Section 1 question 5. I struggled between C and E, because neither seems like it could be false. I finally chose C, and C is not the right answer. And I cannot see the problem. What the heck is going on?

The rules constrain the possible codes to the following:

12034

12043

12304

24031

24013

24103

C is proven wrong because code #2 above violates it.

E is correct because it is the only choice that is true about all six of the possible codes.

The key steps in this problem are realizing what each of the last two rules tell you: the third rule tells you that the code must start with either 12 or 24, because no other possible configuration results in a combination where the second digit is exactly two times the first digit. The last rule tells you that the largest remaining number can't be the third digit, and the smallest remaining number can't be the last digit. From there, you can figure out all 6 possible codes and quickly answer most of the questions just by scanning through each code.