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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?

[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??

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

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?

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

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.

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.

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.