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.
In which among the following flats minimum persons live?
- A.
Flat J
- B.
Flat K
- C.
Flat L
- D.
Flat M
- E.
Either flat K or flat L
Show answer & explanation
Correct answer: C
Concept
In a floors-and-flats arrangement puzzle, each clue pins a person to a floor (vertical) and/or a flat-column (horizontal). The dependable method is to start from the most rigid clue — one that fixes an exact floor or column — then build the 5-floor by 4-flat grid, propagate every remaining clue, and keep two global limits in view: each floor holds 2 or 3 persons, and no two vacant flats are adjacent. The question “minimum persons in a flat” then asks which flat-column (J, K, L or M) is occupied on the fewest floors.
Key relations
Flats run west to east as J, K, L, M, so “east of” means a higher-lettered column on the same floor and “west of” a lower-lettered one.
“Immediately above/below” is read down a single column with vacant flats skipped, and “only one floor gap” means exactly one floor sits between the two floors. So “T immediately above Y” together with “one floor gap” is consistent, not contradictory: T is the nearest occupied flat above Y in the same column, with one (vacant) floor between them.
“Just northwest” means one floor up and one column to the west — an immediate diagonal.
Step-by-step deduction
“An even floor below the 3rd” leaves only floor 2, so U is on floor 2.
W is east of U on the same floor and may not be in K or M, so W can only be in L; that forces U into K, the only flat west of L still open for U on floor 2. Hence on floor 2: U in K and W in L.
U and P are in different columns and exactly one floor separates W and P, so P lies on floor 4. P is west of S but not immediately west, which places P in J and S in L on floor 4.
R is above S and is in a different column from W; combined with R being adjacent to a vacant flat, R takes M on floor 5. O is west of R and east of V on floor 5, fixing V in J and O in K there.
Q is immediately below O in the same column (K), so Q is on floor 3; T is east of Q and is immediately above Y with one floor gap, giving T in M on floor 3 and Y in M on floor 1. Finally Z is just northwest of X, which places X in K on floor 1 and Z in J on floor 2. The 2–3-per-floor limit and the no-adjacent-vacant rule leave exactly one consistent grid.
The solved grid
Floor | J (west) | K | L | M (east) |
|---|---|---|---|---|
5 | V | O | vacant | R |
4 | P | vacant | S | vacant |
3 | vacant | Q | vacant | T |
2 | Z | U | W | vacant |
1 | vacant | X | vacant | Y |
Counting persons per flat-column
Flat | Persons | Occupants |
|---|---|---|
J | 3 | V, P, Z |
K | 4 | O, Q, U, X |
L | 2 | S, W |
M | 3 | R, T, Y |
Cross-check and result
The four column totals add to 3 + 4 + 2 + 3 = 12, matching the twelve persons, so nobody is double-counted or dropped. The smallest total is 2, which occurs in flat L. Therefore the fewest persons live in flat L.