How many people have their interview before the one who likes Mathematics?

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Accepted Answer

Step-by-step reasoning:

1. Number days as $1$ (Mon) to $7$ (Sun). “Only four people between N and Zoology” implies those two are 5 positions apart. The only valid pair (neither on Sunday) is positions $1$ and $6$.

2. If Zoology is $1$, then P (immediately after Zoology) is $2$. With “only two between P and J” we get $J$ at $5$. Psychology must be before $J$ but not on Wednesday ($3$) and not N or P, forcing Psychology to $4$. Then Statistics would be two away at $7$ and Economics at $6$, which makes the count between P and Economics inconsistent with English — contradiction. So Zoology cannot be $1$.

3. Thus Zoology is $6$ and $N$ is $1$. Then P (after Zoology) is $7$. With “only two between P and J” we get $J$ at $4$.

4. Psychology is before $J$ (not on $3$) and not N or P, so Psychology is at $2$. "Only two between Psychology and Statistics" gives Statistics at $5$, and Economics immediately before Statistics puts Economics at $4$, so $J$ likes Economics.

5. Number between P ($7$) and Economics ($4$) is $2$, so number between $J$ ($4$) and English must be $2$; from $4$ that places English at $7$, so $P$ likes English. "Only one between English and K" places $K$ at $5$, so $K$ likes Statistics.

6. "Sociology immediately after O" forces O at $2$ and Sociology at $3$ (since $2$ is free personwise and has Psychology subject). The remaining two subjects are Sociology and Mathematics, so Mathematics must be at position $1$ (with Sociology at $3$).

7. Assign remaining people so that L is after M: $N$ at $1$ (Mathematics), $O$ at $2$ (Psychology), $M$ at $3$ (Sociology), $J$ at $4$ (Economics), $K$ at $5$ (Statistics), $L$ at $6$ (Zoology), $P$ at $7$ (English). All constraints are satisfied.

Conclusion: Mathematics is at day $1$ (Monday), so there are no people before it.

FINAL_ANSWER: c

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