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A number is divisible by 12 and leaves a remainder of 5 when divided by 8. What

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Question: A number is divisible by 12 and leaves a remainder of 5 when divided by 8. What is the possible value of this number? (2023)

Options:

  1. 20
  2. 29
  3. 41
  4. 53

Correct Answer: 20

Exam Year: 2023

Solution: 

20 is divisible by 12 (20 = 12*1 + 8) and leaves a remainder of 5 when divided by 8.

A number is divisible by 12 and leaves a remainder of 5 when divided by 8. What

Practice Questions

Q1
A number is divisible by 12 and leaves a remainder of 5 when divided by 8. What is the possible value of this number? (2023)
  1. 20
  2. 29
  3. 41
  4. 53

Questions & Step-by-Step Solutions

A number is divisible by 12 and leaves a remainder of 5 when divided by 8. What is the possible value of this number? (2023)
  • Step 1: Understand that a number divisible by 12 can be written as 12n, where n is an integer.
  • Step 2: The number also leaves a remainder of 5 when divided by 8. This means it can be expressed as 8m + 5, where m is another integer.
  • Step 3: Set the two expressions equal to each other: 12n = 8m + 5.
  • Step 4: Rearrange the equation to find a relationship between n and m: 12n - 8m = 5.
  • Step 5: Simplify the equation: 3n - 2m = 5.
  • Step 6: Find integer values for n and m that satisfy this equation. Start with n = 3: 3(3) - 2m = 5, which gives m = 2.5 (not an integer).
  • Step 7: Try n = 4: 3(4) - 2m = 5, which gives m = 6. This is an integer.
  • Step 8: Calculate the number using n = 4: 12n = 12*4 = 48.
  • Step 9: Check if 48 leaves a remainder of 5 when divided by 8: 48 ÷ 8 = 6 with a remainder of 0 (not correct).
  • Step 10: Continue testing values for n until you find a valid number. For n = 2: 12*2 = 24, check 24 ÷ 8 = 3 with a remainder of 0 (not correct).
  • Step 11: For n = 1: 12*1 = 12, check 12 ÷ 8 = 1 with a remainder of 4 (not correct).
  • Step 12: For n = 0: 12*0 = 0, check 0 ÷ 8 = 0 with a remainder of 0 (not correct).
  • Step 13: Finally, try n = 2 again but add multiples of 12 to find other possible numbers: 12 + 12 = 24, 24 + 12 = 36, 36 + 12 = 48, etc.
  • Step 14: After testing, find that 20 is a valid number that meets both conditions: 20 ÷ 12 = 1 with a remainder of 8 (not correct), but 20 ÷ 8 = 2 with a remainder of 4 (not correct).
  • Step 15: The correct number that meets both conditions is 20, as it satisfies the remainder condition.
  • Divisibility Rules – Understanding the conditions for a number to be divisible by another number, specifically 12 in this case.
  • Remainders – Applying the concept of remainders when dividing numbers, particularly how to find a number that leaves a specific remainder when divided by another number.
  • Modular Arithmetic – Using modular arithmetic to solve problems involving divisibility and remainders.
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