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A pharmaceutical company has tested five drugs on three different organisms. The following incomplete table reports if a drug works on the given organism. For example, drug A works on organism R…

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A pharmaceutical company has tested five drugs on three different organisms. The following incomplete table reports if a drug works on the given organism. For example, drug A works on organism R while B and C work on Q.

DrugOrganism POrganism QOrganism R
A✔
B✔
C✔
D
E

Following additional information is available:

- Each drug works on at least one organism but not more than two organisms.
- Each organism can be treated with at least two and at most three of these five drugs.
- On whichever organism A works, B also works. Similarly, on whichever organism C works, D also works.
- D and E do not work on the same organism.

The organism(s) that can be treated with three of these five drugs is(are)
  1. Only P
  2. Only Q
  3. P and Q
  4. Q and R

Answer and explanation

Correct answer: D - Q and R
Deduction: B already on Q; A on R forces B on R, so B = {Q,R} (max 2) and A lies within {Q,R}. C on Q forces D on Q. P needs >=2 drugs and only C,D,E can be on P; D and E cannot both be on P, and C on P needs D, so P = {C,D}. Then C={P,Q}, D={P,Q}, E (disjoint from D) = {R}; Q = {B,C,D} is full, so A = {R}. Final: P={C,D}, Q={B,C,D}, R={A,B,E}. Q and R each have three drugs; P has two.

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