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On a certain road 10% of the motorists exceed the posted spe [#permalink]

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16 Jun 2010, 08:31

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On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?

On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?

A. 10.5% B. 12.5% C. 15% D. 22% E. 30%

Say there are 100 motorists.

{# of motorists who exceed speed & receive tickets} + {# of motorists who exceed speed & don't receive tickets} = {Total # of motorist who exceed speed};

Given: {# of motorists who exceed speed & receive tickets}=10;

Also, if {Total # of motorist who exceed speed}=x, then 0.2x={# of motorists who exceed speed & don't receive tickets};

On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit? a)10 1/2% b)12 1/2% c)15% d)22% e)30%

z= total motorists y=motorists who speed and dont get ticket = y motorists who speed = x =.1z+y We are told that .2x=y

On a certain road, 10 percent of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit?

A/ 10 1/2% B/ 12 1/2% C/ 15% D/ 22% E/ 30%

Read one line at a time and analyze it.

On a certain road, 10 percent of the motorists exceed the posted speed limit and receive speeding tickets,

>>>>10% of total motorists exceed speed limit and get tickets

but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets.

>>>>>>20% who exceed the speed limit do not get tickets. Then 80% who exceed the speed limit must be getting tickets.

What percent of the motorists on that road exceed the posted speed limit?

>>>>> So 10% of total motorists = 80% of those who exceed speed limit So those who exceed speed limits are 1/8 = 12.5% of the motorists
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On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit? a)10 1/2% b)12 1/2% c)15% d)22% e)30%

Let's assume total # of motorists to be 100.

{# of motorists who exceed speed & receive tickets} + {# of motorists who exceed speed & don't receive tickets} = {Total # of motorist who exceed speed};

Given: {# of motorists who exceed speed & receive tickets}=10;

Also, if {Total # of motorist who exceed speed}=x, then 0.2x={# of motorists who exceed speed & don't receive tickets};

\(10+0.2x=x\) --> \(x=12.5\).

Answer: B.

Hope it's clear.

i dont understand why cant it be 20 + 0.1 x = x??

as in how do we know we pick 10 for 10% of people who exceeded speed and received tickets and not equate it to 0.1 x = # of people who received tickets ???

we have taken 0.2 x as no. of people who speeded but dd not receive tickets ... so we should have similarly done for 10% of people who exceeded speed and received tickets which is 0.1 x but bunnels explanation just picks a number 10 so i am confused

Kostyan5 can you please explain in detail how did you get to your answer?

If 20% of the motorist who exceeded the speed limit did not get a ticket, then 80% of the motorist who exceeded the speed limit got a ticket. We are also told that 10% of all motorist exceed the limit and get tickets. So 10% of all motorists and 80% of motorist who exceeded the limit refer to the same group of people (exceeded and were ticketed).

\(10% = 80% * motorist who exceeded\) \(motorists who exceeded = \frac{10}{80} =.125 or 12.5%\)

Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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16 Jul 2013, 01:11

chintzzz wrote:

On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?

A. 10.5% B. 12.5% C. 15% D. 22% E. 30%

This is an overlapping set question

Given 10 percent of motorists exceed speed limit and receive tickets

Receive Tickets don't receive tickets

Exceed 10 20/100X X

Don't Exceed

Let the total number for those who exceed be X then 20 percent of those received no tickets

When we solve we get 10 + \(\frac{20}{100 X}\) = X

When we solve we get Answer B
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Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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16 Jul 2013, 04:15

Sorry for offtop- Can you please tell me whether you also edit the level of questions? I mean this question is marked as 700level, but I have some doubts about that. could you please also give me a link to Suggestions topic? I have some ideas.
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Sorry for offtop- Can you please tell me whether you also edit the level of questions? I mean this question is marked as 700level, but I have some doubts about that. could you please also give me a link to Suggestions topic? I have some ideas.

