Understanding the argument -
The running of museums is paid for by the collections from sales of tickets. - The upkeep that may include salaries, utilities, etc., is paid by collections, say $500k.
Keeping a museum that also houses many rare and thus more expensive ancient artefacts operational requires huge funds which is a constraining factor in deciding the kind and number of artefacts to be displayed. - Basically, it highlights the need for funds. It mainly talks about a "museum that also houses many rare and thus more expensive ancient artifacts." How do you keep this museum? By buying more rare and expensive artifacts? Yes. For that we need money.
Now, a small group of extremely rich collectors and patrons donate huge funds to the museum only in lieu of the right to decide the type of artifacts to be bought and displayed. - So people donate money but with a condition. What condition - they choose to decide what to buy and what to display. Maybe they don't trust others with their money (though this part is not important).
However, if the decision was left to the curator of the museum, more rare and ancient artefacts would be on display. - Conclusion. It states a hypothetical situation in which if the decision were left to the curators (what decision? To buy the new and decide what to display), more rare and ancient artifacts would be on display. How? We don't know.
Which of the following, if true, would weaken the argument?
A. In the absence of the collectors and patrons’ funds, the museum will have to sell some existing artefacts to acquire newer ones. - if they sell 5 to buy 2, the number is reduced. Weakener.
B. The sales from the museum will only be able to compensate for about half the amount received from the funds given by the patrons. - Say the tickets were $500k, and patrons were $1 million. Total of $1.5 milllion. This option essentially says that tickets will be $1 million ($500k existing from tickets + $500k equivalent (half of $1 Million) of the funds received). So, in total, they'll have $1 million instead of $1.5 million, which is not as bad as just ticket sales, which is $500k. So curators will still have some money (additional $500k) to buy new ones. Strengthener.
C. The people who visit museums do not really have the knowledge to understand the true value of the rare artefacts on display. - out of scope.
D. Collectors of rare artefacts and patrons of the museums rarely extend their support for reasons other than the sole rights to run the museum. - We know this from the passage. Distortion.
E. Curators of the museum sometimes do not have complete knowledge of the artefacts displayed in the museum. - Out of scope as the argument doesn't link their knowledge with the number of items on display. Despite limited knowledge, they can still display.