# If the third floor is examined on Thursday, which one of the following could be true?

GabiKolb on November 19, 2019

can you explain the answer? I had a really hard time trying to understand this game? Do you have any tricks for this type of set up?

Irina on November 19, 2019

It is helpful to identify the game type and the question type. This is a linear game that requires us to determine the order of floors being examined over a four day period with exactly two floors per 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, the question asks us if the third floor is examined on Th, which of the following could be true?

Since it is a could be true question, we know that only one answer choice could be true and the rest of them must be false. Let's see what inferences we can make.

If 3d floor is examined on Th, we can infer that the 4th floor must be examined on F per rules (5) and (1).

___ 3 4 ___
___ ___ ___ ___
W Th F S

Now remember we have a 3 > 7> 5 chain, thus if the 3d floor is examined on Th, 7th floor must be on F, and 5th floor must be on S.

___ 3 4 5
___ ___ 7 ___
W Th F S

We can eliminate (D), (E) and (B).

Now, we also have 2 > 8 chain per rule (2) but remember our inference above that it cannot originate on the same day as 3 >7 > 5 chain because floors 2 & 3 are consecutive. Thus, we can conclude that floor 2 must be examined on W and floor 8 could be examined either on Th or S.

2 3 4 5
___ ___ 7 ___
W Th F S
/8 /8

The only remaining floors are 1 & 6. Since floors 1 & 2 are consecutive, floor 1 cannot be examined on W and must be examined on either Th or S, thus floor 6 must be examined on W.

2 3 4 5
6 ___ 7 ___
W Th F S
1/8 8/1

Thus we can conclude that (B) must be false, and (A) is the only answer choice that could be true - the first floor could be examined on S, which would require 8th floor to be examined on Th.

2 3 4 5
6 8 7 1
W Th F S

Let me know if this helps and if you have any other questions.