In most Western countries, parents use medicinal pills to help their

In evaluate argument type of questions, we need to find an answer choice that if answer is YES or NO, either strengthens or weakens conclusion. This method is called Variance test, which we will apply today for the question below.

First, let's breakdown the argument. In Western Europe, parents give their children pills to fight simple illnesses but those pills although fight infection they also prevent immune system from fully developing. Such immune that did not fight simple diseases cannot fight more serious ones, such as Ebola or smallpox. Thus, parents harm children by giving them pills and not letting children's immune develop fully (conclusion).
Now, we need an answer choice that if provided opposite answers (YES/NO) will either say that parents indeed harm their children by giving the pills OR that parents do NOT harm children. The process will be clear once we move on to answer choices and apply Variance Test.

A. What the most common pills against viral illnesses such as the flu are. - (Perhaps, this choice is one of those few ones where we cannot use Variance Test but we still can perform analysis). We do not care for names of pills that are helpful in fighting flu. This piece of information does nothing to identify if author's conclusion is true or not. Eliminate

B. Whether the infant mortality rates for children in the West are higher now relative to what they were in the past. -
YES: Infant mortality rates for children in the West are higher now relative to what they were in the past. Can we deduce from this piece of information if pills somehow hurt OR do not hurt children's immune system? I do not think so. Let's try another option
NO: Infant mortality rates for children in the West are not higher now relative to what they were in the past. Again, can we find any helpful information to evaluate author's conclusion? Does not seem so. Eliminate B

C. Whether the lethal viral diseases mentioned are found in Western countries. -
YES: the lethal viral diseases mentioned are found in Western countries. If death occur from these viral diseases such as Ebola and others mentioned in the argument, then, indeed, parents hurt their children by giving them pills because they weaken immune system of children and consequently such immune systems are unable to fight off Ebola and other illnesses.
NO: the lethal viral diseases mentioned are NOT found in Western countries. Even if parents give their children pills that allows no proper development of immune to fight off Ebola and others, and no cases of death occurred from those viral diseases, then we cannot say that parents hurt their children by giving pills because we have no cases of death to prove.
We have two opposite cases here, thus we will hold to C

D. What percentage of parents in Western countries actually give their children pills -
High: If high percentage of parents give their children pills, can we find information if those children fight Ebola successfully or not? No, we cannot find such information. This option is useless.
Low: If not too many parents give their children pills to fight simple diseases, we still do not have any information on how those children deal with Ebola and other illnesses. Do they contract them or nor? Do they successfully fight them or not? Many questions still remain. Thus, this option is useless too. Eliminate D

E. Whether new pills will be developed that will both defeat simple illnesses and aid the development of the immune system. - a very tempting answer, but hold on. They key word here is "will". This option talks about future, and we care for present. Thus, in present this answer does not help us evaluate the author's conclusion. Eliminate

Winner is C