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

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VP
Joined: 22 Nov 2007
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On a certain road 10% of the motorists exceed the posted [#permalink]  13 Dec 2007, 05:27
On a certain road 10% of the motorists exceed the posted speed limit and receive tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What % of the motorists on the road exceed the posted speed limit?

A. 10,5%
B. 12,5%
C. 15%
D. 22%
E. 30%
Intern
Joined: 10 Aug 2007
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Re: settings [#permalink]  13 Dec 2007, 05:47
[quote="marcodonzelli"]On a certain road 10% of the motorists exceed the posted speed limit and receive tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What % of the motorists on the road exceed the posted speed limit?

A. 10,5%
B. 12,5%
C. 15%
D. 22%
E. 30%[/quote]

I think it's E.

The total of motorists on the road exceed the posted speed limit = those only exceed speed limit (20%) + those both exceed speed limit & receive ticket ( 10%) = 30%

I dont know if I just simply simplify the problem??
Manager
Joined: 20 Jun 2007
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12.5%

First, the 10% who get the tickets.

Plus those who don't get the tickets (say x)

Total who exceed the limit: 10%+x%

Now 20% of those who exceed, do not receive tickets.

So x = 20% of 10% + X%
x = (10+x)/5
5x = 10+x
4x = 10
x = 2.5

Senior Manager
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the wording of this question is terrible.
Manager
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Re: settings [#permalink]  13 Dec 2007, 09:47
marcodonzelli wrote:
On a certain road 10% of the motorists exceed the posted speed limit and receive tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What % of the motorists on the road exceed the posted speed limit?

A. 10,5%
B. 12,5%
C. 15%
D. 22%
E. 30%

It is B

Let's put T-total number of motorists; S - number of motorists who exceed speed limit.

So,
0.1T - number of motorists who exceed and receive tickets
0.2S - number of motorists who exceed but don't receive tickets =>0.8S - exceed and receive

0.8S=0.1T =>S/T=1/8=12.5%
CEO
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Re: settings [#permalink]  13 Dec 2007, 22:43
marcodonzelli wrote:
On a certain road 10% of the motorists exceed the posted speed limit and receive tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What % of the motorists on the road exceed the posted speed limit?

A. 10,5%
B. 12,5%
C. 15%
D. 22%
E. 30%

Fell for the E trap.

20% OF 10%...
Intern
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B is the answer. I think it is better to transform percents into persons.
Lets 10% - 10 motorists, then we have proportion 10 mots - 80%
x mots - 20%

from there x -2,5 mots (awkward, but easy understandable)
Total mots 10+2,5= 12,5 or 12,5%
Director
Joined: 12 Jul 2007
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Let's say there are 100 motorists on the road.

10 speed and get tickets
but 20% of those who speed don't receive tickets
Let X = number of people who speed
.8x = 10 (80% of speeders make up the 10 who got tickets because 20% don't get caught)
x - 12.5

CIO
Joined: 09 Mar 2003
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2
KUDOS
Whenever I get a problem with multiple percentages (ie, subgroups), I like to draw a tree to help me see how things break out. I started with 100 motorists.

Also, really big GMAT tip which sounds deceptively simple: FOLLOW THE OF's. Whenever you are thinking about a percentage problem, always make sure you ask "percent of what?" and be sure to take the percentage of the right number. The word "OF" is a signpost for that - whatever is right after of will almost always be the right thing to use.
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Manager
Joined: 14 May 2007
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Re: [#permalink]  18 Mar 2008, 10:08
GMAT TIGER wrote:
ian7777 wrote:
Whenever I get a problem with multiple percentages (ie, subgroups), I like to draw a tree to help me see how things break out. I started with 100 motorists.

Also, really big GMAT tip which sounds deceptively simple: FOLLOW THE OF's. Whenever you are thinking about a percentage problem, always make sure you ask "percent of what?" and be sure to take the percentage of the right number. The word "OF" is a signpost for that - whatever is right after of will almost always be the right thing to use.

nice one.

Thanks for the explanation. I was dam confused but the diagram (tree) cleared up doubts.
Intern
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Re: settings [#permalink]  19 Mar 2008, 00:09
in my view,I could remove D and E directly,especially E,if e is correct,the question is very simply.
the key of problem is 20% refer to those who exceed, do not receive tickets.
Re: settings   [#permalink] 19 Mar 2008, 00:09
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