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A number is divided by 9 and gives a remainder of 2. If this number is multiplie

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Question: A number is divided by 9 and gives a remainder of 2. If this number is multiplied by 3, what will be the remainder when the new number is divided by 9?

Options:

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

Correct Answer: 0

Solution: 

The new number is (original number * 3) = (9k + 2) * 3 = 27k + 6, which gives a remainder of 6 when divided by 9.

A number is divided by 9 and gives a remainder of 2. If this number is multiplie

Practice Questions

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

Questions & Step-by-Step Solutions

A number is divided by 9 and gives a remainder of 2. If this number is multiplied by 3, what will be the remainder when the new number is divided by 9?
  • Step 1: Understand that when a number is divided by 9 and gives a remainder of 2, we can express this number as '9k + 2', where 'k' is some integer.
  • Step 2: Multiply the original number (9k + 2) by 3. This gives us: (9k + 2) * 3 = 27k + 6.
  • Step 3: Now, we need to find the remainder when '27k + 6' is divided by 9.
  • Step 4: Notice that '27k' is a multiple of 9, so it will give a remainder of 0 when divided by 9.
  • Step 5: The only part we need to consider for the remainder is '6'.
  • Step 6: When we divide 6 by 9, the remainder is 6 because 6 is less than 9.
  • Modular Arithmetic – Understanding how remainders work when dividing numbers.
  • Multiplication and Remainders – Applying multiplication to a number and determining the effect on its remainder.
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