Question

Which of the following numbers is divisible by both 11 and 12 ?

• A. 4686
• B. 3584
• C. 2640
• D. 4830

Answer 1

Answer:

C. 2640

Solution: Concept used: Divisibility Rule for 11: Divide the alternate digits in two different groups. Take the sum of alternate digits separately and find the difference of the two numbers. If the difference is 0 or is divisible 11, the number is divisible by 11. Divisibility Rule for 12: If the number is divisible by both 3 and 4, the number is divisible by 12. The divisibility rule of 3 is that sum of digits is divisible by 3 and the divisibility rule of 4 is that the last two digits are divisible by 4. Calculation: Checking option (1), Divisibility rule of 12: Number divisible by both 3 and 4. Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3. Divisibility rule of 4: A number is divisible by 4, if the last two digits are a multiple of 4. The last two digits 86 is not divisible by 4 So, 4686 is not divisible by 12. ∴ Option (1) is false. Checking option (2), 3584 = 3 + 5 + 8 + 4 = 20, it is not divisible by 3 So, 3584 is not divisible by 12. ∴ Option (2) is false. Checking option (3), 2640 = 2 + 6 + 4 = 12, it is divisible by 3 The last two digits 40 are divisible by 4. So, 2640 is divisible by 12. And {2 + 4} - {6 + 0} = 0 So, 2640 is divisible by 11. ∴ Option (C) is correct.