­When the Manor Apartments building was constructed, the parking space

MartyMurray KarishmaB Can you please provide your explanation for this question ?

­When the Manor Apartments building was constructed, the parking spaces for the building were all in a single row and were numbered sequentially, from 1 through 8. Each space was assigned to the apartment with the same number; there were no other apartments in the building. A year later, however, the parking space assignment for Apartment 2 was exchanged with that for another apartment, and then a year after that, the parking space assignment for Apartment 2 was exchanged again, this time with that for yet another apartment. No other exchanges have been made. Currently, the parking space assigned to Apartment 2 is adjacent on one side to the space assigned to Apartment 6 and on the other side to the space assigned to Apartment 5.

Select two apartment numbers such that the one selected for First could have been the number of the apartment whose assignment was exchanged with that of Apartment 2 after the first year, and the one selected for Second could have been the number of the apartment whose assignment was exchanged with that of Apartment 2 after the second year, jointly consistent with the information provided. Make only two selections, one in each column.

There are multiple ways in which the space assigned to Apartment 2 could end up between the spaces assigned to Apartment 5 and Apartment 6. So, our best approach to finding the answer is just to try the answer choices rather than theorize about how the space assigned to Apartment 2 could have ended up between the other two.

1

There's no way the Apartment 2 space could end up between the Apartment 5 and Apartment 6 spaces if the Apartment 2 space is first exchanged with the Apartment 1 space. After all, if the Apartment 2 space is first exchanged with the Aparment 1 space, we end up with the following:

2 1 3 4 5 6 7 8

At that point, there's no way for the Apartment 2 space to end up between 5 and 6 with just one more exchange.

For the Apartment 2 space to be adjacent to the Apartment 5 space, the Apartment 2 space would have to be next exchanged with the space for 4 or 6, and in neither case does the Apartment 2 space end up adjacent to the Apartment 6 space, which would then either be separated from 2 by 5 or be in the spot originally assigned to Apartment 1:

4 1 3 2 5 6 7 8

6 1 3 4 5 2 7 8

Eliminate for First.

3

Exchanging the Apartment 2 and Apartment 3 spaces first creates a situation similar to that created by exchanging the Apartment 2 and Apartment 1 spaces first:

1 3 2 4 5 6 7 8 

At that point, for the Apartment 2 space to end up adjacent to the Apartment 5 space, after 2 is exchanged with 3, 2 would have to be next exchanged with the space for 4 or 6, and in neither case does the Apartment 2 space end up adjacent to the Apartment 6 space, which would then either be separated from 2 by 5 or be in the spot originally assigned to Apartment 3.

1 3 4 2 5 6 7 8

1 3 6 4 5 2 7 8

Eliminate for First.

4

This choice is interesting.

If we first exchange the Apartment 2 space with the Apartment 4 space, the Apartment 2 space is adjacent to the Apartment 5 space. So, we have the following:

1 4 3 2 5 6 7 8

5

Now, we can switch 2 and 5 to end up with 2 between 5 and 6:

1 4 3 5 2 6 7 8

6

8

Correct answer: 4, 5­