Directions (25-29): Study the information carefully and answer the questions given below.

Seven friends - P, Q, R, S, T, U, and V - went to attend a cooking class for a week from Monday to Sunday, not necessarily in the same order. Each person prepared a different number of dishes during these classes.

Q prepared the most dishes. The person who prepared the least dishes attended immediately after R.S prepared the 2ndmost dishes and attended on Sunday. T and the person who prepared the second-most dishes attended on consecutive days. Q prepared 5 dishes more than T who prepared 6 dishes more than P. P attended the classes immediately after the person who prepared 9 dishes. The person who prepared 10 dishes attended immediately before the person who prepared 8 dishes. Q attended on Wednesday, while V attended on Friday. There were 2 people between R and the person who prepared 6 dishes. Only One person prepared half number of dishes than the other one.

Four of the following five are alike in a certain way and hence form a group. Which of the following does not belong to that group?

To find the odd one out among the given options, we first need to determine the schedule and the number of dishes prepared by each of the seven friends (P, Q, R, S, T, U, and V) from Monday to Sunday.

Step 1: Determine the Days of Attendance

1. S attended on Sunday and prepared the 2nd most dishes.
2. T and the person who prepared the second-most dishes (S) attended on consecutive days. Since S is on Sunday, T must have attended on Saturday.
3. Q attended on Wednesday, while V attended on Friday.
4. P attended immediately after the person who prepared 9 dishes. Since Q (Wednesday), V (Friday), T (Saturday), and S (Sunday) are fixed, the only possible day for P to attend immediately after another day is Tuesday (making Monday the day with 9 dishes). Therefore, P attended on Tuesday, and the person who attended on Monday prepared 9 dishes.

Currently, the schedule is as follows:

- Monday: Person with 9 dishes
- Tuesday: P
- Wednesday: Q
- Thursday: (Empty)
- Friday: V
- Saturday: T
- Sunday: S

Step 2: Find the Positions of R and U

1. "The person who prepared the least dishes attended immediately after R."
2. "There were 2 people between R and the person who prepared 6 dishes."
If R attended on Monday, then the person who attended immediately after R is P (on Tuesday), which means P prepared the least number of dishes.
With R on Monday, the person who prepared 6 dishes must be on Thursday (2 days after Monday). Thus, U must have attended on Thursday, leaving R on Monday.

This gives us the complete schedule:

- Monday: R (9 dishes)
- Tuesday: P (least dishes)
- Wednesday: Q (most dishes)
- Thursday: U (6 dishes)
- Friday: V
- Saturday: T
- Sunday: S (2nd most dishes)

Step 3: Determine the Number of Dishes

1. We are given the relationships:
$Q=T+5$
$T=P+6$
Which implies:
$Q=P+11$
2. "The person who prepared 10 dishes attended immediately before the person who prepared 8 dishes." This means V (Friday) prepared 10 dishes and T (Saturday) prepared 8 dishes.
Using $T=8$:
$Q=8+5=13$ dishes
$P=8-6=2$ dishes (which is indeed the least)
3. "Only one person prepared half the number of dishes than the other one." Since U prepared 6 dishes, S (who prepared the 2nd most dishes, less than Q's 13 dishes) must have prepared 12 dishes (making the ratio of S to U equal to 2:1).

The final distribution of dishes is:

- Monday: R = 9 dishes
- Tuesday: P = 2 dishes
- Wednesday: Q = 13 dishes
- Thursday: U = 6 dishes
- Friday: V = 10 dishes
- Saturday: T = 8 dishes
- Sunday: S = 12 dishes

Step 4: Identify the Odd One Out

Let's analyze the number of dishes prepared by the options:
- S: 12 dishes (Even)
- P: 2 dishes (Even)
- T: 8 dishes (Even)
- V: 10 dishes (Even)
- R: 9 dishes (Odd)

All of them prepared an even number of dishes, except R, who prepared an odd number of dishes (9). Therefore, R does not belong to the group.