Which number among 38211, 38121, 32118, and 31128 is divisible by 24?

Formula used:

A number is divisible by 24 if it is divisible by both 3 and 8.

Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.

Divisibility by 8: A number is divisible by 8 if the last three digits of the number are divisible by 8.

Calculation:

Checking 38211:

Sum of digits = 3 + 8 + 2 + 1 + 1 = 15 (Divisible by 3)

Last three digits = 211 (Not divisible by 8)

⇒ 38211 is not divisible by 24

Checking 38121:

Sum of digits = 3 + 8 + 1 + 2 + 1 = 15 (Divisible by 3)

Last three digits = 121 (Not divisible by 8)

⇒ 38121 is not divisible by 24

Checking 32118:

Sum of digits = 3 + 2 + 1 + 1 + 8 = 15 (Divisible by 3)

Last three digits = 118 (Not divisible by 8)

⇒ 32118 is not divisible by 24

Checking 31128:

Sum of digits = 3 + 1 + 1 + 2 + 8 = 15 (Divisible by 3)

Last three digits = 128 (Divisible by 8)

⇒ 31128 is divisible by 24

∴ The correct answer is option (4).