Ten people—J, K, L, M, N, O, P, Q, R, and S —live in a building with five floors and two flats (Flat 1 and Flat 2) on each floor. The floors are numbered from 1 to 5 (1 being the lowermost floor and 5 being the topmost floor).
Note I: Each floor has two flats viz., Flat-1 and Flat-2, where Flat 1 is to the west of Flat 2.
Note II: Flat 1 of floor 2 is immediately above Flat 1 of floor 1 and immediately below Flat 1 of floor 3 and so on. Similarly Flat 2 of floor 2 is immediately above Flat 2 of floor 1 and immediately below Flat 2 of floor 3 and so on.
Note III: The area of each flat is equal.
Note IV: Only two persons live on each floor and only one person lives in each flat.
L lives on an even-numbered floor in Flat-1. P lives in Flat-2 of the topmost floor. N lives west of Q. N lives on a floor immediately below the L’s floor. K and R live on the same named flat. K and L lives in a different named flat. Only one floor is between K and O. K lives below O. S lives to the west of P. M lives immediately below O, but not in the same named flat. One floor between J’s floor and L’s floor.
Which among the following statement is/are false?
Correct Answer :
Q lives above M
Solution :
The correct answer is: Q lives above M
Let us analyze the clues step-by-step to determine the position of each person in the building.
The building has 5 floors (numbered 1 to 5 from bottom to top) and 2 flats on each floor (Flat 1 to the west, Flat 2 to the east).
Step 1: Place P and S.
- "P lives in Flat-2 of the topmost floor." -> P is on Floor 5, Flat 2.
- "S lives to the west of P." -> S is on Floor 5, Flat 1.
Step 2: Place L and related persons (N, Q, J).
- "L lives on an even-numbered floor in Flat-1." Even floors are Floor 2 and Floor 4. But Floor 5 is occupied by S and P, and L is in Flat-1 of an even floor. Thus, L must be on Floor 4 or Floor 2 in Flat 1.
- "N lives on a floor immediately below L’s floor."
- "N lives west of Q." This means N is in Flat 1, and Q is in Flat 2 of the same floor.
- Let us test the two possibilities for L:
Case A: L is on Floor 4, Flat 1.
Then N (immediately below L) is on Floor 3, Flat 1.
Since N lives west of Q, Q must be on Floor 3, Flat 2.
- "One floor between J’s floor and L’s floor." If L is on Floor 4, J's floor could be Floor 2.
Case B: L is on Floor 2, Flat 1.
Then N (immediately below L) is on Floor 1, Flat 1.
Since N lives west of Q, Q must be on Floor 1, Flat 2.
- "One floor between J’s floor and L’s floor." If L is on Floor 2, J's floor must be Floor 4 (since Floor 5 is occupied by S and P).
Step 3: Analyze the remaining clues (K, R, O, M).
- "K and L lives in a different named flat." Since L is in Flat 1, K must be in Flat 2.
- "K and R live on the same named flat." Since K is in Flat 2, R must also be in Flat 2.
- "K lives below O. Only one floor is between K and O." Since K and O have one floor between them, and K is below O:
If K is on Floor 1, O is on Floor 3.
If K is on Floor 2, O is on Floor 4.
If K is on Floor 3, O is on Floor 5 (but Floor 5 is already occupied by S and P, so this is impossible).
- "M lives immediately below O, but not in the same named flat."
If O is on Floor 3, M is on Floor 2. Since M and O are in different named flats, if O is in Flat 1, M must be in Flat 2; if O is in Flat 2, M must be in Flat 1.
If O is on Floor 4, M is on Floor 3.
Let us evaluate Case A: L is on Floor 4 (Flat 1), N is on Floor 3 (Flat 1), Q is on Floor 3 (Flat 2).
- Since J's floor has one floor between it and L's floor (Floor 4), J must be on Floor 2.
- K must be in Flat 2.
- If K is on Floor 1 (Flat 2), then O must be on Floor 3. But Floor 3 is fully occupied by N (Flat 1) and Q (Flat 2). Thus, O cannot be on Floor 3.
