Question

In a survey of​ four-year colleges and​ universities, it was found that

255

offered a liberal arts degree.

110

offered a computer engineering degree.

481

offered a nursing degree.

30

offered a liberal arts degree and a computer engineering degree.

211

offered a liberal arts degree and a nursing degree.

86

offered a computer engineering degree and a nursing degree.

25

offered a liberal arts​ degree, a computer engineering​ degree, and a nursing degree.

33

offered none of these degrees.

A.  How many​ four-year colleges and universities were​ surveyed?

There were

nothing

​four-year colleges and universities surveyed.

Of the​ four-year colleges and universities​ surveyed, how many offered

B.  a

liberal artsliberal arts

degree and a nursing​ degree, but not a

computer engineeringcomputer engineering

​degree?There are

nothing

​four-year colleges and universities that offer a

liberal artsliberal arts

degree and a nursing​ degree, but not a

computer engineeringcomputer engineering

degree.C.  a

computer engineeringcomputer engineering

​degree, but neither a

liberal artsliberal arts

degree nor a nursing​ degree?There are

nothing

​four-year colleges and universities that offer a

computer engineeringcomputer engineering

​degree, but neither a

liberal artsliberal arts

degree nor a nursing degree.

D.  a liberal arts​ degree, a computer engineering​ degree, and a nursing​ degree?

There are

nothing

​four-year colleges and universities that offer a liberal arts​ degree, a computer engineering​ degree, and a nursing degree.

Enter your answer in each of the answer boxes.

Answer 1

Before answering the question, we would draw a 3 circle Venn diagram and then map the data provided to each of the circle and its intersection.

Data Provided and mapping the same to the respective circle

1. 255 offered a liberal arts degree: A

2. 110 offered a computer engineering degree: B

3. 481 offered a nursing degree: C

4. 30 offered a liberal arts degree and a computer engineering degree: w+z

5. 211 offered a liberal arts degree and a nursing degree: y+z

6. 86 offered a computer engineering degree and a nursing degree: x+z

8. 25 offered a liberal arts​ degree, a computer engineering​ degree, and a nursing degree: z

9. 33 offered none of these degrees

Now we have the following equations to solve:

z = 25 ...(i)

x+z = 86 => x = 86-25 = 61 ..(ii)

y+z = 211 => y = 211-25 = 186 ..(iii)

w+z = 30 => w = 30-25 = 5 ..(iv)

Now for circle A : a+w+y+z = 255 => a = 255-(5+186+25) = 39 ..(v)

For circle B: b+w+x+z = 110 => b = 110-(5+61+5) = 19 ..(vi)

For circle C: c+x+y+z = 481 => c = 481-(61+186+25) = 209 ..(vii)

Now redrawing the circle with updated data:

Q(A): How many​ four-year colleges and universities were​ surveyed?

Answer:

The total number of four-year colleges and universities surveyed will be:

a+w+b+y+z+x+c+college which did not offer any of these courses

=> 39+5+19+186+25+61+209+33 = 577

So 577 number of four-year colleges and universities were​ surveyed.

Q(B): Of the​ four-year colleges and universities​ surveyed, how many offered liberal arts degree and a nursing​ degree, but not a computer engineering?

Answer:

The total number of four-year colleges and universities who are offering liberal arts degree and a nursing​ degree, but not a computer engineering: a+y+c = 39+186+209 = 434

So 434 number of four-year colleges and universities are offering liberal arts degree and a nursing​ degree, but not a computer engineering.

Q(C): Of the​ four-year colleges and universities​ surveyed, how many offered computer engineering degree, but neither a liberal arts degree nor a nursing​ degree?

Answer:

The total number of four-year colleges and universities who are offering computer engineering degree, but neither a liberal arts degree nor a nursing​ degree: b = 19

So 19 number of four-year colleges and universities are offering computer engineering degree, but neither a liberal arts degree nor a nursing​ degree.

Q(D): Of the​ four-year colleges and universities​ surveyed, how many offered a liberal arts​ degree, a computer engineering​ degree, and a nursing​ degree?

Answer:

The total number of four-year colleges and universities who are offering a liberal arts​ degree, a computer engineering​ degree, and a nursing​ degree: z = 25

So 25 number of four-year colleges and universities are offering a liberal arts​ degree, a computer engineering​ degree, and a nursing​ degree.