# Any of the following could be true EXCEPT:

mjenei on July 1, 2019

Explanation

The logic games section on this exam were confusing to me, more than normal. Could someone tell me the type of game this is and explain this question me, along with #4?

Replies

SarahA on August 16, 2019

Please Please can we get an explanation for this. There is no video. Nothing.

Irina on August 17, 2019

@mjenei & @msaber,

Thank you for your question. 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. The questions asks which of the following could be true EXCEPT. Just by looking at our diagram, we can see that #5 CANNOT be examined on Th, thus (C) is the correct answer choice. None of the other answer choices appear to violate any of the rules per our initial setup, and thus could be true.

Let's look at question 4 as well. The schedule of the examination is fully determined if which of the following is true.

(A) The second floor is examined on F.

___ ___ 2 8
___ ___ ___ ___
W Th F S

Incorrect. The only inference we can make from this is that 8 is examined on S, so (A) is out.

(B) The third floor is examined on Th.

2 3 7 5
6 ___ 4 ___
W Th F S

Incorrect. This fact allows us to determine the order of all the floors except for 1 & 8, because 1 & 8 could go either on Th & S or S & Th respectively, we cannot determine the schedule fully.

(C) The fifth floor is examined on Fr.

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

Incorrect. This fact allows us to determine the order of all the floors except for 1 & 6, because 1 & 6 could go either on W & S or S & W respectively, we cannot determine the schedule fully.

(D) The sixth floor is examined on Th.

3 6 7 5
8
W Th F S

Incorrect. This fact allows us to infer that floors 3,7, 5 sequence must go on W, F, S, else 7& 6 on the same day would violate rule (1). We can also infer that 2 must go either on Th or F because it cannot go on W per rule (1) or on S per rule (2), and 8 must go on S because it cannot go on F per rule (1). Since 2 could go either on Th or F, and 4 could go on either Th or F, we cannot fully determine the schedule.

(E) The eighth floor is examined on Thursday.

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

Correct. If 8 is examined on Th, 2 must be examined on W per rule (2). Then 3- 7-5 must be examined on Th-F-S because 2 & 3 cannot go on the same day W per rule (1). 4 must go on F per rule (5) because Th is filled with 8 and 3. The only remaining slots are W alongside 2 and S alongside 5. Since 6 cannot go together with 5 and 1 cannot go together with 2 per rule (1), 6 must go on W, and 1 must go on S. Thus, we are able to fully determine the schedule.

This is definitely a challenging question that requires you to make quick inferences.

Does this make sense?

Let me know if you have any further questions.