ACT questions?

Question

I'm working on some ACT problems and could use a little help. The problem is kind of long.If you could explain the answers to me that would be so great. Thank you so much.

1. In teaching a lesson on the concept of thirds, Mr. Chu uses a divide and set aside procedure. He starts with a certain number of colored disks, divides them into 3 equal groups and sets 1 group aside to illustrate 1/3. He repeats the process by taking the disks NOT set aside, dividing them into 3 equal groups, and setting one of these groups aside. If Mr. Chu wants to be able to complete the divide and set procedure at least four times (without breaking any of the disks into pieces) which of the following is the minimum number of colored disks she can start with.

Answer 1

It will work if you start with 3^4 = 81 disks

81 / 3 = 27, remainder is 54
54 / 3 = 18, remainder is 36
36 / 3 = 12, remainder is 24
24 / 3 = 8, remainder is 16 (which isn't divisible by 3)

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On ACT, you usually have four multiple guess answers. When you get stumped, try those answers into the equation and see if they work.