Hi,

To find out the assumption, we first need to find out the premises and the conclusion to locate the gaps.

Premise: In the next four years, the number of doctors, nurses, and other health care workers will increase significantly worldwide.
Premise: median age of the world’s population will increase steadily in this same period of time
Conclusion/Prediction: the average compensation received by such professional will not decline but rather is likely to increase

I think some of the confusion could have been in identifying the conclusion. It's not stated directly using keywords like therefore, as a result etc.

Rather, it's written in a counter observation style "Even so,...". This makes it quite tricky to identify it as the conclusion. However, reading the third statement gives us a clue that the second statement is indeed a conclusion. This is because the third statement tries to explain the second one, while the first statement is treated more or less a factual or certain statement.

Now, after the conclusion has been identified, we can either move directly to the options or pre-think what could be an assumption. The strategy advised by e-GMAT is pre-thinking.

So, let's try to pre-think an assumption:

It says that number of workers will increase and the conclusion is that their average compensation will also increase. We know that increase in compensation could either be the result of increased number of work hours or increased payment per hour. So, older people should either provide more work to these workers or provide more payment for the same amount of time. The first part i.e. more work, is what is given in option C. Therefore, this is the correct choice.

For completion, let's look at other choices too:

(A) The increase in the number of health care workers will be responsible for the increase in the average life span - Incorrect. No confusions.
(B) The compensation of doctors and physical therapists who treat the elderly will increase more than that of other health care workers - We are talking about doctors, nurses and other healthcare workers as a group in the passage while this statement treats them differently. This statement will not even fit in the argument. Incorrect.
(D) Geriatrics, a branch of medicine focusing on the health problems of older people, is the most expensive element of American health care. - We are not talking about America specifically. Incorrect.
(E) Increase in the median age of the population will occur in all regions of the world. - What if this doesn't occur and only Japanese age? Can't workers salaries increase in that case? If salaries in rest of the world remain constant while salaries in Japan rise, average salary will increase. Since negation of this statement doesn't invalidate the conclusion, this is not an assumption.

Hope this helps

Let me know if further clarity is required.

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Thanks,
Chiranjeev