Problem Solving

Official Guide

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

OA E.

AAPL wrote:Official Guide

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

One approach is to use the following equation:
Total = Group 1 + Group 2 - Both + Neither

The big idea is to SUBTRACT THE OVERLAP.
In the problem above, there is an overlap between the applicants with at least 4 years' experience and the applicants with degrees.
Some applicants belong to BOTH groups.
Thus, when we count the members of each group, the OVERLAP -- the applicants who belong to both groups -- is counted twice.
So that we don't double-count these applicants, we must subtract them from the total.

The equation above can be applied to the prompt as follows:
Total = 30
Group 1 = applicants with at least 4 years' experience = 14
Group 2 = applicants with degrees = 18
Both = b
Neither = applicants with less than 4 years' experience and no degree = 3

Plugging these values into equation, we get:
30 = 14 + 18 - b + 3
30 = 35 - b
b = 5.

The correct answer is E.