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On a certain road, 10 percent of the motorists exceed the

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Manager
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On a certain road, 10 percent of the motorists exceed the [#permalink] New post 06 Aug 2007, 11:29
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16. 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) 10.5% (B) 12.5%
(C) 15% (D) 22%
(E) 30%

oa is 12.5%...pls explain
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 [#permalink] New post 06 Aug 2007, 11:56
Here it goes:

we are told that 20% of those who speed, "dont" get ticketed.
it follows that 80% of those who speed "do" get ticketed.

we are also told that 10% of all motorist speed and get ticketed
therefore, those 10% of all drivers must represent the 80% of those who are speeding.

Hence total number of motorists who speed must be 10% * (100% / 80%) = 10% * 5/4 = 12.5%

Answer is B
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 [#permalink] New post 06 Aug 2007, 12:31
i dont get the question.

We are told that 10% who speed get ticketed , so 90 % speed and dont get ticketed, right ?

Where does the 20% come into play ??
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 [#permalink] New post 06 Aug 2007, 13:02
Quote:
We are told that 10% who speed get ticketed , so 90 % speed and dont get ticketed, right ?


We are told that 10% of motorists speed and get ticketed. We don't know anything about the other 90% at this point. We can't assume the other 90% speed and just don't get caught. Then they go on to say that 20% of those who speed don't get ticketed.

So 10% of motorists = 80% of speeders. (100% - 20% that don't speed and don't get caught)

to get 100% of speeders (which is what the question is asking) multiply both sides by 1.25.

10% x 1.25 = 12.5% and 80% x 1.25 = 100%

12.5% of motorists speed. B.
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 [#permalink] New post 06 Aug 2007, 15:03
after reading both the explanations, I get it. its almost like a CR problem with a bit of math tossed in.

I missed a question like this last night and didn't get it. this was helpful.
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 [#permalink] New post 14 Aug 2007, 19:15
Argh, I got this one wrong on a power prep. That's the stupidest wording I've ever heard!
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 [#permalink] New post 14 Aug 2007, 21:44
Draw a table. You will then get this equation 10 + 0.2x = x whre x is the number of people who exceed the speed limit. x = 12.5.
  [#permalink] 14 Aug 2007, 21:44
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