Motorcycle-safety courses, offered by a number of organizations, teach

Hello,

Look at the following situation:
Say 100 people are involved in serious motorcycle accident:

According to the stimulus we know that 92 people did not take the course and 8 people took the course.
Now assume that the overall number of motorcyclists is 1000:
And out of these 920 did not attend the course and 80 attended the course.
So this means that out of 920 people who did not attend the course 92 got involved in accident – 10%

Also 8 people out of 80 who did attend the course got into accident – again 10%

Therefore to confirm that taking the course prevents accidents we need to know whether more than 8% of people take the course.

VeritasKarishma Can you please explain this question ?

92% of the motorcyclists who are involved in a serious motorcycle accident have never taken a motorcycle-safety course.
These courses teach important safety techniques.

Conclusion: If more motorcyclists took these courses, there would be fewer serious motorcycle accidents.

This is a useful to evaluate question - what would help us figure out whether the data cited supports our conclusion.
The data cited just tells us that 92% of motorcyclists who were in serious accidents had not taken the course. Using this, it is urging us that all motorcyclists should take the course. What we need to know is how many of those who are not in an accident took the course.

Say 1000 people ride motorcycles.
Say there were 100 serious accidents in the year. We know that of these 100, 92 have not taken the course and 8 have.
So 900 people did not have any serious accident.

Now what if we find out that out of the remaining 900 people, none had taken the course? It seems that the course teaches something that is causing accidents!! Does it support our conclusion of taking the course - NO

What if we were to find out that of the remaining 900 people, 400 had taken the course? Now it seems that the course did make people follow safety rules. Among non-accident people, a large number had taken the course while among the accident-people, very few had taken the course.

This is what option (A) says.

(A) Whether significantly more than eight percent of motorcyclists have taken a motorcycle-safety course
If overall, much higher percentage of the people take the course then it makes sense that the course helps. If overall only 8% people (or even lower) take the course, the number of 92 is what we would expect anyway so taking the course would not have helped.

All other options are irrelevant.

Answer (A)

Can someone help me explain why A is correct, I have seen expert's replies but I am having a hard time to correlate the two proportion: 1) Proportion of total motocyclists who have taken motocycle-safety-course and 2) Proportion of people involved in Accident who have taken motorcycle-safety-course.

As per my understanding even if 8% of people involved in accident have taken safety course and 4% of the total population have taken a safety course there is a good chance that 8% is only 0.2% of the total population we don't know what proportion of total population of motorcyclists was involved in accident and which will mean we can still prove that motorcyclist lessons were effective even if the proportion is below 8% of the total population. According to me the argument will be strengthened if choice A mentioned that 8% of people involved in accident who took safety course is actually what proportion of the total motocyclists who took motorcycle-safety-course.

The logic of this argument does not depend on knowing the absolute figure or the exact proportion of people who have taken a motorcycle safety course.

The logic of this argument DOES depend on an assumption that the population of motorcyclists who are involved in a serious accident is representative of the entire population of motorcyclists.

While it would certainly be nice to know the exact proportions here, none of the answer choices offer that information. So we're left to pick the choice that most helps us evaluate the logic of the argument. (A) gives us enough information to know whether the population of motorcyclists in a serious accident actually is representative of the greater population of motorcyclists (or not).

That's why (A) is worth keeping. Plus, ultimately no other answer choice does a better job at helping us evaluate the argument.

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If that doesn't resolve your doubt, let's revisit the more thorough explanation I attempted to convey in my earlier post):

First imagine that 92% of motorcyclists have never taken a motorcycle-safety course.

• If we pick a motorcyclist at random, there's a 92% chance that he/she has never taken a motorcycle-safety course.
• So if we pick a group of motorcyclists at random, we would expect that about 92% of the group have never taken a motorcycle-safety course.

Then, imagine that the course is absolutely useless. In other words, it has no impact on your odds of getting into a serious motorcycle accident.

• Now, if we randomly pick a motorcyclist who has been in a serious accident, there's still a 92% chance that he/she has never taken a safety course. These odds haven't changed from our first scenario, because the course has no impact on your odds of being involved in a serious accident).
• So if we randomly pick a group of motorcyclists who have been in serious accidents (and if the course is useless) then we would expect that about 92% of the group have never taken a safety course.

Now, take another look at the passage:

"Data show that 92% of the motorcyclists who are involved in a serious motorcycle accident have never taken a motorcycle-safety course."

• Well, IF 92% of motorcyclists have never taken a safety course and IF the course is useless, then that is exactly the data that we should expect!
• In other words, if (i) 92% of motorcyclists have never taken a safety course and if (ii) 92% of motorcyclists who are involved in a serious motorcycle accident have never taken a safety course, then we have evidence that the safety course has no impact on the odds of being involved in a serious accident.

