A number leaves a remainder of 4 when divided by 6. If this number is multiplied by 3, what will be the remainder when the result is divided by 6? (2023)
Practice Questions
1 question
Q1
A number leaves a remainder of 4 when divided by 6. If this number is multiplied by 3, what will be the remainder when the result is divided by 6? (2023)
0
1
2
3
If the number is 6k + 4, then 3(6k + 4) = 18k + 12, which leaves a remainder of 0 when divided by 6.
Questions & Step-by-step Solutions
1 item
Q
Q: A number leaves a remainder of 4 when divided by 6. If this number is multiplied by 3, what will be the remainder when the result is divided by 6? (2023)
Solution: If the number is 6k + 4, then 3(6k + 4) = 18k + 12, which leaves a remainder of 0 when divided by 6.
Steps: 8
Step 1: Understand that the number leaves a remainder of 4 when divided by 6. This means the number can be expressed as 6k + 4, where k is any whole number.
Step 2: Multiply the number (6k + 4) by 3. This gives us 3(6k + 4).
Step 3: Distribute the 3 in the expression: 3(6k) + 3(4) = 18k + 12.
Step 4: Now, we need to find the remainder when 18k + 12 is divided by 6.
Step 5: Notice that 18k is a multiple of 6, so it leaves a remainder of 0 when divided by 6.
Step 6: Next, divide 12 by 6. The result is 2 with a remainder of 0.
