Problem Solving

VJesus12 wrote: ↑

Fri Feb 19, 2021 6:39 am

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%

Answer: B

Source: Official Guide

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

VJesus12 wrote: ↑

Fri Feb 19, 2021 6:39 am

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%

Answer: B

Source: Official Guide

Solution:


We can let the total number of motorists be 1000. So 100 motorists exceed the posted speed limit and receive speeding tickets. Now if we let x = total number of motorists who exceed the posted speed, we can create the equation:

100 + 0.2x = x

100 = 0.8x

125 = x

Therefore, the percent of the motorists on the road who exceed the posted speed limit is 125/1000 = 12.5%.

Answer: B