However, if only a small portion of all motorcyclists (for instance, 10%) have never taken a safety course, while 92% of motorcyclists who are involved in a serious motorcycle accident have never taken a safety course, then we have evidence that the safety course is actually quite useful. In this case:

• MOST motorcyclists have taken the course.
• Yet, most of the motorcyclists involved in serious accidents have NOT taken the course.
• This suggests that your odds of getting into a serious accident are much higher if you have NOT taken the safety course.

That's why we'd want to know whether significantly less than 92% of motorcyclists have NEVER taken a safety course. If so, then we have evidence that the safety course is effective. If not, we have evidence that the safety course is not effective. This is the same as choice (A), just written a different way.

VeritasKarishma gives a more numerical explanation here.

I hope that makes it more clear! If not, please try to let us know what part of the explanation doesn't make sense to you, and we'll do our best to help!
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If Option A confuses you, elimination of B - D is extremely effective in this case.

(B) I think we can agree passengers are irrelevant here.
(C) The problem discusses a binary situation: either motorcyclists have or have not taken a course. The quality of the course is not relevant.
(D) A motorcycle accident could be serious even if it did not involve another vehicle. Further, the safety courses effectively covered both scenarios: "important techniques for handling and for safely sharing the road with other road users"
(E) This question relates only to preventing specific outcomes. Causes are irrelevant.

Premise:- If 100 motorcyclists have met with accidents, then around 90 haven't taken the safety course.
Conclusion:- Therefore, safety courses would have avoided these accidents.

Let's use the Yes-No test for the tricky Option A. :
i.e. acceptance and denial of the option statement either strengthen or weaken the conclusion.

Option A:- Whether significantly more than eight percent of motorcyclists (say 50% = 50) have taken a motorcycle-safety course

Yes --> 50 motorcyclists in concern have taken the safety course. --> This Weakens the conclusion as it implies that even the motorcyclists trained with safety course have met with accidents. Thus safety training wouldn't have helped much.

No --> Only 10 motorcyclists have taken the safety course. --> This Strengthens the conclusion, indicating that since majority have not taken the safety course they couldn't avoid accidents.


Other options are quite irrelevant, and pretty to easy to spot that they don't work per Yes-No test. Thus Option A is the right answer.

The person has pointed out the exact discrepancy that is evident in the question. It is also exactly what you have mentioned in Point#2 --- 2) Changing the base of the %tages

Data show that 92% of the motorcyclists who are involved in a serious motorcycle accident have never taken a motorcycle-safety course. mentions motorcyclists who are involved in a serious motorcycle accident only.

(A) Whether significantly more than eight percent of motorcyclists have taken a motorcycle-safety course talks about eight percent of motorcyclists have taken a motorcycle-safety course , not motorcyclists who are involved in a serious motorcycle accident.

Why would one consider the 8% in Option A to be part of the 100% to which the previously mentioned 92% belongs?

Can anyone please help in specifying what I missed out?
GMAT does not interchange key words of sets and subsets, which is evidently done here.

I have read all the explanations below but I am still not able to wrap my head around the fact that A is the right answer instead of D. Following is how I approached this question-:

A. How does that matter if more than 8% of motorcyclists have taken the course? We need to concentrate on the motorcyclists with accidents and if 92% of those haven't taken the course, we already ready know that 8%of the motorcyclists have taken the course. So I don't see how A will contribute to us reaching a correct solution. I mean A would have been OK if it would have talked about all motorcyclists and not just 8% of it since (as in what proportion of motorcyclists who take the course and end up in accident). Because no matter what proportion we find out from asking A, until and unless we know about the relation of that proportion to accidents, how does that answer to A matters?

D. Clearly, brings another view int the picture? What proportion of accidents had another moving vehicle in the picture? which means it could be that it is another vehicle's fault and not the motorcyclists' bad handling. which could in turn tell us that motorcyclists' training doesn't matter really?

I understand in the second case as well, we have to make some assumption. But to be honest, in case of A as well that seems to be the case (at least to me)

Did I babble too much? But still thank you for having the patience of reading this whoever did and I really hope someone could clear up this for me in a simple language.

we have only 2 minutes for each cr question. make the reasoning simple.
choice A is the only choice which is relevant to the statistics in the argument. other choices are not relevant. we give choice A a deep analysis.

evaluate question is potential weakening question

if substantially more than 8 percent , say , 15 percent of general drivers take the course and 8 percent=100-92 percent of the persons who involve in accidents take the course, this mean among person who involve in accident, only 8 percent take the course while for all persons, 15 percent take the course- this mean among persons who involve accident , the portion who take the course is lower than the portion of the total population who take the course-this mean if you take the course, you are at risk of 8 percent to be in accident and if you dont take the course, you are at risk of 15 percent to be in accident.

taking course is safer.
this kind of statistic problem is more easy if you know this kind before you are in test room

This is a SAMPLING argument.
Of cyclists involved in accidents, 92% did not take a safety course, implying that 8% DID take a safety course.
The passage offers statistics about SOME cyclists -- those involved in accidents -- and draws a conclusion about ALL cyclists.
Look for an answer choice that could make or break the link between SOME cyclists and ALL cyclists.

