A four-digit number is written as 4,5$\underline{\hspace{0.6em}}$2, where the blank represents a single digit. What is the largest digit that can be placed in the blank to make the number divisible by 6?
- 1
- 4
- 7 (correct answer)
- 9
Explanation: A number is divisible by 6 if it is divisible by both 2 and 3. The number 4,5_2 is already divisible by 2 because its last digit is 2, which is an even number. For the number to be divisible by 3, the sum of its digits must be divisible by 3. The sum of the digits is 4 + 5 + _ + 2 = 11 + _. The possible values for 11 + _ that are multiples of 3 are 12, 15, and 18. If 11 + _ = 12, _ = 1. If 11 + _ = 15, _ = 4. If 11 + _ = 18, _ = 7. The possible digits are 1, 4, and 7. The largest of these is 7.