Study the following information carefully and answer the questions given below:

Nine persons L, N, O, P, Q, W, Y, V and Z live in three different cities Barcelona, Dehradun and Texas but not necessarily in the same order. Q lives with V but neither in Texas nor Dehradun. P lives only with Z but not in Texas. W does not live with V. N neither lives with Y nor in Dehradun. O either lives in Dehradun or Texas. N does not live in Texas. Odd numbers of persons live in Barcelona. O lives with L.

Which of the following statement is true?
I. Q and Y live in same city
II. Y lives with W
III. More than two persons live in Texas

The correct answer is Both II and III.

Step-by-step Explanation:

Let's analyze the given clues step-by-step to determine the city in which each of the nine persons (L, N, O, P, Q, W, Y, V, Z) lives.

1. Identify the cities:
The three cities are Barcelona, Dehradun, and Texas.

2. Analyze clues regarding Q and V:
"Q lives with V but neither in Texas nor Dehradun."
⇒ Since Q and V do not live in Texas or Dehradun, both Q and V must live in Barcelona.

3. Analyze clues regarding P and Z:
"P lives only with Z but not in Texas."
⇒ "P lives only with Z" means that in P's city, there are exactly two persons: P and Z.
⇒ P does not live in Texas, nor can P live in Barcelona (since Barcelona already has Q and V, and P lives only with Z, meaning no one else can live in P's city).
⇒ Therefore, P and Z live in Dehradun, and no other person lives in Dehradun (total 2 persons in Dehradun).

4. Analyze clues regarding O and L:
"O either lives in Dehradun or Texas."
"O lives with L."
⇒ Since Dehradun is strictly occupied by only P and Z, O cannot live in Dehradun.
⇒ Thus, O and L live in Texas.

5. Analyze clues regarding N:
"N does not live in Texas."
"N does not live in Dehradun" (since Dehradun is full with only P and Z).
⇒ Therefore, N lives in Barcelona.

6. Analyze odd number of persons in Barcelona:
"Odd numbers of persons live in Barcelona."
Currently, Barcelona has Q, V, and N (3 persons). Texas has O and L (2 persons). Dehradun has P and Z (2 persons).
The remaining two persons to place are W and Y.
Can W or Y live in Barcelona? If 2 more persons were added to Barcelona, it would have 5 persons, but let's check the constraints on W and Y:
- "W does not live with V." Since V is in Barcelona, W cannot live in Barcelona.
- "N neither lives with Y nor in Dehradun." Since N is in Barcelona, Y cannot live in Barcelona.
⇒ Neither W nor Y can live in Barcelona.
⇒ Therefore, both W and Y live in Texas.

Final Person-City Distribution:

- Barcelona (3 persons): Q, V, N
- Dehradun (2 persons): P, Z
- Texas (4 persons): O, L, W, Y

Evaluating the Given Statements:

I. Q and Y live in same city: False (Q lives in Barcelona, Y lives in Texas).
II. Y lives with W: True (Both Y and W live in Texas).
III. More than two persons live in Texas: True (4 persons live in Texas, which is more than 2).

Hence, statements II and III are true.