A: Whether significantly more than eight percent of [ALL] motorcyclists have taken a motorcycle-safety course
Test what happens if exactly 8% of all cyclists took a safety course.
To organize the data, we can use a double-matrix:

.............................Course..........No course............Total

Accident....................8.....................92..................100

No accident

Total.........................80...................920................1000

In the matrix above:
Of 1000 cyclists, exactly 8% took the course.
Of 100 accident victims, exactly 8% took the course.
Accident rate for course-takers = 8/80 = 10%.
Accident rate for non-course-takers = 92/920 = 10%.
The rate is the SAME in each case, weakening the conclusion that the course prevents accidents.
Thus, to conclude that the course prevents accidents, we need to know whether significantly more than eight percent of motorcyclists have taken a motorcycle-safety course.

.
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Thank you

Hi Suryanshi

You are spot on about option (D) in stating that it requires a leap of faith to assuming that it could be other vehicle's fault and not bad handling by the motor cyclists in question.

Let us come back to answer option (A). We know that 8% of riders in accidents have taken the course and 92% such riders have not. This is used to draw the conclusion that the course helps in rider safety.

However, what if, of all motorcyclists, a proportion much greater than 8% (say, 25%) has taken the course. Now we have a situation where 25% of all motorcyclists have taken the course but only 8% of motorcyclists in accidents have attended the course. If the course has no impact on subsequent rider safety, then we would not expect much difference in the proportion of riders who have taken the course and the proportion of riders in accidents who have taken the course - both should be similar proportions.

Thus, answering option (A) helps to determine if the course has a material impact on rider safety.

Hope this helps.
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Hi

Now say number of motorcyclist who met serious accident are 100 out of which 92 never took course, while 8 took course
Let assume that total number of motorcyclist is 1000 out of which 920 never took course and 80 took course
A: >80 took Course, say 600 out of which only 8 met accident so course does reduces accidents
<80 took course; say 8 took course and 8 met accident then course has no effect.

GMATNinja

"Similarly, if only 8% of motorcyclists have taken a safety course, then this would suggest that the safety courses did NOT have a significant effect on safety, hurting the argument. However, if significantly more than eight percent of motorcyclists have taken a motorcycle-safety course, then the data would suggest that the safety courses were effective."

To evaluate the benefits of taking course, we require ratio Total of motorcyclists who have taken the course and involved in serious accident to Total of motorcyclists who have taken the course, right? Then, The lesser the ratio, the more effective the safety courses.

I have taken tons of time to find a reason why it has to be 8% (finally I did it!!) and the logic that you said "Now, what if only 8% of all motorcyclists have taken a safety course? Well, if the course was useless, then we would expect that 8% of those involved in serious accidents have taken the course. It would be like if we painted blue nail polish on 8% of all motorcyclists. If the nail polish has no effect on safety, then we would expect 8% of those involved in serious accidents to have blue nail polish. In other words, those with blue nail polish are just as likely to be involved in a serious accident as those without blue nail polish."


In CR, do I have to understand the reason of why it has to be "NUMBER" ?
Could you provide good practice to handle this problem?

There's no need to approach a "numbers" question any differently than you would approach a different type of CR question. Here, we have to find the answer choice that would help us to evaluate the argument. As you go through the answer choices, you just want to think about which one would help you assess how valid the author's reasoning is.

(A) features a question about the percentage of motorcycle riders who have taken the safety course. Answering this question would fill in a massive gap in the argument: how effective is the safety course, really? So, (A) would be super helpful in evaluating the argument.

In short, just do the same thing on a "numbers" question as you would in any other CR question. You can find out more about that flexible approach here.

I hope that helps a bit!
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in option A] am actually not clear with the fact that in qsn stem we are saying 92% of the people involved in accident and option A] says 8% of general population

How do I relate the two facts when the basis are not very same?

Among motorcyclists who have had accidents, 8% have taken the course (100% – 92%, from the original information).
Among motorcyclists who have NOT had accidents, let's say X% have taken the course.

Those two pools of motorcyclists combined contain ALL motorcyclists.
Therefore, the percentage of ALL motorcyclists who have taken the course is a weighted average of 8% and X%.

If that weighted average is significantly greater than 8%, then
8% < weighted average < X%
and therefore people who HAVE taken the course are over-represented among all motorcyclists who have NOT had accidents, relative to the overall average. That's evidence that the course is effective in reducing accidents.