Police statistics have shown that automobile antitheft devices reduce

We are looking for the answer choice that is the strongest in resolving the paradox.

Let’s first identify what the paradox is. We have two supposedly conflicting pieces of evidence:

1) Police statistics that show that antitheft devices reduce the risk of car theft, and

2) the insurance industry statistics that show that cars equipped with antitheft devices are more likely to be stolen than cars without the antitheft devices.

So the paradox to resolve is: if antitheft devices reduce the risk of car theft, why are cars equipped with antitheft devices statistically more likely to be stolen?

Ok, let’s look at the answer choices:


This one could explain why the police would receive more reports of stolen cars than the auto insurance industry--owners of stolen cars report theft incidents to the police immediately, and some of those incidents might not end up being reported to the insurance companies (for example, if a stolen vehicle is quickly recovered without any damage).

But even if the police do receive more reports of stolen cars, we don’t know whether those stolen cars had antitheft devices. This choice therefore doesn’t give us the statistical information we’d need to resolve the paradox. Let’s get rid of (A).


This choice seems to support the police statistics, but it doesn't explain the insurance industry's statistics suggesting that "cars equipped with antitheft devices are, paradoxically, more likely to be stolen than cars that are not so equipped."

Because (B) only supports one side of the paradox and not both, it doesn't resolve the discrepancy. We can eliminate (B).


In this statement, we are given information about how many times the antitheft devices were activated, regardless of whether the car was stolen. But to resolve the paradox in the passage, we only care about cars that were stolen.

Because (C) doesn't actually give us any information about the number of stolen cars, it does not resolve the paradox. We can eliminate (C).


As we discussed in an earlier post, (D) provides an explanation for both sides of the paradox:

... The insurance companies' claim could be true, because theft-prone cars in risky areas are more likely to be stolen. If these are the cars with anti-theft devices installed, then it explains why they are stolen more frequently than other cars.

At the same time, the police statistics could be true -- installing anti-theft devices could reduce the overall rate of car theft, even if cars with the antitheft devices are stolen more frequently. Note: we do not need to assume that anti-theft devices reduce the risk of car theft, because this information is given to us in the passage. (D) provides additional information that explains how this is possible, given the surprising finding of the study conducted by the insurance industry.

Here is an example to illustrate how (D) resolves the paradox:

Car thefts BEFORE installing antitheft devices:
Less risky location: 100
More risky location: 1000
Total: 1100

Car thefts AFTER installing antitheft devices:
Less risky location (no antitheft devices installed): 100
More risky location (lots of antitheft devices installed): 500
Total: 600

Here, we see that the overall number of car thefts has been reduced by installing antitheft devices. However, we can also see that theft-prone cars with antitheft devices could be more likely to be stolen, because they are located in a risky area.

Let’s keep (D) for now.


If (E) is true, we would expect very little difference between the theft rate of cars WITH antitheft devices and the theft rate of cars WITHOUT antitheft (if anything, the theft rate might be a little bit smaller for cars with antitheft--though the antitheft devices only offer scant protection, they still might offer some protection).

So, at best, (E) might be consistent with the police statistics (if there is, in fact, a slightly lower theft rate for cars with antitheft). But then why do the insurance statistics suggest that cars WITH antitheft are more likely to be stolen than cars WITHOUT antitheft? While (E) may or may not explain the police statistics, it certainly does not explain the insurance statistics or resolve the paradox. We can eliminate (E).

By process of elimination, the answer is (D).

I hope that helps!