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, 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 daily schedule of the friends
1. S attended on Sunday and prepared the second-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.
4. V attended on Friday.
5. P attended immediately after the person who prepared 9 dishes. Since P can only attend on Monday, Tuesday, or Thursday:

• P cannot be on Monday (no day before Monday in this week).
• If P is on Thursday, the person before P (on Wednesday) is Q. But Q prepared the most dishes, which would mean Q = 9 dishes, which is too low (as Q must be greater than T and P). Thus, P cannot be on Thursday.
• Therefore, P must have attended on Tuesday, and the person who attended on Monday prepared 9 dishes.

6. The only remaining days are Monday and Thursday, and the remaining friends are R and U.
7. There were 2 people between R and the person who prepared 6 dishes.

• If R is on Thursday, the person with 6 dishes must be on Monday (since Monday and Thursday have 2 days in between). But Monday has 9 dishes. So R cannot be on Thursday.
• Therefore, R must be on Monday, meaning R prepared 9 dishes.
• This leaves U to attend on Thursday, which means U prepared 6 dishes.

8. The friend who prepared the least dishes attended immediately after R. Since R is on Monday, the person who prepared the least dishes is P (on Tuesday).

Thus, the schedule of attendance is:
• 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)

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Step 2: Determine the number of dishes prepared by each person
1. We are given:

$Q=T+5$

$T=P+6$

This means:

$Q=P+11$

2. The person who prepared 10 dishes attended immediately before the person who prepared 8 dishes.
Looking at the schedule, the only consecutive days that can have 10 and 8 dishes are Friday (V) and Saturday (T), because U (on Thursday) has 6 dishes.
Therefore, V prepared 10 dishes and T prepared 8 dishes.
3. Using $T=8$:

$P=T-6=8-6=2$ (which is indeed the least number of dishes).

$Q=T+5=8+5=13$ (which is the most number of dishes).

4. S prepared the second-most dishes (greater than V's 10, but less than Q's 13). So S prepared either 11 or 12 dishes.
Since only one person prepared half the number of dishes of another, and U has 6 dishes, S must have prepared 12 dishes (since 6 is half of 12).

The final counts of dishes are:
• R: 9
• P: 2
• Q: 13
• U: 6
• V: 10
• T: 8
• S: 12

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Step 3: Finding the odd one out
Let's check the number of dishes prepared by the options:
• S = 12 (Even number)
• P = 2 (Even number)
• T = 8 (Even number)
• R = 9 (Odd number)
Since R is the only person in the options who prepared an odd number of dishes, R does not belong to the group.