This is a strengthen with a necessary premise question. We're looking for the answer choice that's required for the argument. We can use the negation test, as the negation of the correct answer choice will make the argument fall apart.
(A) says, "older workers have acquired skills that are extremely valuable and that their younger colleagues lack"
(A)'s negation is, "Older workers have not acquired any skills that are extremely valuable and that their younger colleagues lack."
The problem with (A) is that older workers don't need to do anything that their younger colleagues don't do. They simply need to be extra bodies; they don't have to be anything unique or special, so we can get rid of (A), as its negation doesn't wreck the argument.
(C) says, "a large number of workers in some industrialized countries would continue working beyond the age of sixty-five if workers in those countries were allowed to do so"
(C)'s negation is, "something less than a large number of workers would continue working beyond the age of sixty-five even if they were allowed to do so"
(C) is great. We must assume that if older workers were not forced to retire, they'd continue working beyond the age of 65. Otherwise, they would not help to solve the labor shortage if they simply decided to retire at 65. Thus, (C)'s negation wrecks the argument, showing that (C) in its original form is required for the argument.
Does this make sense? Let us know if you have any other questions!
