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

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New post 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.
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New post 10 Sep 2013, 00:55
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.
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New post 10 Sep 2013, 01:03
I think I got it with the grid...:)
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New post 10 Sep 2013, 02:00
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.
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On a certain road 10% of the motorists exceed the posted spe [#permalink]

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New post 14 Aug 2015, 06:00
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!
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Last edited by bgpower on 17 Aug 2015, 23:37, edited 1 time in total.
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New post 17 Aug 2015, 23:31
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
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Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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New post 31 Oct 2015, 11:24
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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New post 25 Nov 2016, 03:04
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).

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

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New post 25 Nov 2016, 12:44
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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New post 25 Nov 2016, 13:17
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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.
Image

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.
Image

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.
Image

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.
Image

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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New post 19 Feb 2017, 17:35
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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New post 19 Feb 2017, 18:24
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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New post 19 Feb 2017, 20:45
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.
Image

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.
Image

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.
Image

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.
Image

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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New post 19 Feb 2017, 21:15
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: On a certain road 10% of the motorists exceed the posted spe   [#permalink] 19 Feb 2017, 21:15

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