- If K is on Floor 2 (Flat 2), O must be on Floor 4. Since L is on Floor 4 (Flat 1), O must be on Floor 4 (Flat 2).
- Now, "M lives immediately below O, but not in the same named flat." Since O is on Floor 4 (Flat 2), M must be on Floor 3, in Flat 1. But N is already on Floor 3 (Flat 1). This is a contradiction.
Hence, Case A is invalid.
Let us evaluate Case B: L is on Floor 2 (Flat 1), N is on Floor 1 (Flat 1), Q is on Floor 1 (Flat 2).
- Since J's floor has one floor between it and L's floor (Floor 2), J must be on Floor 4.
- K must be in Flat 2. K cannot be on Floor 1 (occupied by N and Q).
- If K is on Floor 2 (Flat 2): O must be on Floor 4. Since J is on Floor 4, J and O will share Floor 4.
- Since K is in Flat 2, and K is on Floor 2, we have:
Floor 2: L (Flat 1), K (Flat 2).
- O is on Floor 4. M lives immediately below O (on Floor 3), in a different named flat than O.
- Let us check the options for O's flat on Floor 4. J and O are on Floor 4.
If O is in Flat 1, J must be in Flat 2. Then M (immediately below O on Floor 3) must be in Flat 2.
If O is in Flat 2, J must be in Flat 1. Then M (immediately below O on Floor 3) must be in Flat 1.
- Let us check the remaining positions:
We have R, who must be in Flat 2. The available spaces in Flat 2 are on Floor 3 or Floor 4.
Since R lives in Flat 2, let's place the remaining people.
Suppose J is on Floor 4 (Flat 1), and O is on Floor 4 (Flat 2).
Then M must be on Floor 3 (Flat 1) because M is immediately below O (Floor 4) and in a different flat (Flat 1).
This leaves Floor 3 (Flat 2) for R (since R is in Flat 2).
Let us double check if all conditions are satisfied with this arrangement:
Floor 5: S (Flat 1), P (Flat 2)
Floor 4: J (Flat 1), O (Flat 2)
Floor 3: M (Flat 1), R (Flat 2)
Floor 2: L (Flat 1), K (Flat 2)
Floor 1: N (Flat 1), Q (Flat 2)
Let us verify all statements:
- L lives on an even-numbered floor in Flat-1: L is on Floor 2, Flat 1. (True)
- P lives in Flat-2 of the topmost floor: P is on Floor 5, Flat 2. (True)
- N lives west of Q: N is on Floor 1, Flat 1, Q is on Floor 1, Flat 2. (True)
- N lives on a floor immediately below L's floor: Floor 1 is immediately below Floor 2. (True)
- K and R live on the same named flat: Both are in Flat 2. (True)
- K and L live in different named flats: K is in Flat 2, L is in Flat 1. (True)
- Only one floor is between K (Floor 2) and O (Floor 4). (True)
- K lives below O. (True)
- S lives to the west of P: S is on Floor 5, Flat 1. (True)
- M lives immediately below O (Floor 3 is below Floor 4), but not in the same named flat (O is in Flat 2, M is in Flat 1). (True)
- One floor between J's floor (Floor 4) and L's floor (Floor 2). (True)
Now, let us evaluate the given options to see which statement is false:
1. Two floors between P’s floor and L’s floor: P is on Floor 5, L is on Floor 2. The floors between them are Floor 3 and Floor 4 (2 floors). (True)
2. J lives above L: J is on Floor 4, L is on Floor 2. (True)
3. N lives immediately below K: N is on Floor 1, K is on Floor 2. (True)
4. Q lives above M: Q is on Floor 1, M is on Floor 3. Therefore, Q lives below M. This statement is False.
5. K lives east of L: K is on Floor 2, Flat 2 (east), L is on Floor 2, Flat 1 (west). (True)
Therefore, the false statement is "Q lives above M".
Access expert-curated educational resources and study materials—completely free.
Create, conduct, and manage professional online assessments with Mindyard. Perfect for teachers and institutes.
Copyright © 2026 Mindyard. All Rights Reserved.