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posted speed limit

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by Ankitaverma » Wed Dec 04, 2013 12:27 pm
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*1/2%
(B) 12*1/2%
(C) 15%
(D) 22%
(E) 30%

Q/a-b can someone explain
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posted speed limit

by Brent@GMATPrepNow » Wed Dec 04, 2013 12:29 pm
Ankitaverma wrote: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*1/2%
(B) 12*1/2%
(C) 15%
(D) 22%
(E) 30%

Q/a-b can someone explain
We can use the Double Matrix Method to solve this question.

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.
Image

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.
Image

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.
Image

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.
Image

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
Last edited by Brent@GMATPrepNow on Mon Apr 16, 2018 11:06 am, edited 2 times in total.
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by [email protected] » Wed Dec 04, 2013 2:42 pm
Hi Ankitaverma,

Brent presents a solid way to organize the information in the prompt and figure out the correct answer. Here's another way to organize the information:

The prompt doesn't give us any numbers to use, so let's TEST Values:

Let's say there are 100 motorists. From the prompt, we know that some exceeded the speed limit and some didn't...

X = number of exceeded the speed limit
(100 - X) = number of did not exceed the speed limit

We're told that 10% exceeded the speed limit AND got a ticket, so that's 10 people.

This means that the X people who exceeded the speed limit can be broken into 2 groups: those who got a ticket and those who didn't.

X = (those who got tickets) + (those who didn't)
X = 10 + (those who didn't)

Next, we're told that 20% of the motorists who EXCEEDED THE SPEED LIMIT did not receive tickets. That's the equivalent of .2X

X = 10 + .2X

Now, solve for X

.8X = 10
X = 12.5

Final Answer: B

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by Mathsbuddy » Thu Dec 05, 2013 3:14 am
Questions like this require careful reading.

Let
M = total number of motorists
S = total number who speed

So here is the question reworded for those who don't see it:

10% of M speed and receive speeding tickets
20% of S don't receive tickets
Find S/M * 100%
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posted speed limit

by GMATGuruNY » Thu Dec 05, 2013 4:54 am
on a certain road 10% of the motorists exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive a speeding ticket. 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%
This is an EITHER/OR group problem.
Every motorist EITHER speeds OR doesn't.
Every motorist EITHER receives a ticket OR doesn't.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data:
Image
In the grid above, the entries in any given row or column must add up to the TOTAL of that row or column.

Let the motorists who exceed the speed limit = 10.
The following grid is yielded:
Image

20% of the motorists who exceed the posted speed limit do not receive a speeding ticket.
Since 20% of 10 = 2, the following grid is yielded:
Image

10% of the motorists exceed the posted limit and receive speeding tickets.
Since the 8 motorists who receive a ticket are 10% of the total number of motorists -- and 8 is 10% of 80 -- the following grid is yielded:
Image

Thus:
(exceed the speed limit)/(total number of motorists) = 10/80 = 12.5%.

The correct answer is B.
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posted speed limit

by bkastan » Tue Apr 11, 2017 6:34 pm
GMATGuruNY wrote:
on a certain road 10% of the motorists exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive a speeding ticket. 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%
This is an EITHER/OR group problem.
Every motorist EITHER speeds OR doesn't.
Every motorist EITHER receives a ticket OR doesn't.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data:
Image
In the grid above, the entries in any given row or column must add up to the TOTAL of that row or column.

Let the motorists who exceed the speed limit = 10.
The following grid is yielded:
Image

20% of the motorists who exceed the posted speed limit do not receive a speeding ticket.
Since 20% of 10 = 2, the following grid is yielded:
Image

10% of the motorists exceed the posted limit and receive speeding tickets.
Since the 8 motorists who receive a ticket are 10% of the total number of motorists -- and 8 is 10% of 80 -- the following grid is yielded:
Image

Thus:
(exceed the speed limit)/(total number of motorists) = 10/80 = 12.5%.

The correct answer is B.


GmatGuru, Why did you do (20%)(10)? Isn't it (20%)(10%)? I know i'm wrong, i'm just trying to understand your logic
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by GMATGuruNY » Wed Apr 12, 2017 4:23 am
bkastan wrote:GmatGuru, Why did you do (20%)(10)? Isn't it (20%)(10%)? I know i'm wrong, i'm just trying to understand your logic
Since all of the values in the problem are percentages, we can plug in ANY VALUE for the number of motorists who exceed the speed limit.
In my solution above, I plugged in the following:
Number of motorists who exceed the speed limit = 10 people.
The prompt states that 20% of the motorists who exceed the speed limit do not receive a ticket.
Thus, in my solution above:
Number of motorists who exceed the speed limit but do not receive a ticket = 20% of the 10 people who exceed the speed limit = 2 people.
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by Scott@TargetTestPrep » Wed Apr 19, 2017 3:07 pm
Ankitaverma wrote: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*1/2%
(B) 12*1/2%
(C) 15%
(D) 22%
(E) 30%
We can let the total number of motorists = m and the number of motorists who exceed the speed limit = n. Thus, we need to determine the value of n/m x 100.

We are given that 10 percent (or 0.1m) of the motorists exceed the posted speed limit and receive speeding tickets.

We are also given that 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets. Since we let n = the number of motorists who exceed the speed limit, 0.2n = the number of motorists who speed who do not receive a speeding ticket.

We can create the following equation:

number of motorists who exceed the limit = number of motorists who speed and get a ticket + number who speed but do not get a ticket

n = 0.1m + 0.2n

0.8n = 0.1m

8n = m

Thus n/m x 100 = n/(8n) x 100 = 1/8 x 100 = 12.5 percent.

Answer: B

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