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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.
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.
Drug C is used on organism Q. So, drug D also must be used on Q (from condition(iii))
Also, drug A is used on organism R. So, drug B must also be used on R (from condition (iii))
So, we can fill the table like,
Now, organism Q has already been treated with 3 drugs. So, it must not be treated with A and E.
(In condition (ii), it is mentioned an organism can be treated with a maximum of three drugs).
Also, drug B is working on 2 organisms Q and R. So, it must not work on P.
(In condition (i), it is mentioned a drug can work on maximum 2 organisms)
Now, drug B is not working on P, so drug A also must not work on P.
(The reason is if drug A works on P, then drug B must also work on P (condition (iii))
So, we can fill the table upto this,
(Symbol X denotes either drug does not work or the organism was not treated with that drug)
Now in organism P, neither A nor B works.
Now out of the remaining three drugs, only one out of D and E will work (condition (iv)). Also, we need minimum 2 drugs to work (condition (ii)). So, drug C has to work on P.
Now, if drug C works on P, then drug D also has to work on P.
So, now the table will be like:
Now, drug C and drug D are working on organisms P and Q. So they won't work on R definitely.
(condition (i) states, a drug can work on a maximum of 2 organisms)
Also, drug E is not working on P and Q. So, it must work on R for sure.
(condition (i) states, a drug has to work on atleast 1 organism)
So, our final table will be like:
So, organism P can be treated with only C and D.
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