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[sana.noor]

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)10.5%,
b) 12.5%,
c) 15%,
d) 22%,
e) 30%.

OA is B

[vivekchandrams]

Hi sana.noor,

The question says 10% of the motorists exceeded the posted speed limit.

So let the total no:of motorists be 1000.

So 100 motorists exceeded the limit.

The question also says that 20% of those who exceeded escaped without a ticket.

So let's assume the total no:of motorists who exceeded limit to be x.

'x' includes all those who exceeded i.e., those who got tickets as well as those who didn't.

Hence, we can say

80 % of x = 100.

(Since 20% escaped the tickets, 80% got the tickets. From the previous statement we have the number of motorists who received tickets = 100)


On solving, x = 125

Hence, % of motorists who exceeded the speed limit is 125/1000 = 12.5%

Hence ans B


Pls hit 'thank' button if you find my post useful

[GMATGuruNY]

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)10.5%,
b) 12.5%,
c) 15%,
d) 22%,
e) 30%.

OA is B

Let the total number of speeders = 10.

20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets.
Thus, nonticketed speeders = .2*10 = 2, implying that ticketed speeders = 8.

10 percent of the motorists exceed the posted speed limit and receive speeding tickets.
Thus, the 8 ticketed speeders are equal to 10% of the total number of motorists:
8 = .1x
x = 80.

Thus:
(total speeders)/(total motorists) = 10/80 = 12.5%.

The correct answer is B.

[Brent@GMATPrepNow]

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)10.5%,
b) 12.5%,
c) 15%,
d) 22%,
e) 30%.

OA is B

It may be useful to use the Double Matrix Method to help us arrange our information. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of motorists, and the two characteristics are:
- speeder (S) or non-speeder (~S)
- get ticket (T) or not get ticket (~T)

Aside: To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Since this question concerns percents (instead of actual values), let's assign a "nice" value to the total number of motorists in this population. Let's say there are 100 motorists.

So, to begin, our matrix looks like this.


10 percent of the motorists exceed the posted speed limit and receive speeding tickets
The top left box is for motorists who speed and receive speeding tickets. So, 10% of the entire population will be in this box.


20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets.
The motorists referred to here are those who go in the top right box. Unfortunately, we don't know the total number of speeders, so we can't find 20% of that value.
So, let's let x = the total number of speeders.


Now we can deal with this: 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets.
In other words, 20% of x will go in the top right box.


At this point, we know that the sum of the top 2 boxes is x.
So, we can write: 10 + 0.2x = x (now solve)
Arrange: 10 = 0.8x
Divide: 10/0.8 = x
12.5 = x

Since x represents the total number of speeders, we know that 12.5 out of 100 motorists speed.
In other words, [spoiler]12.5%[/spoiler] of motorists speed.
Answer: B


Here are some additional practice questions that can be solved using the Double Matrix Method:
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping- ... 83320.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html

Cheers,
Brent