Which of the following statements is TRUE as per the given arrangement?

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Accepted Answer

Step 1: Let days be numbered Monday = 1 through Sunday = 7. From “only four people between N and Zoology”, we get |pos_N - pos_Z| = 5. Since neither N nor Zoology is on Sunday (day 7), the only possible positions are day 1 and day 6. So N and the Zoology person occupy days 1 and 6.

Step 2: “P is immediately after the one who likes Zoology” places P on the day after the Zoology day. If Zoology is on day 6, P is on day 7. (This placement leads to a consistent full solution as shown below.)

Step 3: With P on day 7 and “only two people between P and J”, J must be on day 4 (since |7 - pos_J| - 1 = 2 ⇒ pos_J = 4).

Step 4: “Psychology is on a day before J but not Wednesday” and “neither N nor P likes Psychology” force Psychology to be on day 2 (it must be before day 4 and not day 3, and day 1 is N who does not like Psychology).

Step 5: “Two people between Psychology and Statistics” places Statistics on day 5 (day 2 → day 5). “Economics immediately before Statistics” places Economics on day 4, so J (day 4) likes Economics.

Step 6: The number between P and Economics equals the number between J and English. Between P (day 7) and Economics (day 4) there are 2 people, so English must be 3 days away from J (day 4) — i.e. on day 7. Thus P (day 7) likes English.

Step 7: “Only one person between English and K” gives K on day 5, so K likes Statistics (day 5).

Step 8: “The one who likes Sociology is immediately after O.” The only placement that fits all filled slots is O on day 2 and Sociology on day 3. Since day 2 is the Psychology day, O must like Psychology.

Step 9: Remaining placements (consistency): day 1 = N (Mathematics), day 2 = O (Psychology), day 3 = M (Sociology), day 4 = J (Economics), day 5 = K (Statistics), day 6 = L (Zoology), day 7 = P (English). All given constraints are satisfied.

Thus O likes Psychology, so statement (3) is true.

FINAL_ANSWER: c

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