Critical Reasoning involving rates

CAT Exam
Let’s  look at an question and  convince you of the right answer: The faster a car is traveling, the less time the driver has to avoid a potential accident, and if a car does crash, higher speeds increase the risk of a fatality. Between 1995 and 2000, average highway speeds increased significantly in the United States, yet, over that time, there was a drop in the number of car-crash fatalities per highway mile driven by cars. Which of the following, if true about the United States between 1995 and 2000, most helps to explain why the fatality rate decreased in spite of the increase in average highway speeds? (A) The average number of passengers per car on highways increased. (B) There were increases in both the proportion of people who wore seat belts and the proportion of cars that were equipped with airbags as safety devices. (C) The increase in average highway speeds occurred as legal speed limits were raised on one highway after another. (D) The average mileage driven on highways per car increased. Let’s break down the given argument:
  • The faster a car, the higher the risk of fatality.
  • In a span of 5 years, the average highway speed has increased.
  • In the same time, the number of car crash fatalities per highway mile driven by cars has reduced.
This is a paradox question. In last 5 years, the average highway speed has increased. This would have increased the risk of fatality, so we would expect the number of car crash fatalities per highway mile to go up. Instead, it actually goes down. We need to find an answer choice that explains why this happened. (A) The average number of passengers per car on highways increased. If there are more people in each car, the risk of fatality increases, if anything. More people are exposed to the possibility of a crash, and if a vehicle is in fact involved in an accident, more people are at risk. It certainly doesn’t explain why the rate of fatality actually decreases. (B) There were increases in both the proportion of people who wore seat belts and the proportion of cars that were equipped with airbags as safety devices. This option tells us that the safety features in the cars have been enhanced. That certainly explains why the fatality rate has gone down. If the cars are safer now, the risk of fatality would have reduced, hence this option does help us in explaining the paradox. This is the answer, but let’s double-check by looking at the other options too. (C) The increase in average highway speeds occurred as legal speed limits were raised on one highway after another. This option is irrelevant – why the average speed increased is not our concern at all. Our only concern is that average speed has, in fact, increased. This should logically increase the risk of fatality, and hence, our paradox still stands. (D) The average mileage driven on highways per car increased. This is the answer choice that troubles us the most. The rate we are concerned about is number of fatalities/highway mile driven, and this option tells us that mileage driven by cars has increased. Now, let’s consider the parallel with our previous distance-rate-time example: Rate = Distance/Time We know that if I drive for more time, it doesn’t mean that my rate changes. Here, however: Rate = Number of fatalities/highway mile driven In this case, if more highway miles are driven, it doesn’t mean that the rate will change. It actually has no impact on the rate; we would need to know what happened to the number of fatalities to find out what happened to the rate. Hence this option does not explain the paradox. Our answer is, therefore, (B).

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