A recent survey of all auto accident victims in Dole County found that

I felt this to be a great question.
But a little time taking.
say 1000 total accidents occured.
100 of them S.Injured .
80 --> X seat belt.
20 ---> Seat belt.
Now,
Option A: for suppose its exactly 20% of people wore seat belt.
20 / 200 = 10% of accidents of seat belt are SI .
80 / 800 = 10 % of accidents of X Seat belt are SI
For suppose, it is less than 20% of people wore seat belt.
% of accidents of seat belt are SI Increases as 200 value increases while 20 remains constant.
Destroying the conclusion .
Hence, Answer should be A. .

Hi,

This is pure Quants problem landed in CR bucket.

The argument wants to show wearing seat belts is safety.

how? by showing -

(no of serious accidents with seat belts / no of accidents with seat belts) < (no of serious accidents with NO seat belts / no of accidents with NO seat belts)

So if above ratio is true, wearing seat belt is safety and people are less prone to serious accidents

Given data: no of serious accidents with seat belts- 20%
no of serious accidents with NO seat belts - 80%

Let no of serious accidents be 10, so
no of serious accidents with seat belts- 2
no of serious accidents with NO seat belts - 8

Let number of total accidents be 100
no of accidents with seat belts = x
no of accidents with NO seat belts = 100 - x

And question is indirectly asking, what is the value of x or rather, what is range of x

now substitute in ratio equation we defined,
(no of serious accidents with seat belts / no of accidents with seat belts) < (no of serious accidents with NO seat belts / no of accidents with NO seat belts)
(2/x) < (8 / (100-x))
rearranging => 200 + 2x < 8x => 20 < x

So x (no of accidents with seat belts) > 20

Wow, this is what answer choice A says !! Bingo !! - safely eliminate other answer choices all we do in quants section - problem solving, once we find the right answer.

To be honest, I didnt get this question correct at first, by after reading all explanations, tried to come up with my own reasoning.

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?

Explanation:
--------------------
(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. ---> We know from the excerpt that
Drivers + Front-Seat Passengers = Severely Injured (20% Wearing Seat-Belts + 80% Not Wearing Seat-Belts) + Not Severely Injured (No Information)

Now, what if more than 80% of the drivers and front-seat passengers who were NOT severely injured were NOT wearing seat-belts? Using this scenario, we can say that wearing seat-belts will NOT reduce the risk of being severely injured. So the conclusion cannot be properly drawn.

Since we have to show that author's conclusion was properly drawn, we have to show that the scenario I cited above was not possible. To make the above scenario impossible, we can say that more than 80% (actually it should be 100% otherwise these people will come under the category of ‘severely injured’ ones) of the drivers and front-seat passengers who were NOT severely injured were wearing seat-belts. Also, excerpt mentions that 20% people from the severely injured category were wearing seat-belts.

So, if we add people (who were wearing seat-belts) from both the categories (severely injured & not severely injured), we'll arrive at the assumption stated in this option.

(B) Considerably more than 20 percent of drivers and front-seat passengers in Dole County always wear seat belts when traveling by car. ---> Mentions about car. Irrelevant.

(C) More drivers and front-seat passengers in the survey than rear-seat passengers were very severely injured. ---> Will not help us in any way to prove that the conclusion was properly drawn.

(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. ---> This cannot be the assumption in order to arrive at the author’s conclusion.

(E) Most of the auto accidents reported to police in Dole County do not involve any serious injury. ---> Irrelevant.

i did not understand why we chose A

Hello Expert

In the stated question, I did arrive at the correct answer (A), through the process of elimination. However, I still cannot understand how this is correct.

Let the total number of accidents surveyed was 100.
100 will be divided in 2 categories: Serious Accidents (SA) and Non-Serious accidents (~SA)
Serious Accidents again in 2 categories: Wearing Seatbelts (SW) (20%) and Not Wearing Seat-belts (~SW) (80%)
Similarly, Non-Serious Accidents again in 2 categories: Wearing Seatbelts (NSW) and Not Wearing Seat-belts (~NSW)

To concretely conclude the conclusion, we should know that ~SW>SW (Requirement 1, given) and NSW>~NSW (Requirement 2).

Option A states that a minimum of 20 people were wearing seat belts. But we do not know how the distribution between SA and ~SA is taking place. Without that information, we can make cases either cases for requirement 2, and hence our conclusion falls apart.

Can you please help clarify this doubt. None of the comments in the thread allows a good explanation. Thanks.

GMATNinja GMATNinjaTwo

This is a bad argument, I thinked. Firstly, my answer was C, but expert told us the correct answer was A. Then I input the argument to CHATGPT, the answer of AI was B, so confused.

since the only thing we know is that 20% of the SEVERELY injured people used seat belt, in order to make the argument work, we need to say that 20% of the total people in car accidents is greater than 20% of SEVERELY injured people wearing seat belts. That would imply that most of the people mildly injured were using seat belt.