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# On a certain road 10% of the motorists exceed the posted speed limit

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

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Updated on: 11 Dec 2018, 03:18
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Difficulty:

65% (hard)

Question Stats:

63% (02:15) correct 37% (02:05) wrong based on 905 sessions

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

Originally posted by chintzzz on 16 Jun 2010, 09:31.
Last edited by Bunuel on 11 Dec 2018, 03:18, edited 2 times in total.
Renamed the topic and edited the question.
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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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16 Jun 2010, 09:57
10
9
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%

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};

$$10+0.2x=x$$ --> $$x=12.5$$.

Hope it's clear.
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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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27 Feb 2011, 20:46
11
5
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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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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28 Feb 2011, 01:55
11
1
Using double matrix.
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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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16 Jul 2013, 05:15
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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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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16 Jul 2013, 06:14
LalaB wrote:
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 speed limit  [#permalink]

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16 Jul 2013, 08:22
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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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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16 Jul 2013, 08:34
1
LalaB wrote:
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 speed limit  [#permalink]

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16 Jul 2013, 08:46
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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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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16 Jul 2013, 08:52
LalaB wrote:
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

have-a-suggestion-post-it-here-76017.html Thanks in advance for any input you provide.
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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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16 Jul 2013, 21:10
4
LalaB wrote:
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 speed limit  [#permalink]

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Updated on: 17 Jul 2013, 08:31
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.

Posted from my mobile device
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Originally posted by LalaB on 17 Jul 2013, 08:24.
Last edited by LalaB on 17 Jul 2013, 08:31, edited 1 time in total.
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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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17 Jul 2013, 20:49
1
LalaB wrote:
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.

Posted from my mobile device

Dear LalaB,

As Bunuel said, the question of offend does not arise. When someone asks me the level of a question, I usually look at the question and judge according to my experience and move on. I do not go into details of why it is an inaccurate exercise. In this case I got into an explanation because you are a seasoned and valued participant of this community - with people like that, your mind instinctively tries to go out of its way to help, discuss and give what you think is the best answer (I might have offended someone else now!) I actually did not go to the question to judge what level it is before putting my response because that was irrelevant to the point I was trying to make.
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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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Updated on: 18 Aug 2015, 00:37
1
Quote:
On a certain road 10 percent of the motorists exceed the posted speed limit and receive speeding tickets, but 20 percent 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%

I don't know whether it's just me, but I find the wording of this question to be horrible. I actually got it right and came to 12,5%. Nevertheless, at least from my understanding the question looks for something completely different, namely - ''What percent of the motorists on the road exceed the posted speed limit?". So the question is rather looking for a comparison between motorists that exceed the limit and such that don't. Here we rather compare those that got tickets to the ones that didn't.

Am I the only one with this doubt or is it a way that exam makers want to confuse you?

Thanks!
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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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18 Aug 2015, 00:31
1
bgpower wrote:
Quote:
On a certain road 10 percent of the motorists exceed the posted speed limit and receive speeding tickets, but 20 percent 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%

I don't know whether it's just me, but I find the wording of this question to be horrible. I actually got it right and came to 12,5%. Nevertheless, at least from my understanding the question looks for something completely different, namely - ''What percent of the motorists on the road exceed the posted speed limit?". So the question is rather looking for a comparison between motorists that exceed the limit and such that don't. Here we rather compare those that got tickets to the ones that didn't.

Am I the only one with this doubt or is it a way that exam makers what to confuse you?

Thanks!

The question is fine.

Some fraction of the motorists exceed the speed limit. Say x%. We need to find x%.

Some of these x% motorists get speeding tickets (say y%) and others do not. Anyone who gets a speeding ticket (belongs to y%) must belong to these x%.

You are given that y% of x% of Total motorists = 10% of Total motorists (people who exceed the limit and get tickets)

Also, 20% of x% do not get tickets. This means 80% of x% do get tickets.

This 80% of x% of Total= 10% of Total (we are already given)

So x% of Total = 12.5% of Total
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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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31 Oct 2015, 12:24
1
let's say we have 100 motorists
10 received tickets for speeding.
we know that 0.2 of the total people who were speeding did not receive tickets.
that means that 10+0.2y = y, where y stands for all people who were speeding.
10 = 0.8y -> rewrite 10*10/8 = 100/8 = 25/2 = 12.5. B.
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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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Updated on: 16 Apr 2018, 12:44
Top Contributor
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%

We can use the Double Matrix Method to solve this question.

This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.

Here, we have a population of motorists, and the two characteristics are:
- speeder (S) or non-speeder (~S)
- get ticket (T) or not get ticket (~T)

Since this question concerns percents (instead of actual values), let's assign a "nice" value to the total number of motorists in this population. Let's say there are 100 motorists.

