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# On a certain road 10% of the motorists exceed the posted spe

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Senior Manager
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On a certain road 10% of the motorists exceed the posted spe [#permalink]

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14 Jun 2005, 09:00
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55% (hard)

Question Stats:

63% (02:28) correct 37% (01:28) wrong based on 265 sessions

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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%

OPEN DISCUSSION OF THIS QUESTION IS HERE: on-a-certain-road-10-of-the-motorists-exceed-the-posted-spe-95947.html
[Reveal] Spoiler: OA
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14 Jun 2005, 09:29

This question is in the OG and thus well explained by ets.

those who exceed : X

so X = 10%+0,2X

id est X = 12,5%
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Re: PS motoristS exceeding speed limits [#permalink]

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14 Jun 2005, 11:35
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mandy wrote:
:? Hello

On a certain road, 10 percent of the motorists exceed the posted speed limit and receive speeding tickets, but 20 percent 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%

Let the no. of motorists on the road be 100x.
No of ppl who overspeed and receive tickets = 10% of 100x = 10x.
The stem says that 20% of those who oversped got away without tickets, hence 80% of the ppl who overspead received tickets.
ie. 80% ( no of ppl who overspead ) = 10x
ie (no of ppl who overspead = 10x/.8 = 12.5x.

which is 12.5 % of the total. Hence B.

HMTG.
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14 Jun 2005, 14:28
It's E, because percentage of people speeding is (percentage of speeding and receive ticket ) + (pecertange of speeding but not receive ticket)= 30%
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14 Jun 2005, 15:45
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For these I like to draw a tree rather then ven diagram.

I get easily confused.
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Re: On a certain road, 10 percent of the motorists exceed [#permalink]

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06 Apr 2014, 16:21
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Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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06 Apr 2014, 16:55
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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};

$$10+0.2x=x$$ --> $$x=12.5$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: on-a-certain-road-10-of-the-motorists-exceed-the-posted-spe-95947.html
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Re: On a certain road 10% of the motorists exceed the posted spe   [#permalink] 06 Apr 2014, 16:55
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