Explanation

This is a Weaken question with a heavy Causal element, so let's start by examining the argument in the stimulus, finding the conclusion, and then discussing the cause and effect relationship(s) present.

The author begins by introducing what is said to be a common claim: dumping of nuclear waste poses no threat to people living nearby. Typically when a stimulus begins with a belief attributed to some group the author will proceed to argue that that belief is incorrect, and that's exactly what occurs here.

The next sentence begins the author's counterargument, stating that if the claims of safety could be made with certainty then nuclear waste would (or at least could) be dumped in areas of dense population. However, the policy of dumping nuclear waste only in sparsely populated regions indicates that at least some misgivings exist among policy makers about how safe that waste is.

Note the causality here: the author has observed an occurrence--the dumping of nuclear waste only in more sparely populated regions--and concluded its cause, that dumping that waste in densely populated areas would pose a threat to the people living there.

Cause: Nuclear waste is dangerous (i.e. People's safety) / Effect: Dumping nuclear waste away from people

We're asked to weaken this relationship, and as is often the case with Weaken questions and Causality, the most powerful way to do it is to introduce any alternate cause that could also lead to the observed effect. Here the author is arguing for safety as the cause, so if we can show any other reason besides safety for dumping waste in sparsely populated areas we'd seriously undermine that belief.

Answer choice (A): This is about the safety of people in the event of an accident and how evacuations are more likely to fail with large populations, meaning it strengthens the argument! It gives further evidence that safety is in fact the cause, which is what the author has concluded.

Answer choice (B): Again, another strengthening answer supporting the idea that safety concerns are the reason for dumping nuclear waste away from densely populated areas. This is precisely what we DON'T want to show.

Answer choice (C): This is the correct answer choice. Here we're given an alternate cause to safety as the reason for dumping waste in sparsely populated areas: fewer economic and bureaucratic problems. That is, it's not safety that's behind the dumping decisions, it's money and legislative/bureaucratic headaches. This is classic Weaken-Causality at work.

Answer choice (D): This is perhaps less helpful than (A) and (B), but it still provides some support to the author's position. If chemical waste is treated similarly to nuclear waste (dumped away from people), and chemical waste is known to be dangerous, then it stands to reason that safety/danger concerns are driving the dumping decisions involving both. Regardless, this certainly doesn't attack the link between safety concerns and where the waste is dumped, so it doesn't weaken the argument.

Answer choice (E): Once more, we're given information that agrees with the author's view. Here it's suggested that some doubts do exist about the safety of nuclear dumps, and those doubts about safety are why it's sensible to dump the waste where it poses the least threat to the public. So safety is again the reason behind the dumping practice, and the author's argument is ever so slightly helped.

Answer: C