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by tvtt2010 » Fri Jul 08, 2011 8:27 am
on a certain road 10% of the mototorist exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speedlimit do not receive speeding ticket. 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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by Frankenstein » Fri Jul 08, 2011 8:35 am
Hi,
Let the total number of motorists be 100n
Let the number of motorists who exceed be x
Of these 20% do not receive speeding ticket i.e. 0.2x
The remaining 0.8x receive speeding tickets
Given that 10% of the total motorists exceed and receive speeding tickets
So, 0.8x = 10%(100n)
So, 0.8x = 10n => x = 12.5n

Hence, B
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by GMATGuruNY » Fri Jul 08, 2011 9:00 am
tvtt2010 wrote:on a certain road 10% of the mototorist exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speedlimit do not receive speeding ticket. 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%

Thanks
Let motorists who exceed the speed limit = 10.
Motorists who don't receive a ticket = .2*10 = 2.
Thus, motorists who receive a ticket = 10-2 = 8.
Since the 8 motorists who receive a ticket are 10% of the total, total = 80. (8 is 10% of 80.)
Motors who exceed the speed limit/Total = 10/80 = 12.5%.
Last edited by GMATGuruNY on Fri Jul 08, 2011 11:01 am, edited 1 time in total.
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by top_business_2011 » Fri Jul 08, 2011 9:21 am
tvtt2010 wrote:on a certain road 10% of the mototorist exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speedlimit do not receive speeding ticket. 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%

Let us use the following representations:

Let E= The event of exceeding the speed limit.
E'= The event of not exceeding the speed limit.
T = The event of receiving tickets
T'= TThe event of not receiving tickets
Given:
P(E n T)= 0.1 [read as 'probability of E intersection T' ]
P(T'/E)= 0.2 [read as 'probability of T' given E']
Since P( T'/E) + P(T/E) = 1
= 0.2 + P(T/E) = 1
Therefore, P(T/E) =0.8

Required: P(E)=?
Now you can use the conditional rule of probability:
P(T/E) = P(T n E)/ P(E)
0.8 = 0.1/ P(E)
P(E)= 0.1/0.8
= 0.125
= 12.5%
Hope this helps.






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by BY » Sat Jul 09, 2011 11:55 am
GMATGuruNY wrote:
tvtt2010 wrote:on a certain road 10% of the mototorist exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speedlimit do not receive speeding ticket. 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%

Thanks
Let motorists who exceed the speed limit = 10.
Motorists who don't receive a ticket = .2*10 = 2.
Thus, motorists who receive a ticket = 10-2 = 8.
Since the 8 motorists who receive a ticket are 10% of the total, total = 80. (8 is 10% of 80.)
Motors who exceed the speed limit/Total = 10/80 = 12.5%.
Thanks for the explanation Guru!

But i have some confusion in the first sentence of the Qs.

10% of the mototorist exceed the posted limit and receive speeding tickets

say there are total 100 motorist.

10 exceed the posted limit and receive the ticket (as well).

Does the sentence mean : 10 % of the motorist exceed the posted limit and some of them receive speeding tickets.[/b][/u]
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by GMATGuruNY » Sat Jul 09, 2011 1:05 pm
BY wrote:
GMATGuruNY wrote:
tvtt2010 wrote:on a certain road 10% of the mototorist exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speedlimit do not receive speeding ticket. 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%

Thanks
Let motorists who exceed the speed limit = 10.
Motorists who don't receive a ticket = .2*10 = 2.
Thus, motorists who receive a ticket = 10-2 = 8.
Since the 8 motorists who receive a ticket are 10% of the total, total = 80. (8 is 10% of 80.)
Motors who exceed the speed limit/Total = 10/80 = 12.5%.
Thanks for the explanation Guru!

But i have some confusion in the first sentence of the Qs.

10% of the mototorist exceed the posted limit and receive speeding tickets

say there are total 100 motorist.

10 exceed the posted limit and receive the ticket (as well).

Does the sentence mean : 10 % of the motorist exceed the posted limit and some of them receive speeding tickets.[/b][/u]
The first sentence means that 10% of the total number of motorists BOTH exceeded the speed limit AND received speeding tickets.
In my solution, since the number of motorists who both exceeded the speed limit and received speeding tickets is 8, there are 80 total motorists.
8 = 10% of 80.
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

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