Difficulty level is somewhat subjective, notice though that 45% of the users answered the question incorrectly. What would you say the difficulty level of this question should be?
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Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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16 Jul 2013, 07:22

Imho it is 600 level I have read once that 700level question is the one that needs at least 2 steps to be solved or the one that covers hard topics like combinatorics etc

Actually i didnt mean anything bad. I am not a math guru at all (unfortunately hehe) and have no right to judge a question. All i want to know is that whether you Bunuel edit that "level" tag. I rely on ur experience. But sometimes i get confused by these tags and just wonder what you think and whether u pay attention to the tags Ok, now i know that u edit these tags too. Thnx for the information
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Imho it is 600 level I have read once that 700level question is the one that needs at least 2 steps to be solved or the one that covers hard topics like combinatorics etc

Actually i didnt mean anything bad. I am not a math guru at all (unfortunately hehe) and have no right to judge a question. All i want to know is that whether you Bunuel edit that "level" tag. I rely on ur experience. But sometimes i get confused by these tags and just wonder what you think and whether u pay attention to the tags Ok, now i know that u edit these tags too. Thnx for the information

Actually you have the same right to judge as anyone else. In fact you can change the difficulty tag (or any other tag for that matter) if you strongly feel that it's not correct. As for this question, I concur, it's not 700 level, though let's wait some time and see how the stats change.

P.S. Yes, I do pay attention to the tags and permanently review them.
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Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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16 Jul 2013, 07:46

Bunuel, thanks for ur kind reply. Could u plz send me a link to the suggestion topic? As a user I have some minor suggestions.i tried to find that topic
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Bunuel, thanks for ur kind reply. Could u plz send me a link to the suggestion topic? As a user I have some minor suggestions.i tried to find that topic

I have read once that 700level question is the one that needs at least 2 steps to be solved or the one that covers hard topics like combinatorics etc

I would like to give my opinion on this statement:

Let's think about how the GMAT software decides the level of a question (simplifying the process by saying that it allots a level number to each question instead of a difficulty graph). The difficulty level is assigned by the people who take the test and not by the question setters.

You have experimental questions, right? They are there to estimate the difficulty level (among other things) of the new question. Say, most test takers spend 3-4 mins on a particular question and still get it wrong. The software is likely to assign it a high difficulty level. It doesn't matter how many steps it needed or the topic it tested. Some of the most tricky questions are from number properties which I think is extremely simple theoretically.

So what defines the difficulty level? The perception of the people. Why are combinatorics questions usually considered hard? Because people assume they are hard - they could be extremely straight forward but the moment people see 'how many ways' or 'what is the probability', they tend to take a step back. Similarly, function questions are usually considered difficult because of the notation but if you get over that notation you will see that those questions are usually very simple with a step wise process. Also, the answer to a question may be apparent to you with no steps needed if you understand the basics very well. To many others, it might seem very tricky and they might work on it for 5 mins before arriving at the solution. Therefore, when you think about the level of a question, think of how people will perceive it (hard to do without any data and/or experience in this field) rather than what you feel about the question. You may be very good at a topic and hence may feel that a certain question is simple but many others may not share your opinion. At the end of the day, opinion of the masses is what decides the question level (which implies a huge opportunity to do well by being comfortable in questions people consider hard).
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Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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17 Jul 2013, 07:24

I agree that the level of a question depends on real gmat test takers' results. But imho this tag on a forum shouldnt be assessed by the level of only current gmatclub users, since perhaps current guys can be math genious or vise versa dummies like me:)

So , i wanted Bunuel to assess the level of a question, using his experience. He solved lots of gmat questions and knows well all ins&outs of this test. I feel better when i see his assessment rather than the one generated by some unknown to me users.

Anyways, i dont insist on anything. It is ur forum and ur rules. I just expressed my thoughts as a user and hope didnt offend anyone.

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Last edited by LalaB on 17 Jul 2013, 07:31, edited 1 time in total.