ritula
A recent survey of all auto accident victims in Dole County found that, of the severely injured drivers and front-seat passengers, 80 percent were not wearing seat belts at the time of their accidents. This indicates that, by wearing seat belts, drivers and front-seat passengers can greatly reduce their risk of being severely injured if they are in an auto accident.
The conclusion above is not properly drawn unless which of the following is true?
(A) Of all the drivers and front-seat passengers in the survey, more than 20 percent were wearing seat belts at the time of their accidents.
(B) Considerably more than 20 percent of drivers and front-seat passengers in Dole County always wear seat belts when traveling by car.
(C) More drivers and front-seat passengers in the survey than rear-seat passengers were very severely injured.
(D) More than half of the drivers and front-seat passengers in the survey were not wearing seat belts at the time of their accidents.
(E) Most of the auto accidents reported to police in Dole County do not involve any serious injury.
A more numeric approach:
The conclusion of the arguement is that
by wearing seat-belts, drivers and front-seat passengers can reduce the risk of being .....
Let's assume that out of all the people surveyed,say x, 100 were severly injured. So the remaining were not severly injured(Mild injury,no injury,etc).Now, out of these 100 people, 80 were not wearing seat belts at the time of accident. Thus, 20 were wearing seat belts and still got serious injuries. Now, to re-inforce/buttress the fact that wearing seat-belt greatly reduces the risk of being
severly injured[and hence the conclusion of the arguement], the author would need support from the group of people who didn't suffer serious injury
because they were wearing seat-belts.
Now, if option A is true, then that means that: # of people wearing seat belts >\(\frac{x}{5}\) --> # of people wearing seat belts > 20[as x>100 is inherently understood]. This directly means that atleast some of the people who are from the
not serious injuries group must have worn seat-belts, thus cementing the conclusion.
Also, as per Option D, we would have the condition : # of people
not wearing seat belts >\(\frac{x}{2}\). Just as above, we have x>100. Thus, # of people
not wearing seat belts >50. However, we anyways know that the # of people
not wearing seat belts is atleast 80. Thus, this option doesn't really add anything conclusive to cement the conclusion.