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A number is divided by 7 and gives a remainder of 4. If this number is increased

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Question: A number is divided by 7 and gives a remainder of 4. If this number is increased by 10, what will be the new remainder when divided by 7?

Options:

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

Correct Answer: 1

Solution: 

The new number is (original number + 10) = (7k + 4 + 10) = 7k + 14, which gives a remainder of 1 when divided by 7.

A number is divided by 7 and gives a remainder of 4. If this number is increased

Practice Questions

Q1
A number is divided by 7 and gives a remainder of 4. If this number is increased by 10, what will be the new remainder when divided by 7?
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

A number is divided by 7 and gives a remainder of 4. If this number is increased by 10, what will be the new remainder when divided by 7?
  • Step 1: Understand that when a number is divided by 7 and gives a remainder of 4, it can be written as 'original number = 7k + 4', where k is some integer.
  • Step 2: Increase the original number by 10. This gives us 'new number = (7k + 4) + 10'.
  • Step 3: Simplify the new number: 'new number = 7k + 14'.
  • Step 4: Now, we need to find the remainder when '7k + 14' is divided by 7.
  • Step 5: Since '7k' is divisible by 7, it gives a remainder of 0. Now, consider the 14: '14 divided by 7' gives a remainder of 0.
  • Step 6: Therefore, the total remainder when '7k + 14' is divided by 7 is '0 + 0 = 0'.
  • Step 7: However, we need to find the remainder of '14' when divided by 7, which is actually 0.
  • Step 8: Since we are looking for the new remainder after adding 10, we realize that '14' can be expressed as '7 * 2', which gives a remainder of 0.
  • Step 9: Finally, we conclude that the new remainder when the number increased by 10 is divided by 7 is 0.
  • Modular Arithmetic – Understanding how remainders work when dividing numbers.
  • Algebraic Manipulation – Ability to manipulate expressions involving variables and constants.
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