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Bunuel
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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%

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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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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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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If someone can explain this - why have we not taken 10% as the 10% of x (which is the total no. of motorists who exceed) and then 20% of x, adding them gives us 30%. Am I wrong somewhere in interpreting this?
Bunuel


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.
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It says, 20% of the motorists who exceed the speed limit didn't receive tickets. That means 80% has got tickets.
Lets assume 100 motorists were there and 10% of the motorists exceed the posted speed limit and receive speeding tickets.
That means 10 motorists receive tickets,
ie, 80% of total motorists who exceed speed limit =10
Total motorists= (10*100)/80=12.5%

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%

Drill more questions that test the same idea in GMAT Club Timed Quiz → Free.
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Deconstructing the Question

10% of all motorists receive speeding tickets.

Among those who exceed the speed limit, 20% do not receive tickets, so 80% do.

Let the percentage of motorists who exceed the speed limit be \(x\).

Step-by-step

The percentage who both exceed the limit and receive tickets is

\(0.8x\)

This equals the total percentage receiving tickets:

\(0.8x = 10\%\)

Solve:

\(x = \frac{10\%}{0.8} = 12.5\%\)

Answer: B

ANOTHER APPROACH

Deconstructing the Question

Let \(S\) be the set of motorists who exceed the speed limit, and let \(T\) be the set of motorists who receive speeding tickets.

The problem says that \(10\%\) of all motorists are in \(T\).

It also says that \(20\%\) of motorists in \(S\) do not receive tickets, so \(80\%\) of motorists in \(S\) do receive tickets.

Step-by-step

Let the total set of motorists be \(U\).

Then

\(|T| = 0.10|U|\)

Since \(20\%\) of speeders do not get tickets, \(80\%\) of speeders do get tickets, so

\(|T| = 0.80|S|\)

Now equate the two expressions for \(|T|\):

\(0.80|S| = 0.10|U|\)

So

\(|S| = \frac{0.10}{0.80}|U| = 0.125|U|\)

Thus the percentage of motorists who exceed the speed limit is

\(12.5\%\)

Answer: B
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Let total motorists = 100. Let x
x = % who exceed speed.
Of those, 20% don’t get tickets → 80% do get tickets.
Given: 10% of all motorists get tickets →
0.8x=10

Solve:
x=10/0.8=12.5

Answer: (B) 12.5%
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wording of this question is really strange.
let total number of motorists be x
motorists who speed and get ticket = 0.1x

let total motorists who speed is y
motorist who speed and do not get any ticket = 0.2y so automatically motorists who get ticket = 0.8y

0.1x=0.8y
which means 0.8y is 10% of all those who were on the road.
so y will be 12.5% of all motorists


-----------------------------------------------------------------------

If you understood the ask then below method is much easier.
let total motorists be 100, and total motorists who exceeded the speed limit be Y

Got TicketsGot NO tickets
Exceeded Speed limit10 = 0.8Y0.2Y
Do not exceed speed limit

Those who exceeded the speed limit and got ticket are 10% of 100 and also 80% of Y
10=0.8Y
y=12.5
y/100*100=12.5% Answer
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%
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