There are far fewer kidneys available for transplants than there are

Premises:

1. Last year, only 16,000 kidney transplants took place.
2. This year, nearly 85000 patients are on the list.

Conclusion:
There are far fewer kidneys available than there are patients.

All we know is that there are many patients but last year, very few transplants took place. We are concluding that kidneys available are few and that is the reason that transplants are few (because we know that number of patients is definitely high). What is the assumption? The assumption is that had more kidneys been available, more transplants would have taken place. Note that from the "number of transplants" figure, we are concluding something about "number of kidneys available". What if the number of kidneys available is far more but transplants are fewer because of reasons such as a match doesn't happen, most kidneys available are not suitable for transplant etc. Hence (C) is our assumption.

Option (E) is not correct.
E) The number of available kidneys has not increased since last year.
Even if the number of available kidneys has increased this year, it is still possible that number of kidneys available is far less than the number of patients. We don't know how many kidneys were available last year and how many patients were there last year. We don't know how many kidneys are available this year. The point is that number of available kidneys and number of transplants may not be proportional.