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A number is divided by 7 and gives a remainder of 3. If this number is increased

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Question: A number is divided by 7 and gives a remainder of 3. If this number is increased by 4, what will be the new remainder when divided by 7?

Options:

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

Correct Answer: 0

Solution: 

The new number is (7k + 3 + 4) = 7k + 7, which gives a remainder of 0 when divided by 7.

A number is divided by 7 and gives a remainder of 3. If this number is increased

Practice Questions

Q1
A number is divided by 7 and gives a remainder of 3. If this number is increased by 4, 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 3. If this number is increased by 4, 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 3, it can be written as '7k + 3', where 'k' is some whole number.
  • Step 2: Increase the number by 4. So, we take '7k + 3' and add 4 to it, which gives us '7k + 3 + 4'.
  • Step 3: Simplify the expression from Step 2. This becomes '7k + 7'.
  • Step 4: Notice that '7k + 7' can be factored as '7(k + 1)'.
  • Step 5: When '7(k + 1)' is divided by 7, it divides evenly with no remainder.
  • Step 6: Therefore, the new remainder when this number 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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