### Instruction: What is the greatest digit that can be placed in the circle so that the six-digit number is divisible by 4? $$3\:5\:2\:9 \bigcirc 2$$.### Response: To check if a number is divisible by 4, I only need to look at the last two digits.
If the last two digits form a multiple of 4, then the whole number is a multiple of 4.
So I want to find the largest digit that makes the number in the circle and 2 a multiple of 4.
The multiples of 4 that end with 2 are 12, 32, 52, 72, and 92.
The largest digit among these is 9, so that's my answer.