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On a certain road 10% of the motorists exceed the posted spe [#permalink]
 16 Jun 2010, 09:31
Question Stats:
53% (02:08) correct
46% (01:05) wrong based on 1 sessions
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%
Last edited by Bunuel on 22 Jan 2013, 06:15, edited 1 time in total.
Renamed the topic and edited the question.
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Re: need help on % question [#permalink]
16 Jun 2010, 09:40
If you give a value for the motorist .. x=100
then
10% exceed/ticketed = 10
20% exceed/not ticketed = 20
since they were either ticketed or not ticketed, all options have been covered; you have 30 total people that have exceeded the speed limit. This is 30% of 100.
IMO: E
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Re: need help on % question [#permalink]
16 Jun 2010, 09:57
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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% 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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Re: need help on % question [#permalink]
16 Jun 2010, 11:55
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 1/2%
b)12 1/2%
c)15%
d)22%
e)30% z= total motorists y=motorists who speed and dont get ticket = y motorists who speed = x =.1z+y We are told that .2x=y x=.1z+.2x -> .8x=.1z -> x=1/8z or 12.5% B
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Percentage problem [#permalink]
27 Feb 2011, 11:58
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%
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Re: Percentage problem [#permalink]
27 Feb 2011, 12:00
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Re: need help on % question [#permalink]
27 Feb 2011, 14:06
Good question! 30% seemed too straightforward to be the answer!
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Re: Percentage problem [#permalink]
27 Feb 2011, 20:46
Madelaine88 wrote: 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
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Re: need help on % question [#permalink]
27 Feb 2011, 23:02
0.1 M = 0.80 E => E/M = 1/8 * 100 = 12.5% So answer is B. M - # of Motorists E - # of Motorists exceeding speed
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Re: need help on % question [#permalink]
28 Feb 2011, 01:55
Using double matrix.
Attachments
percentage.jpg [ 21.09 KiB | Viewed 1540 times ]
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Re: need help on % question [#permalink]
09 Mar 2011, 17:49
80 % = 10% means 1/8 x100 = 12.5
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Re: need help on % question [#permalink]
09 Mar 2011, 20:59
Good question
(10/100)(M) = E & get tickets
(20/100)(E) = no tickets
(80/100)(E) = tickets
(80/100)E = (10/100)M => E = (10/80)M = 12.5% of M
Answer is B.
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Re: need help on % question [#permalink]
10 Mar 2011, 03:58
I've solved via some kind of hybrid method.
Out of 100 drivers, 10 receive a ticket. Those represent 80% of drivers who exceed the speed limit, denominated by X.
Thus follows:
X * 0,8 = 10
X = \frac{10}{0,8}
X = \frac{100}{8}
X = 12,5
=> \frac{12,5}{100} = 0,125 = 12,5% (B)
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Re: need help on % question [#permalink]
14 Jun 2011, 18:56
Good question...12.5%
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Re: need help on % question [#permalink]
04 Nov 2011, 02:17
Bunuel wrote: 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 1/2%
b)12 1/2%
c)15%
d)22%
e)30% Let's assume total # of motorists to be 100. {# 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. i dont understand why cant it be 20 + 0.1 x = x?? as in how do we know we pick 10 for 10% of people who exceeded speed and received tickets and not equate it to 0.1 x = # of people who received tickets ??? we have taken 0.2 x as no. of people who speeded but dd not receive tickets ... so we should have similarly done for 10% of people who exceeded speed and received tickets which is 0.1 x but bunnels explanation just picks a number 10 so i am confused
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Re: need help on % question [#permalink]
05 Nov 2011, 11:58
I concur with 12.5%.
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Re: need help on % question [#permalink]
05 Nov 2011, 12:11
kostyan5 wrote: I concur with 12.5%. Kostyan5 can you please explain in detail how did you get to your answer? 
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Re: need help on % question [#permalink]
05 Nov 2011, 19:15
siddhans wrote: kostyan5 wrote: I concur with 12.5%. Kostyan5 can you please explain in detail how did you get to your answer? If 20% of the motorist who exceeded the speed limit did not get a ticket, then 80% of the motorist who exceeded the speed limit got a ticket. We are also told that 10% of all motorist exceed the limit and get tickets. So 10% of all motorists and 80% of motorist who exceeded the limit refer to the same group of people (exceeded and were ticketed). 10% = 80% * motorist who exceededmotorists who exceeded = \frac{10}{80} =.125 or 12.5%
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Re: need help on % question
[#permalink]
05 Nov 2011, 19:15
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