**Passage.** A group of six students — M, N, O, P, Q and R — is in a c…

Question

**Passage.** A group of six students — M, N, O, P, Q and R — is in a class. Each student opts for two subjects: one compulsory and one optional.

1. P's optional subject is Geography; three others have it as compulsory.
2. Q and R have Chemistry as one of their subjects.
3. R's compulsory subject is Physics, which is optional for both O and Q.
4. M's compulsory subject is Geography and the optional is English.
5. Biology is optional for only one student.
6. The only female student has Geography as optional and English as compulsory.

**Question.** Which group has Geography as a compulsory subject?

Accepted Answer

D. M, N and O

**Working out the assignment.**
From (4): **M** — Geo (comp) / English (opt).
From (3): **R** — Physics (comp); Physics is opt for **O** and **Q**.
From (2) + (3): **Q** must take Chemistry as her *other* subject → Q is Chemistry (comp) / Physics (opt).
From (1): P_opt = Geo, and three *others* have Geo as compulsory. M is one; the other two must come from {N, O, P} — but P has Geo as optional, not compulsory. So **N** and **O** have Geo as compulsory.
From (6): the female has English (comp) + Geo (opt). Only P has Geo as optional, so **P is the female** and P_comp = English.
From (5): Biology is optional for exactly one. The remaining open slot is N's optional → **N_opt = Biology**.
| Student | Compulsory | Optional |
|---|---|---|
| M | Geography | English |
| N | Geography | Biology |
| O | Geography | Physics |
| P | English | Geography |
| Q | Chemistry | Physics |
| R | Physics | Chemistry |
**Answer:** D — Condition 1 says three students (besides P) have Geography compulsory. Working through the chain, those three are M, N and O.

Answer

M, O and P

Answer

O, N and P

Answer

O, P and R