On a certain road 10

[guest 22]

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 the road exceed the posted speed limit?
(A) 2110%
(B) 2112%
(C) 15%
(D) 22%
(E) 30%

[Guest]

whats the OA? E?
[/u]

[guest22]

oops.
I just realized the answer choices are wrong. Here is the correct version.

A) 10.5
B) 12.5
C) 15
D) 22
E) 30

The correct answer is B, but I can't figure out how to get the answer

[divya]

I used a double set matrix for this problem

So you can state as

From the question stem 10% of M exceeded speed limits and recieved tickets.
2. 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets. Let the total ## of motorist who exceed speed limit be x

Motorist get tickets Motorist do not get tickets. total
Motorist Exceed Limit 10 .20x x
Motorist Do not Ex. L

From grid 1 we know:

10 + .20x = x
10 = .80x

x = 100/8 = 12.5

thus, answer B

[Guest]

[divya]

Please refer to the preceding table/matrix uploaded, since the table in my 1st post got misformatted

[Gmat11]

Can someone explain this in detail..i am still confused and think 30% should be the answer

[Gmat11]

RON-- Can you please help on this?

Thnx

[so19]

Let the total # of motorists = Y
Also let the total # of motorists who exceed the speed limit = X
The question is asking what % of the motorists (=Y) exceed the speed limit (=X), in other words, what % of Y is X = what is X/Y?

Quick interpretation:
# of motorists who exceed the speed limit = # of motorists who exceed the speed limit and receive tickets + # of motorists who exceed the speed limit and do not receive tickets

Given:
10% of the motorists exceed the speed limit and receive tickets = 0.1Y
20% of the motorists who exceed the speed limit do not receive tickets = 0.2X

Therefore,
0.1Y + 0.2X = X
0.1Y = 0.8X
Y = 8X
X/Y = 1/8 = 0.125 = 12.5%

[DIVYA]

sol9 has definitely explained it well!!

The only difference between sols & my interpretation was that I am taking y as 100 because what we need to find is x/y * 100 ( as a percentage) and if you take y as 100, you are relatively left with X, which should be your answer.

[RonPurewal]

RON-- Can you please help on this?

Thnx

hey - do you understand the basic workings of the double-set matrix? if so, then the posted solution (the uploaded graphic), which is fantastic, should serve you very well indeed.

if you don't understand the workings of the double-set matrix, you may want to check it out in the word translations strategy guide. the VERY BASIC idea is that you put one set of ALTERNATIVE OPTIONS (here, speed vs. don't speed) on the rows, the other set of ALTERNATIVE OPTIONS (here, ticket vs. no ticket) on the columns, add in a "total" row and a "total" column (so that your table contains 3 rows and 3 columns in total), and then #1 + #2 = total in every row and also in every column.

let me know if this doesn't make sense.

[anoo.anand]

can somebody please explain this.. one.... using Double matrix ?

[anoo.anand]

wihtout double matrix:

Let 100 be the total no of motorist....

Hence those who get ticket and exceed speed limit = 10

Let x be the no of motorist who exceed the limit.

Hence we have the equation :
x = 0.2x + 10
x = 10/0.8 = 12.5

[RonPurewal]

can somebody please explain this.. one.... using Double matrix ?

the fifth post on this thread contains a double set matrix for this problem. the corresponding explanation is in the fourth post.