On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% 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%

Read one line at a time and analyze it.

On a certain road, 10 percent of the motorists exceed the posted speed limit and receive speeding tickets,

>>>>10% of total motorists exceed speed limit and get tickets

but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets.

>>>>>>20% who exceed the speed limit do not get tickets. Then 80% who exceed the speed limit must be getting tickets.

What percent of the motorists on that road exceed the posted speed limit?

>>>>> So 10% of total motorists = 80% of those who exceed speed limit
So those who exceed speed limits are 1/8 = 12.5% of the motorists
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Sorry for offtop-
Can you please tell me whether you also edit the level of questions? I mean this question is marked as 700level, but I have some doubts about that.
could you please also give me a link to Suggestions topic? I have some ideas.
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Imho it is 600 level
I have read once that 700level question is the one that needs at least 2 steps to be solved or the one that covers hard topics like combinatorics etc

Actually i didnt mean anything bad. I am not a math guru at all (unfortunately hehe) and have no right to judge a question. All i want to know is that whether you Bunuel edit that "level" tag. I rely on ur experience. But sometimes i get confused by these tags and just wonder what you think and whether u pay attention to the tags
Ok, now i know that u edit these tags too. Thnx for the information
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Bunuel, thanks for ur kind reply.
Could u plz send me a link to the suggestion topic? As a user I have some minor suggestions.i tried to find that topic
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I would like to give my opinion on this statement:

Let's think about how the GMAT software decides the level of a question (simplifying the process by saying that it allots a level number to each question instead of a difficulty graph). The difficulty level is assigned by the people who take the test and not by the question setters.

You have experimental questions, right? They are there to estimate the difficulty level (among other things) of the new question. Say, most test takers spend 3-4 mins on a particular question and still get it wrong. The software is likely to assign it a high difficulty level. It doesn't matter how many steps it needed or the topic it tested. Some of the most tricky questions are from number properties which I think is extremely simple theoretically.

So what defines the difficulty level? The perception of the people. Why are combinatorics questions usually considered hard? Because people assume they are hard - they could be extremely straight forward but the moment people see 'how many ways' or 'what is the probability', they tend to take a step back. Similarly, function questions are usually considered difficult because of the notation but if you get over that notation you will see that those questions are usually very simple with a step wise process. Also, the answer to a question may be apparent to you with no steps needed if you understand the basics very well. To many others, it might seem very tricky and they might work on it for 5 mins before arriving at the solution. Therefore, when you think about the level of a question, think of how people will perceive it (hard to do without any data and/or experience in this field) rather than what you feel about the question. You may be very good at a topic and hence may feel that a certain question is simple but many others may not share your opinion. At the end of the day, opinion of the masses is what decides the question level (which implies a huge opportunity to do well by being comfortable in questions people consider hard).
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Dear LalaB,

As Bunuel said, the question of offend does not arise. When someone asks me the level of a question, I usually look at the question and judge according to my experience and move on. I do not go into details of why it is an inaccurate exercise. In this case I got into an explanation because you are a seasoned and valued participant of this community - with people like that, your mind instinctively tries to go out of its way to help, discuss and give what you think is the best answer (I might have offended someone else now!) I actually did not go to the question to judge what level it is before putting my response because that was irrelevant to the point I was trying to make.
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The question is fine.

Some fraction of the motorists exceed the speed limit. Say x%. We need to find x%.

Some of these x% motorists get speeding tickets (say y%) and others do not. Anyone who gets a speeding ticket (belongs to y%) must belong to these x%.

You are given that y% of x% of Total motorists = 10% of Total motorists (people who exceed the limit and get tickets)

Also, 20% of x% do not get tickets. This means 80% of x% do get tickets.

This 80% of x% of Total= 10% of Total (we are already given)

So x% of Total = 12.5% of Total
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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)

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, 12.5% of motorists speed.
Answer: B

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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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