4. 5

Questions & Step-by-Step Solutions

A number is divided by 15 and gives a remainder of 9. If this number is decreased by 4, what will be the new remainder when divided by 15? (2023)
  • Step 1: Understand that when a number is divided by 15 and gives a remainder of 9, it can be expressed as '15k + 9', where 'k' is some integer.
  • Step 2: Decrease the original number by 4. This means we calculate '15k + 9 - 4'.
  • Step 3: Simplify the expression from Step 2: '15k + 9 - 4' becomes '15k + 5'.
  • Step 4: Now, we need to find the remainder when '15k + 5' is divided by 15.
  • Step 5: When dividing '15k + 5' by 15, the '15k' part divides evenly (giving a remainder of 0), and we are left with the remainder of 5 from the '+ 5'.
  • Step 6: Therefore, the new remainder when the number decreased by 4 is divided by 15 is 5.
  • 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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