To WEAKEN an argument, we must first find the logical flaws / unstated assumptions in the argument.

Premises:
- On average, the emergency treatment for an elderly person for injuries resulting from a fall costs $11,000.
- A new therapeutic program can significantly reduce an elderly person's chances of falling.
- this treatment program will cost $12,500

Conclusion:
This treatment program cannot be justified.

Logical Flaws:
We're given that emergency treatment is $11,000. But are there other costs? Follow-up treatments, long-term hospital stay, physical therapy? And are there other factors that would justify an additional $1,500 price tag? E.g. emotional well-being, long-term future health benefits, etc?

We're looking for a new piece of information that would suggest that the $1,500 difference is not the only factor worth considering.

(A) Among elderly people who had followed the program for only a few months, the number of serious falls reported was higher than it was for people who had followed the program for its recommended minimum length of one year.
We don't want to make distinctions within the group of those who do the treatment program. This just further justifies that the treatment prevents falls. It doesn't discrepancy between $12,500 for the program and $11,000 for falls.

(B) Falls resulting in serious injuries are less common among elderly people living in nursing homes than they are among elderly people who live alone at home.
We're not talking about the benefits of nursing homes. We want to know about the treatment program. Irrelevant.

(C) A frequent result of injuries sustained in falls is long-term pain, medication for which is not counted among the average per-person costs of emergency treatment for elderly people's injuries from such falls.
This tells us about an another cost of falls in addition to the $11,000 emergency room bill. This now casts doubt on our conclusion - it's possible that the total costs of a fall might be over $12,500 per person.

(D) The new therapeutic program focuses on therapies other than medication, since overmedication can cause disorientation and hence increase the likelihood that an elderly person will have a serious fall.
This just explains how the therapeutic program works. It doesn't help to weaken the idea that the $12,500 price tag is too high to be justifiable.

(E) A significant portion of the cost of the new therapeutic program is represented by regular visits by health care professionals, the costs of which tend to increase more rapidly than do those of other elements of the program.
Again, this just gives more detail about the program itself. It doesn't help to weaken the idea that the $12,500 price tag is too high to be justifiable.

The answer is C.

This argument style is very common on the GMAT: it compares 2 things (cost of emergency care v. cost of therapeutic program) but fails to take into account any other factors. Here are some other CR questions with similar logical flaws:
https://www.beatthegmat.com/ledland-une ... tml#716308
https://www.beatthegmat.com/princeton-r ... tml#717367
https://www.beatthegmat.com/firms-adopt ... tml#769255
https://www.beatthegmat.com/gmatprep-un ... tml#800378
https://www.beatthegmat.com/weaken-olex ... tml#564585