Final answer:
The correct answer is:
D) 1, 4, and 7
Step-by-step explanation:
To find which digit(s) make the number 4,610 divisible by 3, we need to use the divisibility rule for 3 which states that if the sum of all digits in a number is divisible by 3, then the entire number is divisible by 3. In this case, the question is asking about the number 4,610 with an unspecified digit in the thousands place. The digits 4, 6, 1, and 0 add up to 11 plus whatever the missing digit is. To be divisible by 3, the sum of the digits must be a multiple of 3. Therefore, the missing digit can be 1, 4, or 7, as adding any of these numbers to 11 will result in a number that is a multiple of 3 (12, 15, 18 respectively).
The correct answer is:
D) 1, 4, and 7