Problem Solving

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. Waht 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%

Answer is B

set up a 2 by 2 matrix, let there be 100 motorists

let x motorists exceed limit, 10 exceeded limit and received ticket.
=>exceeded limit but not ticketed: x-10

x-10=20%*x
solving x=25/2=12.5%

hence, B

You have two groups:
- motorists who exceed the speed limit - call them a
- motorists who do not exceed the speed limit - call them b

You have that a + b = t (total motorists).

Out of group a, you'll also have two subgroups:
- speeders who get tickets - call them x
- speeders who don't get tickets - call them y.

x + y = a.

Now, 10% of motorists exceed the speed limit and get tickets, meaning that 10% of t are part of this other group, so 0.1*t = x.
20% of the motorists who exceed the speed limit don't get tickets, meaning that 0.2*a = y.

You're looking for a relationship between a and t.

Replace x and y in x + y = a to get:

0.1t + 0.2a = a
0.1t = 0.8a
t = 8a
a = t/8 = 0.125 * t = 12,5 * t.

thank you

Can't you pick numbers at this problem?

scoobydooby solved this problem by picking numbers. I'm actually considering writing my own version of "picking numbers strategy guide", since I see most people really like this method.... What do you think? Would you be interested in seeing such a post?

Yes it would be nice DanaJ. I really like the picking numbers, because it makes me pace .


I picked 100 as a total score but I got a answer of 28%.


100 x 0.10 = 10 ( who exceeded the posted speed limit and receive speeding tickets )

90 x 0.20 = 18 ( who exceeded the posted speed limit do not receive speeding tickets )

28 / 100 = 28 %

What did I wrong at my calculation?