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

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EMPOWERgmat Instructor
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Status: GMAT Assassin/Co-Founder
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GMAT 1: 800 Q51 V49
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Re: On a certain road 10% of the motorists exceed the posted spe [#permalink]

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New post 29 Mar 2018, 11:53
Hi All,

Brent has shown you a particular way to organize your information, which you might find helpful on these types of questions. Whether you put your information into a table or not, this question is ultimately testing your ability to notice that the given information is (first) about the overall group, then (second) about a sub-group within the overall group.

First piece: 10% of motorists exceed the speed limit and receive tickets.

If we say there are 100 motorists, then we can break them into 3 groups:

Speed and Got Ticket
Speed and Didn't Get a Ticket
Didn't speed

With 100 total motorists, we know that 10 of them exceeded the speed limit and received tickets:

Total: 100
Speed and Got Ticket = 10
Speed and Didn't Get a Ticket = ?
Didn't speed = ?

Second piece: 20% of the motorists WHO EXCEEDED THE SPEED LIMIT did NOT receive tickets.

This is NOT 20% of the 100, it's 20% of those who EXCEEDED THE SPEED LIMIT. Let's call THAT sub-group X:

X = Those who got a ticket + those who didn't

So, X = 10 + .2X

Now, solve for X
.8X = 10
X = 12.5

Final Answer:

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Re: On a certain road 10% of the motorists exceed the posted spe   [#permalink] 29 Mar 2018, 11:53
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On a certain road 10% of the motorists exceed the posted spe

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