We know that an apartment building has five floors, each with either one or two apartments.
1: _ _ 2: _ _ 3: _ _ 4: _ _ 5: _ _
There are exactly eight apartments in the building. This means that two of the spaces outlined in our diagram above must remain empty.
There are eight residents who each live in a different apartment: J, K, L, M, N, O, P, and Q
Now let's go through the conditions.
Rule 1 - J lives on a floor with two apartments.
Rule 2 - K lives on the floor directly above P
Therefore, P cannot live on floor 5 and K cannot live on floor 1.
Rule 3 - The second floor only has one apartment.
Therefore, J cannot live on the second floor.
Rule 4 - M and N live on the same floor.
Therefore, M and N cannot live on the second floor.
Rule 5 - O does not live on the same floor as Q
O --> Not Q Q --> Not O
Rule 6 - L lives in the only apartment on her floor
Therefore, L could live on the second floor.
Rule 7 - Q does not live on the first or second floor
1: _ _ Not K or Q 2: _ Not J, M, N, or Q 3: _ _ 4: _ _ 5: _ _ Not P
The question stem imposes an additional condition: O lives on the second floor.
1: _ _ 2: O 3: _ _ 4: _ _ 5: _ _
We are looking for the answer choice which cannot be true.
The main limiting variable here is that K must live on the floor directly above P. So, what are our options for K and P and how do these impact the remaining apartments?
Option 1 - P and K live on floors 3 and 4
1: _ _ 2: O 3: P Q/J 4: K J/Q 5: _ _
M and N either live on floor 5 or 1. L lives on either floor 1 or 5 and that floor only has one apartment. Q and J live on the same floors as P and K.
Option 2 - P and K live on floors 4 and 5
1: _ _ 2: O 3: _ _ 4: P Q/J 5: K J/Q
M and N either live on floor 3 or 1. L lives on either floor 1 or 3 and that floor has only one apartment. Q and J live on the same floors as P and K.
Now let's go through the answer choices.
We can eliminate answer choices (A) and (B) because K lives on floor 4 in option 1 and floor 5 in option 2.
We can eliminate answer choices (C) and (D) because L lives on either floor 1 or 3 in option 2 and either floor 1 or 5 in option 1.
Therefore, the correct answer choice must be (E).
Why can L not live on the fourth floor? Because P and K must either live on floors 3 and 4 or 4 and 5 and L lives in the only apartment on her floor; therefore, she cannot share a floor with anyone.
Hope this is helpful! Please let us know if you have any further questions.
on May 11, 2021
Doesn't it say that K lives directly above P? Therefore K can't be in 5 because where would P go?
on May 11, 2021
nvm I was counting It 1,2,3,4,5 instead of 5,4,3,2,1 all good
