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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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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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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

Video solution by GMATinsight

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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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KarishmaB
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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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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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