Who has an interview immediately after K?

Question

Accepted Answer

Step-by-step deduction:

1. Number days Monday to Sunday as positions $1\ldots7$.

2. "Only four people between N and Zoology" means their positions differ by $5$. Possible pairs in $1\ldots7$ are $(1,6),(6,1),(2,7),(7,2)$. Since neither N nor Zoology is on Sunday (position $7$), the only possible positions are $1$ and $6$. So N and Zoology occupy positions $1$ and $6$ in some order.

3. "P immediately after Zoology" forces P to be at position $	ext{Zoology}+1$. The only viable assignment (avoiding Sunday for Zoology) is Zoology at $6$ and P at $7$. Thus N is at $1$.

4. "Only two people between P and J" with P at $7$ gives J at $4$ (since $7-4-1=2$).

5. "Psychology is before J but not Wednesday, and neither N nor P likes Psychology." The only available day before $4$ and not $3$ (Wednesday) is $2$, so Psychology is at $2$ (person not N or P).

6. "Two people between Psychology and Statistics" places Statistics at $5$ (since $2+3=5$). Then "Economics immediately before Statistics" places Economics at $4$, so J (at $4$) likes Economics.

7. "Number between P and Economics equals number between J and English." Between P($7$) and Economics($4$) are positions $5,6$ so count $2$. Thus J($4$) and English must have $2$ between them, so English is at $7$ (since position $1$ is N and N does not like English). Hence P at $7$ likes English.

8. "Only one person between English and K" (English at $7$) forces K at $5$ or $3$. But $5$ is Statistics, so K can be at $5$ (Statistics) or $3$ (Sociology candidate). Keep both in mind.

9. "Sociology immediately after O": possible consecutive slots reduce to O at $2$ and Sociology at $3$ (because $3$ is the only spot immediately after $2$ not already occupied by another subject). That makes the person at $2$ = O (Psychology) and the person at $3$ = Sociology.

10. Remaining persons are K, L, M to place in positions $3,5,6$. "L is after M" forces M at $3$ and L at $6$. Therefore K must be at $5$.

11. Final consistent arrangement by position:
- $1$: N — Mathematics
- $2$: O — Psychology
- $3$: M — Sociology
- $4$: J — Economics
- $5$: K — Statistics
- $6$: L — Zoology
- $7$: P — English

12. Who is immediately after K (position $5$)? Position $6$ is L who likes Zoology. Therefore the person immediately after K is the one who likes Zoology.

FINAL_ANSWER: b

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