Overlapping sets can be solved in several ways; you could use Venn diagrams, the groups formula (total = group 1 + group 2 + neither - both), or use the groups table (also called a matrix). I go through the question in detail in the full solution below (taken from the GMATFix App).



-Patrick

BlueDragon2010 wrote:Of 30 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?

A) 14
B) 13
C) 9
D) 7
E) 5

Check the Diagram carefully , we are only interested in finding the Yellow Intersecting Part and nothing else...

Now calculate -

Candidates in total having Atleast 4 Years of Experience , Degrees and Less than 4 Years Experience is 14 + 18 + 3 = 35

However according to the Question the Total number of applicants who appeared for the Interview is 30

The this excess Counting ( 35 ) is due to the double Counting Error which we have overlooked ..

Hence the Yellow Intersecting Part is 35 - 30 = 5 Applicants...


Answer will be definitely be [spoiler](E)[/spoiler]

BlueDragon2010 wrote:Of 30 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?

A) 14
B) 13
C) 9
D) 7
E) 5

Solution:

For this we can setup a table with 2 main categories: years of experience and degrees. These can be broken down further into:

1) Had at least 4 years of experience

2) Had less than 4 years of experience

3) Had a degree

4) Did not have a degree

In addition we are given the following information:

1) There are 30 total applicants

2) 14 applicants had at least 4 years of experience

3) 18 applicants had degrees

4) 3 applicants had less than 4 years of experience and did not have a degree

Let's fill all this information into a table.



We can use the information to fill in the rest of the table. Remember the "Total" label in each column or row represents the sum of the preceding two cells in each column or row, respectively.



We are asked how many of the applicants had at least 4 years' experience and a degree. We can see from our table that the answer is 5.

Answer: E