Question

Luna writes down all the five-digit numbers that contain each of the digits 1,2,3,4 and 5 exactly once. What is the smallest number in Luna's list that is divisible by 6?

A) 12,345
B) 12,354
C) 12,435
D) 12,534

Answer 1

The smallest number in Luna's list that is divisible by 6 is option B) 12,354.

Step-by-step explanation:

The smallest number in Luna's list that is divisible by 6 is option B) 12,354.

1. Start by noticing that an integer is divisible by 6 if it is divisible by both 2 and 3.
2. Since the number must be a five-digit number that contains each of the digits 1, 2, 3, 4, and 5 exactly once, it must start with the digit 1.
3. The next two digits can be any combination of 2, 3, 4, and 5.
4. The final two digits must be divisible by 3, which means they must add up to a multiple of 3.
5. Considering all these conditions, the smallest possible number is 12,354.