Directions (77-81): Read the following information carefully and answer the questions given below:
Ten persons- M, N, O, P, Q, R, S, T, U and V live on different floors of a ten-storey building where ground floor is numbered as 1, above it is 2 and so on till the topmost floor is numbered as 10.
Four persons live between N and O who lives immediate below P. N lives on an even numbered floor but not on top floor. Q lives three floors below P. The number of persons live above R is same as the number of persons live below S but they do not live adjacent to each other. T lives adjacent to S. U lives on an odd numbered floor but above V and below M.
The number of persons live above V is same as the number of persons live below _____?
Correct Answer :
P
Solution :
The correct answer is Option 1: P.
To solve this, we must first deduce the exact floor arrangement of all ten persons using the given clues, then answer the question.
Step 1: Establish Key Relationships
Let's list the constraints:
— Four persons live between N and O → |Floor(N) - Floor(O)| = 5
— O lives immediately below P → Floor(O) = Floor(P) - 1
— N is on an even floor, but NOT floor 10
— Q lives three floors below P → Floor(Q) = Floor(P) - 3
— Persons above R = Persons below S, and R & S are NOT adjacent
— T lives adjacent to S
— U is on an odd floor, with V < U < M (in terms of floor number)
Step 2: Find P, O, N, Q Positions by Trial
Since O = P - 1 and |N - O| = 5, we have two cases: N = O + 5 or N = O - 5.
Testing P = 10, O = 9, N = 4, Q = 7:
— N = 4 (even ✓, not floor 10 ✓)
— Q = 10 - 3 = 7 ✓
— Four persons between N(4) and O(9): floors 5, 6, 7, 8 → 4 persons ✓
This case works. Remaining floors for M, R, S, T, U, V: 1, 2, 3, 5, 6, 8.
Step 3: Place R and S
Persons above R = 10 - Floor(R). Persons below S = Floor(S) - 1.
Setting them equal: 10 - r = s - 1 → r + s = 11.
From available floors {1, 2, 3, 5, 6, 8}, valid pair summing to 11:
— r = 8, s = 3 → R on floor 8, S on floor 3. |8 - 3| = 5, not adjacent ✓
Step 4: Place T
T must be adjacent to S (floor 3): T = 2 or T = 4. Floor 4 is taken by N, so T = 2 ✓.
Step 5: Place M, U, V
Remaining floors: 1, 5, 6 for M, U, V.
U must be on an odd floor → U = 1 or U = 5.
Condition: V < U < M.
— If U = 1: no floor below for V → impossible ✗
— If U = 5: V < 5 and M > 5 → V = 1, M = 6 ✓
Final Floor Arrangement:
Floor 10 → P
Floor 9 → O
Floor 8 → R
Floor 7 → Q
Floor 6 → M
Floor 5 → U
Floor 4 → N
Floor 3 → S
Floor 2 → T
Floor 1 → V
Step 6: Answering the Question
V lives on Floor 1. The number of persons living above V = 9 (everyone on floors 2 through 10).
We need to find who X is such that the number of persons living below X is also 9.
Persons below X = Floor(X) - 1 = 9 → Floor(X) = 10.
The person on floor 10 is P.
Verification: Above V (floor 1) = 9 persons. Below P (floor 10) = 9 persons. ✓
Therefore, the answer is P.
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