Total = 30 applicants. Look at it this way: there are only four categories for an applicant:
a. more than 4 years' experience + degree
b. more than 4 years' experience but no degree
c. less than 4 years' experience + degree
d. less than 4 years' experience but no degree

Then you get 14 people with at least 4 years' experience. This makes the number of people with less than 4 years' experience = 30 - 14 = 16. Of these 16 people, 3 did not have a degree, making the number of people who had at least 4 years' experience but no degree 13.

Now, 18 of them had a degree, meaning that 12 of them did not have a degree. Since 3 of these had less than 4 years' experience, then 9 of them have more than 4 years' experience and hold a degree.

The number you are looking for is 30 - 3 - 13 - 9 = 5.

DanaJ wrote:Total = 30 applicants. Look at it this way: there are only four categories for an applicant:
a. more than 4 years' experience + degree
b. more than 4 years' experience but no degree
c. less than 4 years' experience + degree
d. less than 4 years' experience but no degree

Great explanation!

In fact, there's a formula for this type of question:

True # of objects = (# with characterstic 1) + (# with characteristic 2) + (# with neither characteristic) - (# with both characteristics)

Applying the formula to this question (which is exactly what Dana did):

True # = 30
Char 1 = 4+ years experience = 14
Char 2 = degree = 18
neither = 3
both = b

30 = 14 + 18 + 3 - b
30 = 35 - b
-5 = -b
b = 5

Thanks, guys! Makes much more sense now.

Simple explaination:

We are can solve this by Venn Diagram
Exp set: denotes people with 4+ yrs of work experince(14)
Degree: people with degree(18)

There are also 3 people who are without degree+work exp. so they are outside the two circles(sets)

And the total is 30(Universal set)

So the common between the two circles can easily be found.
ie: 14+18= people who have degree or exp or both
but there are 3 people with none
so 14+18+3 = total=35
but total is given to be 30

So the number common to both is 35-30

Let me know if you find this approach easy or not

Hi all,

Just to help him visualize better using the Venn Diagram.

kevind147 wrote:OK I always have trouble with these kinds of questions. Here's one that I just don't get:

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

Can someone walk me through this as well as how to approach this kind
of problem? This is #166 on page 174 from the 11th edition of the OG. Thanks!

This is a typical set problem. You have to draw a Venn's diagram. You have 2 sets of people: 14 with experience and 18 with degree out of 30. You also know that 3 don't fall under any category, so they are out of the equation. Let x be the # of people who belong to to both categories, then
the 1st group with experience is 14-x (need to exclude the overlap), and 2nd group is 18-x (same here). Then you get an equation:

14-x+x(the overlap)+18-x=27
14+18-x=27
32-x=27
x=5

Another way to easily to solve this problem is by representing the problem in a dual matrix (see the attachemnt).
U can fill in the matrix easily, by simple arithmetic as follows:

The Total row (last row) 3rd col is 30 - 14 = 16.
Fill the "less than 4 yr exp" col: as follows:
ppl have a Degree And < 4 yrs exp: 16 - 3 = 13.
U get the picture...so u can fill the entire matrix...

By being a little smart, we can fill the cell that the Q asks first and dont both the rest.

HT Helps

I absolutely love the matrix.. makes life better