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.

Four of the following five are alike in a certain way and thus form a group, then who among the following doesn’t belong to that group?

  1. A.

    O

  2. B.

    Q

  3. C.

    U

  4. D.

    X

  5. E.

    P

Show answer & explanation

Correct answer: E

Concept: In a “four alike, one different” floor-and-flat puzzle, the shared trait is never obvious up front — it only emerges once the entire grid (which floor and which flat each person occupies) is uniquely pinned down from the clues, including the special allowance that a vacant floor may sit between two people described as “immediately above/below.” Every step below either fixes a value directly or eliminates the alternatives that a later clue rules out — nothing is asserted without a reason. Once every named person's floor and flat are fixed, compare the asked attribute (here, the flat column) across all five options to see which four match and which one differs.

  1. U lives on an even floor below the 3rd floor, so U is on Floor 2.

  2. W lives east of U but is in neither flat K nor flat M, so W must be in flat L; this restricts U to flat J or flat K.

  3. Only one floor gap separates W and P, so P is on Floor 4 (two floors above W's Floor 2), on the same floor as S (since P is west of S).

  4. R lives above S, so R is on Floor 5 (the only floor above Floor 4), and O sits between V and R, west to east, on that same floor. Since R cannot share flat L with W, the only west-to-east placement that keeps R out of flat L is R = flat M, with V and O occupying two of flats J, K, L to its west.

  5. On any floor with exactly 2 occupants, the rule that adjacent flats cannot both be vacant forces the occupied pair to be one of only three patterns (west to east): (J, L), (J, M) or (K, M). Floor 4 has exactly P and S, with P west of S and not immediately west, so (P, S) must be one of these same three patterns.

  6. Q sits one floor below O's flat with a vacant floor in between, so Floor 4's flat matching O must be vacant — this ties O's flat to whichever of K or L is vacant on Floor 4 under each (P, S) pattern. Checking every resulting branch against 'R is adjacent to a vacant flat' (R = M on Floor 5, whose only possible vacant neighbours are flat L on Floor 5 or flat M directly below on Floor 4) and against the rule that two vertically stacked flats can't both be vacant: (P, S) = (K, M) forces O into flat L, which leaves Floor 4's flat M occupied (by S) and Floor 5's remaining vacant flat not adjacent to R either way — R never gets a vacant neighbour, so this pattern fails regardless of where V sits. (P, S) = (J, M) allows O to be K or L: with O = L, R again has no vacant neighbour and fails the same way; with O = K, Floor 5's vacant flat becomes L (adjacent to R, so that check passes), but Floor 4 is then also vacant at L under this pattern — stacking two vacant L's on adjacent floors, which the rule forbids. Only (P, S) = (J, L) survives every check, with O forced to K: Floor 5's vacant flat (L) sits directly below R with no Floor-4 vacancy stacked under it. So P is in flat J, S is in flat L, O is in flat K (with V in flat J's row on Floor 5 and R confirmed in flat M), and Floor 4's vacant flats are K and M.

  7. U and P must live in different named flats, and P is now fixed at flat J, so U — restricted to J or K in step 2 — is pushed into flat K.

  8. Q, one floor below O with the buffered gap already established in step 6, lands in flat K on Floor 3 (matching O's flat).

  9. T is east of Q on Floor 3; the same 2-occupant vacancy rule allows only (K, M) or (K, L) as a valid pair starting at K, so T is provisionally either M or L, to be settled next.

  10. T and Y have one floor gap between them with a vacant floor in between, so Y is on Floor 1 and the intervening Floor 2 flat (matching T and Y's flat) must be vacant. Floor 2 already holds U in K and W in L; its third resident Z cannot be in flat M (Z is just northwest of X, one flat west of X, and flat M has no flat further east for X to occupy), so Z takes flat J — leaving flat M as Floor 2's only vacant flat. That vacant M is exactly the buffer flat the T–Y clue needs, which settles step 9: T and Y are both in flat M (Floor 3 and Floor 1 respectively).

  11. Z is in flat J on Floor 2; since Z lives just northwest of X (one floor below and one flat east of Z), X is in flat K on Floor 1.

  12. The completed grid below satisfies every clue, with each floor holding 2 or 3 residents and no two adjacent flats — in the same row or in the same column across floors — ever both vacant at once.

Floor

J

K

L

M

5 (top)

V

O

(vacant)

R

4

P

(vacant)

S

(vacant)

3

(vacant)

Q

(vacant)

T

2

Z

U

W

(vacant)

1 (bottom)

(vacant)

X

(vacant)

Y

Cross-check: Reading down flat K shows O (Floor 5), Q (Floor 3), U (Floor 2) and X (Floor 1) all occupy it — four of the five named residents share the same flat column. P, however, sits in flat J on Floor 4, a different column altogether. So O, Q, U and X form the alike group by shared flat, and P is the one that does not belong to that group.

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