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

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Accepted Answer

Step-by-step reasoning

1. “Only four people between N and Zoology” means their positions differ by $5$, so they occupy days $1$ and $6$ (Monday and Saturday).
2. "P immediately after Zoology" forces Zoology at day $6$ and $P$ at day $7$ (Sunday). Thus $N$ is at day $1$ (Monday).
3. "Only two between P and J" with $P$ at $7$ gives $J$ at day $4$ (Thursday).
4. "Psychology before J but not Wednesday" and neither $N$ nor $P$ likes Psychology. The only available day before $4$ (excluding Wed) is day $2$, so Psychology is at day $2$ (Tuesday).
5. "Two between Psychology and Statistics" places Statistics at day $5$ (Friday). "Economics immediately before Statistics" places Economics at day $4$, so $J$ (day $4$) likes Economics.
6. "Number between P and Economics = number between J and English" — between $P(7)$ and Economics$(4)$ are days $5,6$ (two people), so there must be two between $J(4)$ and English; that puts English at day $7$. $N$ does not like English, consistent since $N$ is day $1$.
7. "Only one between English and K" with English at $7$ forces $K$ to day $5$ (Friday). So day $5$ is $K$ who likes Statistics.
8. Remaining subjects are Sociology and Mathematics for days $1$ and $3$. Sociology must be immediately after $O$, so $O$ is day $2$ (Psychology) and Sociology is day $3$. Thus Mathematics is day $1$ (N).
9. Remaining people fill remaining slots with $M$ at day $3$ (Sociology) and $L$ at day $6$ (Zoology), satisfying "L after M."

Final arrangement (Day: Person - Subject):
- Monday (1): N - Mathematics
- Tuesday (2): O - Psychology
- Wednesday (3): M - Sociology
- Thursday (4): J - Economics
- Friday (5): K - Statistics
- Saturday (6): L - Zoology
- Sunday (7): P - English

Since L is on Saturday and Friday is K, the statement "Friday - L" is false; option (5) does not belong to the group.

FINAL_ANSWER: e

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