Critical Reasoning

jainrahul1985 wrote: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.

I know this question has been discussed many times but I am still not sure why A is correct and [spoiler]B/D[/spoiler] wrong . Can some expert please explain using numbers .

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?

GMATGuruNY wrote:

Conclusion: Seat belts reduce risk of serious injury if a driver or passenger in the front seat is in an accident.

Premise: 80% of those who were seriously injured did not wear seat belts.

Assumption: The argument connects those who were seriously injured with all accident victims who were in the front seat. The assumption is that a sampling (those who were seriously injured) = the whole group (all front-seat drivers and passengers who were in accidents.). The correct answer choice will show that the given sampling is representative of the whole group.

(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. Correct. This answer choice connects the sampling in the survey (those in serious accidents) to all front-seat drivers and passengers. This answer choice passes the negation test. Negated, answer choice A would say:

Of all the drivers in the survey, fewer than 20% were wearing seat belts.

If this information is true, then more than 80% of the drivers and passengers in the front seat did not wear seat belts and avoided serious injury, invalidating the conclusion that seat belts prevent serious injury. Since the argument falls apart when answer choice A is negated, answer choice A is the assumption: what must be true for the conclusion to be valid.

The correct answer is A.

A is still not clear to me.
If we negate A, it is,
of ALL the drivers, fewer than 20% were wearing sear belts.
So, more than 80% were NOT wearing seat belts.
Among them, we can have people with serious injury and non-serious injury. Did not get how they are avoiding serious injury.

tetura84 wrote:

GMATGuruNY wrote:

Conclusion: Seat belts reduce risk of serious injury if a driver or passenger in the front seat is in an accident.

Premise: 80% of those who were seriously injured did not wear seat belts.

Assumption: The argument connects those who were seriously injured with all accident victims who were in the front seat. The assumption is that a sampling (those who were seriously injured) = the whole group (all front-seat drivers and passengers who were in accidents.). The correct answer choice will show that the given sampling is representative of the whole group.

(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. Correct. This answer choice connects the sampling in the survey (those in serious accidents) to all front-seat drivers and passengers. This answer choice passes the negation test. Negated, answer choice A would say:

Of all the drivers in the survey, fewer than 20% were wearing seat belts.

If this information is true, then more than 80% of the drivers and passengers in the front seat did not wear seat belts and avoided serious injury, invalidating the conclusion that seat belts prevent serious injury. Since the argument falls apart when answer choice A is negated, answer choice A is the assumption: what must be true for the conclusion to be valid.

The correct answer is A.

A is still not clear to me.
If we negate A, it is,
of ALL the drivers, fewer than 20% were wearing sear belts.
So, more than 80% were NOT wearing seat belts.
Among them, we can have people with serious injury and non-serious injury. Did not get how they are avoiding serious injury.

Plug in that 100 in the survey were seriously injured.
According to the argument, 20 wore seat belts, 80 did not.
Negated, answer choice A would say that perhaps only 10% of all the drivers/passengers wore seat belts.
Since 20 = 10% of 200, we could have 200 total in the survey, 20 who wore seat belts, 200-20=180 who did not.
Since 80 did not wear seat belts and were seriously injured, and 180 in total did not wear seat belts, 180-80 = 100 did not wear seat belts and avoided serious injury.
Thus, a majority of those who did not wear seat belts would have avoided serious injury, invalidating the conclusion that seat beats prevent serious injury.
Since the scenario above invalidates the conclusion and is possible when answer choice A is negated, the argument is assuming that answer choice A is true: that more than 20% of the people in the survey wore seat belts.

amaelle wrote:@GmatGuruNy

Thanks a lot for your explanation, but i need to discuss this further under a numerical example as i'm not really convinced by answer A.

if we consider a sample of 100 accidents 20 are grave and 80 are non grave.( as no indication can prohibit to make such a hypothesis)

*16 drivers and front seat passengers gravely injured are thus without belt (80% out of 20)
*4 are those gravely injured and wore belt during the accident. (20% out of 20)

on the other hand i supposed that 90% of those that weren't seriousely injured didn't wear a belt during the accident while 10% wore it.
this give me

*72 not seriousely injured without belt
*8 not seriousely injured with belt

at the end we have
16+72=88 without belt
4+8=12 with belt

12/100= 12%

i think that having such figures do not undermine the conclusion but make from answer A an unnecessary assumption.

Please correct me if i'm wrong.

Many thanks in advance

Ama