Directions: Study the following information carefully and answer the questions…
2023
Directions: Study the following information carefully and answer the questions given below:
Twelve persons live in a five-floor building such that the bottommost floor is numbered as 1, the floor just above it is numbered as 2 and so on till the topmost floor is numbered as 5. Each floor has four flats – J, K, L and M from west to east respectively. Flat K is to the east of flat J and to the west of flat L which is to the west of flat M. 8 flats are vacant.
Note: 1) At least two but not more than three persons live on each floor. The adjacent flats are not vacant. Adjacent flats are immediate left, immediate right, immediately above and immediately below.
2) If it is given that A lives immediately above/immediately below B’s flat then either a vacant flat is between A and B or there is no vacant flat (no floor) between A and B. U lives on an even number floor below the 3rd floor. W lives to the east of U but neither in flat K nor in flat M. Only one floor gap is between W and P who lives to the west of S but not just west. U and P live in different named flats. R lives above S and adjacent to one of the vacant flats. R and W live in different named flats. O lives to the west of R and east of V. Q lives immediately below O’s flat. T lives to the east of Q. Only one floor gap between T and Y. T lives immediately above Y’s flat. Z lives just northwest of X.
Which among the following statements is not true?
- A.
Z and P live in the same named flat
- B.
Only one flat is vacant on floor 2
- C.
P lives on an even-numbered floor
- D.
On floor 2, even number of persons live
- E.
None is true
Show answer & explanation
Correct answer: D
Concept
In a floor-and-flat arrangement puzzle, the phrases used to link two people are governed by the puzzle's own definitions, not by everyday wording. Here the note explicitly defines "immediately above/below" so that the two flats share the same column and there may be either no floor between them or exactly one wholly-vacant floor between them. So a clue can simultaneously say "immediately above" and "one floor gap" without contradiction – it simply forces one empty floor in that column.
The fixed quantities are the anchor: 5 floors × 4 flats = 20 flats, 8 vacant, so 12 are occupied; with each floor holding 2 or 3 persons, the only split that totals 12 is two floors with 3 and three floors with 2.
Application – building the grid
U is on an even floor below the 3rd, so U is on floor 2. W must be in flat L (east of U, and neither K nor M), so W is also on floor 2.
“One floor gap between W and P” puts P two floors from W, i.e. on floor 4; P is in flat J (west of S, but not immediately west, and a different flat from U).
P is in flat J and S to its east on floor 4 lands in flat L. R is above S, and R differs from W's flat, placing R in flat M on floor 5.
O is west of R and east of V on floor 5 → O in flat K, V in flat J. Q sits in the same column as O (flat K) with the one-vacant-floor rule, on floor 3.
T is east of Q on floor 3 → flat M. T is “immediately above” Y with a one-floor gap, so Y is in flat M on floor 1.
Z is just north-west of X. The only consistent fit is Z in flat J on floor 2 and X in flat K on floor 1, which also satisfies “no two vacant flats are adjacent” and “R is adjacent to a vacant flat.”
This yields one unique arrangement (flats shown west→east as J, K, L, M; a dot is vacant):
Floor | J | K | L | M |
|---|---|---|---|---|
5 | V | O | – | R |
4 | P | – | S | – |
3 | – | Q | – | T |
2 | Z | U | W | – |
1 | – | X | – | Y |
Cross-check the statements
Read each statement against this single grid:
Z (flat J) and P (flat J) share the same named flat – a true statement.
On floor 2 only flat M is empty, so exactly one flat is vacant there – a true statement.
P sits on floor 4, an even-numbered floor – a true statement.
Floor 2 is occupied by Z, U and W – three persons, an odd number. So “an even number of persons live on floor 2” is the statement that does not hold.
Hence the statement “On floor 2, an even number of persons live” is the one that is not true.