The schedule for the air-quality examination is fully determined if which one of the following is true?

Dina on January 31, 2021

for this question i was personally stuck between B and C. which involved the 3-7-5 cube. for B it was 3 on Thursday which meant that 4 needed to be on Friday along with 7 and 5 needed to be on Saturday. 2 would be on Wednesday with 6 and you would have a mixture of 1/8 that could go on Thursday and Saturday either way. so it wasn't B.

C on the other hand had 5 on Friday winch meant 4 is going to be on Thursday with 7. 3 needs to be on Wednesday so that means 2 needs to be on Friday and 8 in Saturday so the 6/1 combination is in Wednesday and Saturday so its not the answer.

however answer choice E is the right answer. when you put 8 in the Thursday 2 would go on Wednesday and only 6 can go on Wednesday. (we can't have 1,3 thanks to rule one) (we cant have 5 and 7 because of our block 3-7-5) (and we cant have 4 since it can only go on Thursday or Friday). the next step is that you put 3 in Thursday because again you need space for the block and you cant put it anywhere else, 7 goes on Friday and 5 on Saturday. you put 4 on Friday so Friday is full. 8 and 2 would go Wednesday and Thursday and the only remaining one spot open is in Saturday which is with 5 and you put 1.

this is my reasoning for the question, in the end it made sense for me, i hope it helps.