When the Manor Apartments building was constructed, the parking space

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.

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.

PeachSnapple1 · Accepted Answer

Because if you switch 2 with 5 before switching 2 with 4, you would end up with the following order: 1-5-3-2-4-6-7-8, which isn't correct according to the prompt (you need 2 in between of 5 and 6)
But if you switch 2 with 4 first before switching 2 with 5, the order will be correct
In detail:
At the beginning, the order is: 1-2-3-4-5-6-7-8
First year (you switch 2 and 4): 1-4-3-2-5-6-7-8
Second year (you switch 2 and 5): 1-4-3-5-2-6-7-8 (correct because 2 is in between of 5 and 6)

MartyMurray · Answer

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.

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

susan_chen15 · Answer

can anybody explain why it's first 4 second 5 instead of the opposite

sayan640 · Answer

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

kayze · Answer

I believe you read the question wrong, as did I when I first did this question. The problem states that the space currently assigned to Apartment 2 is the one that shifts both times, not the space that Apartment 2 originally owned.

vishujn2 · Answer

what if apartment 2 is first exchanged with apartment 7 and than apartment 6
1-2-3-4-5-6-7-8
first exchange 1-7-3-4-5-6-2-8
second exchange 1-7-3-4-5-2-6-8
could someone explain why this explanation is wrong
 Bunuel

sannidhyar · Answer

hi, your explanation is absolutely correct, but notice that they haven't given 7 as an option, so this case gets eliminated.

Cheers!

LL132 · Answer

If 7 were in the answer choices, then first 2 could have come in the place of 7 and then exchanged with 6 the second time. is that correct?

Bunuel · Answer

Yes, that would work if 7 were in the choices.

First swap 2 with 7:

1  7  3 4 5 6  2  8

Second swap 2 with 6:

1  7  3 4 5  2   6  8

So (First =   7  , Second =   6  ) would also satisfy the conditions, it just is not an allowed option.

Goldenfuture · Answer

The trick is after lot of thinking - whichever position I want to send 5 to - I need to first swap at that position and then swap with 5.

Advait01 · Answer

I don't understand this statement - 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.

If the final positioning is - 14352678, the parking for Apartment 2 is adjacent to the space assigned to 6 (original), but how is it adjacent to the original space for Apartment 5?

Bunuel · Answer

First swap 2 with 4:

1  4  3  2  5 6 7 8

Second swap 2 with 5:

1  4  3  5   2  6 7 8

So: First =   4  , Second =   5  .

It means the spaces currently assigned to Apartments 5 and 6, not the original space numbers 5 and 6.

In   1  4  3  5   2  6 7 8   , Apartment 2 is in space 5, and the adjacent spaces are space 4 and space 6, which are currently assigned to Apartments 5 and 6.

egmat · Answer

Hi Advait01,

Great question — this is a subtle but  important  distinction that  trips up many students .

You've correctly traced the final arrangement as:
Space  1 : Apt  1 
Space  2 : Apt  4 
Space  3 : Apt  3 
Space  4 : Apt  5 
Space  5 : Apt  2 
Space  6 : Apt  6 
Space  7 : Apt  7 
Space  8 : Apt  8

Key Insight:  The question says the space CURRENTLY assigned to Apartment  5 , not the ORIGINAL space for Apartment  5 .

After both swaps, Apartment  5  is no longer in Space  5 . Apartment  5  moved to Space  4  (because it swapped with Apartment  2  in the second exchange). So the space currently assigned to Apartment  5  is Space  4 .

Now check the  adjacency condition  for Apartment  2 , which sits in Space  5 :
- One side: Space  4 , currently assigned to Apartment  5 . Adjacent? Yes.
- Other side: Space  6 , currently assigned to Apartment  6 . Adjacent? Yes.

Both conditions are satisfied.

Note that  your confusion was that you were looking at Apartment  5 's original space (Space  5 ). But Apartment  2  is sitting IN Space  5  now — so obviously it can't be adjacent to itself.  This is a common mistake.  The question is asking about where Apartment  5  currently lives, which is Space  4 , right next door.

Think of it this way: the two swaps created a chain reaction. First, Apartment  2  moved from Space  2  to Space  4  (swapping with Apartment  4 ). Then Apartment  2  moved from Space  4  to Space  5  (swapping with Apartment  5 ). That second swap is exactly what placed Apartment  5  into Space  4  — making them neighbors in the final arrangement.

Answer: 3A, 4B

Usernamevisible · Answer

For 2 to be adjacent to 5 and 6, its first move has to be adjacent to 5 i.e. position 4 or adjacent to 6 i.e. position 7.

Now position 7 is not there in option so start with position 1,

First 2 moves with 4 
then 2 moves with 5 to come between 5 and 6

Harsh_ · Answer

It is not opposite, cause it's a  exchange  , if we move '5' first then '5' will now be at position of Original '2' that along '1', therefore then we can not get the desired formation of '2' between 5 & 6.

When the Manor Apartments building was constructed, the parking space

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When the Manor Apartments building was constructed, the parking space