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

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Senior Manager
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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17 Jul 2013, 08:24
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.

Posted from my mobile device
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I am still on all gmat forums. msg me if you want to ask me smth

Last edited by LalaB on 17 Jul 2013, 08:31, edited 1 time in total.
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Posts: 39673
Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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17 Jul 2013, 08:28
LalaB wrote:
I just expressed my thoughts as a user and hope didnt offend anyone.

Posted from my mobile device

Of course not. In contrast I think it's very healthy and useful discussion.
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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, 20:49
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Expert's post
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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 06 Feb 2013 Posts: 59 On a certain road 10 percent of the motorists exceed the pos [#permalink] ### Show Tags 10 Sep 2013, 01:55 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% It is an old OG problem that has not been explained clearly before. Please provide a detailed solution to the problem. On another note, I notice that the overlapping sets are very often tested in this fairly confusing way, where I personally feel I am unable to use the grid advocated by MGMAT or Venn Diagram for that matter. I'm wasting plenty of time on setting it up. Any other methods you guys suggest to solve these? Or should I just "think better":) Since this is the last problem of the set I presume it to be a 700+ level question, but it seems to me that in general GMAT is much harder these days that it was 10 years ago, so I'd guess it is hardly a 650 level today. Share your thoughts. _________________ There are times when I do not mind kudos...I do enjoy giving some for help Manager Joined: 06 Feb 2013 Posts: 59 Re: On a certain road 10 percent of the motorists exceed the pos [#permalink] ### Show Tags 10 Sep 2013, 02:03 I think I got it with the grid... _________________ There are times when I do not mind kudos...I do enjoy giving some for help Math Expert Joined: 02 Sep 2009 Posts: 39673 Re: On a certain road 10 percent of the motorists exceed the pos [#permalink] ### Show Tags 10 Sep 2013, 03:00 obs23 wrote: 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% It is an old OG problem that has not been explained clearly before. Please provide a detailed solution to the problem. On another note, I notice that the overlapping sets are very often tested in this fairly confusing way, where I personally feel I am unable to use the grid advocated by MGMAT or Venn Diagram for that matter. I'm wasting plenty of time on setting it up. Any other methods you guys suggest to solve these? Or should I just "think better":) Since this is the last problem of the set I presume it to be a 700+ level question, but it seems to me that in general GMAT is much harder these days that it was 10 years ago, so I'd guess it is hardly a 650 level today. Share your thoughts. Merging similar topics. Please refer to the different approaches offered on page 1 and ask if anything remain unclear. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 15980 Re: On a certain road 10% of the motorists exceed the posted spe [#permalink] ### Show Tags 23 Sep 2014, 06:38 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Senior Manager Joined: 03 Aug 2011 Posts: 296 Concentration: Strategy, Finance GMAT 1: 640 Q44 V34 GMAT 2: 700 Q42 V44 GMAT 3: 680 Q44 V39 GMAT 4: 740 Q49 V41 GPA: 3.7 WE: Project Management (Energy and Utilities) On a certain road 10% of the motorists exceed the posted spe [#permalink] ### Show Tags 14 Aug 2015, 07:00 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! _________________ Thank you very much for reading this post till the end! Kudos? Last edited by bgpower on 18 Aug 2015, 00:37, edited 1 time in total. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7440 Location: Pune, India Re: On a certain road 10% of the motorists exceed the posted spe [#permalink] ### Show Tags 18 Aug 2015, 00:31 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 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Joined: 17 Jul 2014
Posts: 2524
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20
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GPA: 3.92
WE: General Management (Transportation)
Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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31 Oct 2015, 12:24
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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 spe [#permalink]

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25 Nov 2016, 04:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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25 Nov 2016, 13:44
VeritasPrepKarishma wrote:
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

Hi,
I would agree with bgpower , the language is extremely confusing (at least to me)- the questions asks for "What percent of the motorists on the road exceed the posted speed limit?" In my opinion, the question suggests that it is asking about the percent of motorists, who exceed the speed limit regardless of who was named on the ticket and who wasn't. I mean some people won't pay fine but they did in fact still exceeded the speed limit. How to deal with such confusions? Wouldn't it be better formulated question had it asked about the percentage of motorist who received a ticket.
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Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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25 Nov 2016, 14:17
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.
Answer:
[Reveal] Spoiler:
B

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

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19 Feb 2017, 18:35
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%
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Posts: 4565
Re: On a certain road 10 percent of the motorists exceed the posted speed [#permalink]

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19 Feb 2017, 19:24
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%

Hi,

Although this must have been already discussed, but since you want a way to go about such Qs..

Let the overall 100% be 100...
So 10 exceed limit and get speeding ticket.

Now 20% exceed limit and do not get speeding ticket, MEANS remaining (100-20)% get speeding ticket..

The above info tells us that 80% of total exceeding limit=10..
So TOTAL= $$\frac{10*100}{80}$$= 12.5%

B
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Re: On a certain road 10 percent of the motorists exceed the posted speed [#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.
Answer: B

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Posts: 39673
Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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19 Feb 2017, 22:15
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%

Merging topics. Please search before posting.
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Re: On a certain road 10% of the motorists exceed the posted spe   [#permalink] 19 Feb 2017, 22:15

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

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