So, to begin, our matrix looks like this.

10 percent of the motorists exceed the posted speed limit and receive speeding tickets
The top left box is for motorists who speed and receive speeding tickets. So, 10% of the entire population will be in this box.

20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets.
The motorists referred to here are those who go in the top right box. Unfortunately, we don't know the total number of speeders, so we can't find 20% of that value.
So, let's let x = the total number of speeders.

Now we can deal with this: 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets.
In other words, 20% of x will go in the top right box.

At this point, we know that the sum of the top 2 boxes is x.
So, we can write: 10 + 0.2x = x (now solve)
Arrange: 10 = 0.8x
Divide: 10/0.8 = x
12.5 = x

Since x represents the total number of speeders, we know that 12.5 out of 100 motorists speed.
In other words, 12.5% of motorists speed.

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Originally posted by GMATPrepNow on 25 Nov 2016, 14:17.
Last edited by GMATPrepNow on 16 Apr 2018, 12:44, edited 2 times in total.
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Re: On a certain road 10% of the motorists exceed the posted speed limit  [#permalink]

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19 Feb 2017, 21:45
Top Contributor
ammuseeru wrote:
I always get confuse with below question. I am not able to understand wordings of question. I searched question in GMAT club and found earlier posts are inactive. Could you please advise how to approach this question.

On a certain road 10 percent of the motorists exceed the posted speed limit and receive speeding tickets, but 20 percent 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%

We can also use the Double Matrix Method to solve this question.

This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of motorists, and the two characteristics are:
- speeder (S) or non-speeder (~S)
- get ticket (T) or not get ticket (~T)

Aside: To learn more about the Double Matrix Method, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

Since this question concerns percents (instead of actual values), let's assign a "nice" value to the total number of motorists in this population. Let's say there are 100 motorists.

So, to begin, our matrix looks like this.

10 percent of the motorists exceed the posted speed limit and receive speeding tickets
The top left box is for motorists who speed and receive speeding tickets. So, 10% of the entire population will be in this box.

20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets.
The motorists referred to here are those who go in the top right box. Unfortunately, we don't know the total number of speeders, so we can't find 20% of that value.
So, let's let x = the total number of speeders.

Now we can deal with this: 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets.
In other words, 20% of x will go in the top right box.

At this point, we know that the sum of the top 2 boxes is x.
So, we can write: 10 + 0.2x = x (now solve)
Arrange: 10 = 0.8x
Divide: 10/0.8 = x
12.5 = x

Since x represents the total number of speeders, we know that 12.5 out of 100 motorists speed.
In other words, 12.5% of motorists speed.

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

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13 Dec 2017, 16:46
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%

We can let the total number of motorists = m and the number of motorists who exceed the speed limit = n. Thus, we need to determine the value of n/m x 100.

We are given that 10 percent (or 0.1m) of the motorists exceed the posted speed limit and receive speeding tickets.

We are also given that 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets. Since we let n = the number of motorists who exceed the speed limit, 0.2n = the number of motorists who speed who do not receive a speeding ticket.

We can create the following equation:

number of motorists who exceed the limit = number of motorists who speed and get a ticket + number who speed but do not get a ticket

n = 0.1m + 0.2n

0.8n = 0.1m

8n = m

Thus n/m x 100 = n/(8n) x 100 = 1/8 x 100 = 12.5 percent.

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

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29 Mar 2018, 11:53
Hi All,

Brent has shown you a particular way to organize your information, which you might find helpful on these types of questions. Whether you put your information into a table or not, this question is ultimately testing your ability to notice that the given information is (first) about the overall group, then (second) about a sub-group within the overall group.

First piece: 10% of motorists exceed the speed limit and receive tickets.

If we say there are 100 motorists, then we can break them into 3 groups:

Speed and Got Ticket
Speed and Didn't Get a Ticket
Didn't speed

With 100 total motorists, we know that 10 of them exceeded the speed limit and received tickets:

Total: 100
Speed and Got Ticket = 10
Speed and Didn't Get a Ticket = ?
Didn't speed = ?

Second piece: 20% of the motorists WHO EXCEEDED THE SPEED LIMIT did NOT receive tickets.

This is NOT 20% of the 100, it's 20% of those who EXCEEDED THE SPEED LIMIT. Let's call THAT sub-group X:

X = Those who got a ticket + those who didn't

So, X = 10 + .2X

Now, solve for X
.8X = 10
X = 12.5

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Re: On a certain road 10% of the motorists exceed the posted speed limit   [#permalink] 29 Mar 2018, 11:53

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