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

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CEdward
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Re: On a certain road 10% of the motorists exceed the posted speed limit [#permalink] On a certain road 10% of the motorists exceed the posted speed limit   25 Jan 2021, 18:51
Let the total number of people be 100.
Let y be the total number of speeders <--- This is the count we want.

10% of 100 = 10 <--- Speeders who got a ticket.
20% x y = y/5 <---- Speeders who did not get a ticket.
80% x y = 4y/5 <----- Speeders who did get a ticket

4y/5 = 10
y = 12.5

Answer is B.
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Re: On a certain road 10% of the motorists exceed the posted speed limit [#permalink] On a certain road 10% of the motorists exceed the posted speed limit   27 Jan 2021, 03:44
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gmat1220 ,why did we choose variable x when this problem can be solved without 'x' but with different answer(Answer = 30), please explain
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On a certain road 10% of the motorists exceed the posted speed limit [#permalink] On a certain road 10% of the motorists exceed the posted speed limit   27 Jan 2021, 17:55
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Saransh123
gmat1220 ,why did we choose variable x when this problem can be solved without 'x' but with different answer(Answer = 30), please explain

Hi Saransh123,

To start, the original poster that you're referring to has not logged into GMATClub in almost a year, so you might not receive a direct response from him/her. Most GMAT questions can be approached in more than one way, so when dealing with any individual prompt, you have 2 goals: correctly answer the question (in a reasonable amount of time, if possible) AND do your work in an efficient way (meaning that you don't want to over-commit and spend too much time on any one prompt).

From your post, it's not clear what method you used to answer this question, but if you read the other posts in the thread, you'll see that by TESTing VALUES and doing a little Algebra/Arithmetic, it's possible to answer this question relatively quickly.

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Re: On a certain road 10% of the motorists exceed the posted speed limit [#permalink] On a certain road 10% of the motorists exceed the posted speed limit   13 Feb 2021, 11:24
Bunuel
chintzzz
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};

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

Answer: B.

Hope it's clear.

Hi Bunuel - how can "X" (Which is Total # of motorist who exceed speed} ever by a non integer ?

We are talking about human beings here..

Do you find that strange ? I also got the 12.5 and I thought "hmmm something must be wrong here as we can't have 12.5 human beings"

Thoughts ?
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Re: On a certain road 10% of the motorists exceed the posted speed limit [#permalink] On a certain road 10% of the motorists exceed the posted speed limit   13 Feb 2021, 11:35
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jabhatta2
Bunuel
chintzzz
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};

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

Answer: B.

Hope it's clear.

Hi Bunuel - how can "X" (Which is Total # of motorist who exceed speed} ever by a non integer ?

We are talking about human beings here..

Do you find that strange ? I also got the 12.5 and I thought "hmmm something must be wrong here as we can't have 12.5 human beings"

Thoughts ?

We assumed that there were 100 motorists. So, basically we took the total number of motorists as 100%, so x = 12.5 is the percentage of motorist who exceed speed.
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Re: On a certain road 10% of the motorists exceed the posted speed limit [#permalink] On a certain road 10% of the motorists exceed the posted speed limit   17 Apr 2021, 01:39
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chintzzz
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%

Answer: Option B

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Re: On a certain road 10% of the motorists exceed the posted speed limit [#permalink] On a certain road 10% of the motorists exceed the posted speed limit   26 Jul 2022, 09:07
This is one of those Questions where you feel pissed because of the language of the question. My threshold for dealing with such questions is minimal. Thus, I am going to leave this one
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On a certain road 10% of the motorists exceed the posted speed limit [#permalink] On a certain road 10% of the motorists exceed the posted speed limit   12 May 2023, 07:00
KarishmaB
Madelaine88
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
Oh my god Karishma! You are truly a genius! My mind is blown. :)
On Quant, you singlehandedly blow all the other so called "Experts" out of the water. :P
Just amazing. :)
Thanks for such great work. :)
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Re: On a certain road 10% of the motorists exceed the posted speed limit [#permalink] On a certain road 10% of the motorists exceed the posted speed limit   21 Jun 2024, 12:28
gmat1220
Using double matrix.
­Why is the 20% done as 0.2 while the 10% is left as it is. Shouldn't it be 0.1 as well?!
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Re: On a certain road 10% of the motorists exceed the posted speed limit [#permalink]
21 Jun 2024, 12:28
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