In a certain group of 50 people, how many are doctors who have a law

Target question: How many are doctors who have a law degree?

Given: There are 50 people

When I scan the two statements, I see that we have the ingredients for applying the Double Matrix method
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of 50 people, and the two characteristics are:
- Doctor or NOT a doctor
- Has law degree or doesn't have law degree

So, we can set up our double matrix as follows:

NOTE: I have placed a star in the box that represents doctors who have a law degree, since this is what the target question is asking us about

Statement 1: In the group, 36 people are doctors.
If the group has 50 people, and 36 are doctors, we can conclude that there are 14 non-doctors in the group.
Let's add this information to our matrix:


As you can see, there's no way to determine the value that must go in the starred box.
As such, statement 1 is NOT SUFFICIENT

Statement 2: In the group, 18 people have a law degree
If 18 of the 50 people have a law degree, than the remaining 32 people do NOT have a law degree.
Let's add this information to our matrix:


As you can see, there's no way to determine the value that must go in the starred box.
As such, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the two statements, we get the following:


There are several ways to complete this matrix. Here are two cases:

case a:

In this case, there are 10 doctors with law degrees.

case a:

In this case, there are 5 doctors with law degrees.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

RELATED VIDEO