If the three-digit number 52 is divisible by 6, which of the following values of * works?

Given data

• Number: 52 must be divisible by 6.

Concept / Approach

• Divisible by 6 ⇔ divisible by 2 and by 3.
• Ends with 2 ⇒ already divisible by 2.
• Divisible by 3 ⇒ digit sum multiple of 3.

Step-by-step condition

Digit sum = 5 + * + 2 = 7 + *Require 7 + * ≡ 0 (mod 3) ⇒ * ≡ 2 (mod 3)Digits 0–9 satisfying * ≡ 2 (mod 3): {2, 5, 8}Therefore the acceptable values are 2, 5 and 8.

Common pitfalls

• Forgetting the divisibility-by-3 condition (checking only evenness).

Final Answer

Valid digits: 2, 5 and 8.