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.

How many persons live between T and O?

The correct answer is Six.

We need to place ten persons — M, N, O, P, Q, R, S, T, U, V — on floors 1 through 10, then find how many persons live between T and O. Let us decode each clue systematically.

Step 1: Fix N, O, P, and Q

Clue: Four persons live between N and O → N and O are exactly 5 floors apart.
Clue: O lives immediately below P → P = O + 1.
Clue: N lives on an even-numbered floor, but not floor 10.
Clue: Q lives three floors below P → Q = P − 3.

Testing the valid combination where N is below O:
N = 4, O = 9, P = 10, Q = 7
Check: Four persons between floors 4 and 9 (floors 5, 6, 7, 8) ✓, N is even and not 10 ✓, Q = 10 − 3 = 7 ✓

Step 2: Place R and S

Clue: Number of persons above R = Number of persons below S, and they are not adjacent.
Persons above R = 10 − r; persons below S = s − 1.
Setting equal: 10 − r = s − 1 → r + s = 11.

From the remaining available floors {1, 2, 3, 5, 6, 8}, valid pairs summing to 11 (non-adjacent):
→ R = 8, S = 3 �� |8 − 3| = 5 (not adjacent ✓)

Step 3: Place T

Clue: T lives adjacent to S (floor 3).
T = 2 or T = 4 (floor 4 is taken by N) → T = 2

Step 4: Place M, U, and V

Remaining floors: 1, 5, 6 for M, U, V.
Clue: U lives on an odd-numbered floor, above V, and below M.
Odd floor from {1, 5, 6}: U = 5.
V below U (floor 5): V = 1.
M above U (floor 5): 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 5: Answer the Question

T is on floor 2. O is on floor 9.
Persons on floors strictly between 2 and 9 (i.e., floors 3, 4, 5, 6, 7, 8):

Floor 3 → S
Floor 4 → N
Floor 5 → U
Floor 6 → M
Floor 7 → Q
Floor 8 → R

That gives us 6 persons living between T and O.

✅ The answer is Six.