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A number is divided by 6 and gives a remainder of 4. If this number is multiplie

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Question: A number is divided by 6 and gives a remainder of 4. If this number is multiplied by 2, what will be the remainder when divided by 6? (2023)

Options:

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

Correct Answer: 1

Exam Year: 2023

Solution: 

Multiplying the number by 2 gives a new remainder of 2 (4*2 = 8, and 8 mod 6 = 2).

A number is divided by 6 and gives a remainder of 4. If this number is multiplie

Practice Questions

Q1
A number is divided by 6 and gives a remainder of 4. If this number is multiplied by 2, what will be the remainder when divided by 6? (2023)
  1. 0
  2. 1
  3. 2
  4. 4

Questions & Step-by-Step Solutions

A number is divided by 6 and gives a remainder of 4. If this number is multiplied by 2, what will be the remainder when divided by 6? (2023)
  • Step 1: Understand that when a number is divided by 6 and gives a remainder of 4, it can be written as: number = 6k + 4, where k is some integer.
  • Step 2: Multiply the number by 2: (6k + 4) * 2 = 12k + 8.
  • Step 3: Now, we need to find the remainder when 12k + 8 is divided by 6.
  • Step 4: Notice that 12k is divisible by 6, so it gives a remainder of 0.
  • Step 5: Now, focus on the 8: When 8 is divided by 6, it gives a remainder of 2 (since 8 = 6 * 1 + 2).
  • Step 6: Therefore, the remainder when the new number (12k + 8) is divided by 6 is the same as the remainder of 8 divided by 6, which is 2.
  • Modular Arithmetic – Understanding how remainders work when dividing numbers.
  • Multiplication and Remainders – Applying multiplication to a number and determining the new remainder.
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