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

on August 22 at 09:20PM

Question 21 Explanation

Could you please break this question down? Thanks!

on February 15 at 01:19PM

I approached this vertically with:
W__
T__
F__
S__

W:__
T:8_
F:__
S:__

For rule #2, 2 must come before 8, so now we have:

W:2_
T:8_
F:__
S:__

Then, from rule #3 and #4, we have the 3-7-5 chain that must each be on different days. The chain cannot start on Wednesday because of rule #1 that says you can't have two floors in a row, so the 3-7-5 chain must start on Thursday.

W:2_
T:83
F:7_
S:5_

Then our last rule #5 says that 4 must be on T or F. Since T is full now, it must be on Friday.

W:2
T:83
F:74
S:5

And finally, using rule #1 a second time, we must put floor 1 on Saturday because if we put floor 6 on Saturday, we would violate rule #1 by having 5 & 6 on the same day.

W:26
T:83
F:74
S:51

So by putting floor 8 on Thursday, we can actually determine one single scenario and thus it's the correct answer.