Which one of the following assignments of floors to the first two days could be part of an acceptable schedule for al...

Irina on August 21, 2019

@Sidra,

Happy to help. Let's look at the setup for this game.

An environmental consultant examines air quality on 8 floors 1-8 on four days - W, Th, F, S. Exactly 2 floors are examined each day.

___ ___ ___ ___
___ ___ ___ ___
W Th F S

The following rules apply:

(1) On any given day, the two floors examined must be separated by at least one floor.
This rule tells us that no two adjacent floors can be examined on the same day, e.g. it is impossible to have 2&3 or 1&2 on Monday.

(2) The second floor is examined on an earlier day than the eighth floor

2 > 8

(3) The third floor is examined on an earlier day than the seventh floor

3 > 7

(4) The seventh floor must be examined on an earlier day than the fifth floor.

7 > 5

Combined with rule (3), we can conclude that:

3 > 7 > 5

We can also make the following inferences:

#8, 7,5 cannot be examined on W per rules (2) - (4) because floors #2 &3 must come before them. Floor #5 cannot be examined on Th because both floors #7 & 3 must come before it, floor #3 cannot be examined on F because two floors - #7 &5 must come after it, and floors #2 & 3 cannot be examined on S because floors #7,5, and 8 must come after them. Let's put all these inferences on our diagram:

___ ___ ___ ___
___ ___ ___ ___
W Th F S
~8 ~3 ~2
~7 ~5 ~3
~5

We could also note that rules (2) - (4) result in two sequences:

3 > 7 > 5 and
2 > 8

and it is impossible for them to originate the same day as consecutive floors cannot be examined on the same day per rule (1), and floors 3 & 2 are consecutive.

(5) The fourth floor must be examined on either Thursday or Friday.
/4 /4
___ ___ ___ ___
___ ___ ___ ___
W Th F S
~8 ~3 ~2
~7 ~5 ~3
~5

Now that we have completed the initial setup, let's look at the question. Which of the following floors could be examined on W and Th.

(A)
1 6
3 8
W Th

Incorrect. This setup violates rule (2) - 2d floor must be examined earlier than the 8th floor.

(B)

1 2
6 3
W Th

Incorrect. This setup violates rule(1), we cannot have two consecutive floors on the same day - 2 & 3.

(C)

2 3
4 8
W Th

Incorrect. This setup violates rule (5), 4th floor must be on Th or F.

(D)

2 4
6 8
W Th

Incorrect. This setup leaves no room for the 3 > 7 > 5 chain per rules (3) & (4) because we only have two days left.

(E)

3 2
6 7
W Th

Correct. This is a valid scenario that complies with all the conditions.

Does this help?

Let me know if you have any further questions.

Sidra on August 22, 2019

for D:

We have 2 days left but 4 floors to place. Since we have to place 2 floors on each day and we've placed 2,6,4 and 8, wouldn't we be able to place 3 & 1 on Friday and 7 & 5 on Saturday? which also allows the 3>7>5 chain to happen?

Irina on August 22, 2019

@Sidra, No, because the rules tell us that 7 must be on an earlier DAY than 5, so they cannot be on the same day.