# Hard Venn Diagram Problem?

#### Rido12

##### Well-known member
MHB Math Helper
The question as follows:

Hypothetically, there are 158 grade 12 students at FLC High School, 92 have enrolled in Data Management, 71 have enrolled in Advanced Functions, and 40 have enrolled in Calculus. The math students include 14 who are taking both Data Management and Advanced Functions, 18 are taking Data Management and Calculus, 11 are taking Advanced Functions and Calculus. Lastly there are 8 brave souls taking all three maths.

How many grade 12 students at FLC High school not enrolled in any math class?

Note: I keep getting -10 as an answer.
According to my teacher this question isn't wrong and it's do-able.
But there is a trick. (?)

+++++

Ended up with 8 in the center of the diagram.

10 between calculus and data.
6 between data and Advanced Functions.
3 between Advanced Functions and Calculus.

Lastly 60 in Data, 54 in Advanced Functions, and 19 in Calculus.

These are all the students enrolled in the courses.

So to get not not enrolled I did:

=158-68-19-54-6-10-3-6-8
=-10

(Or total students in grade 12 - ∑all the numbers in the Venn Diagram

The problem is I can't have negative number for students not enrolled in any math course.
They are more people taking math courses then there are students.in the school.

Last edited:

#### soroban

##### Well-known member
Hello, Rido12!

There are 158 students at FLC High School.
92 in Data Management (D).
40 in Calculus (C).
14 in both D and A.
18 in both D and C.
11 in both A and C.
8 in all three.

How many students are not enrolled in any math class?

Note: I keep getting -10 as an answer. . I agree.
According to my teacher this question isn't wrong
. . and it's do-able.

Either your teacher has a typo in the problem
. . or you copied it incorrectly.

Code:
              * * *       x x x
*     D     x     A     x
*           x   *           x
*           x     *           x
6
*           x       *           x
*    68     x       *     54    x
*           x o o o *           x
o           o
*      o    x  8  *    o      x
*    o  10  x   *   3  o    x
*           x           x
o * * *       x x x o
o                   o
o                   o
19
o                 o
o               o
o     C     o
o o o
I too get a total 168 students.

#### Rido12

##### Well-known member
MHB Math Helper
Hello, Rido12!

Either your teacher has a typo in the problem
. . or you copied it incorrectly.

Code:
              * * *       x x x
*     D     x     A     x
*           x   *           x
*           x     *           x
6
*           x       *           x
*    68     x       *     54    x
*           x o o o *           x
o           o
*      o    x  8  *    o      x
*    o  10  x   *   3  o    x
*           x           x
o * * *       x x x o
o                   o
o                   o
19
o                 o
o               o
o     C     o
o o o
I too get a total 168 students.
I've attempted a solution that might work.

Because of the wording of the question,

Code:
              * * *       x x x
*     D     x     A     x
*           x   *           x
*           x     *           x
14
*           x       *           x
*   52     x       *  38  x
*           x o o o *           x
o           o
*      o    x  8  *    o      x
*    o  18  x   *   11 o    x
*           x           x
o * * *       x x x o
o                   o
o                   o
3
o                 o
o               o
o     C     o
o o o
The people that were exclusively taking for example Data Management and Calculus, DO NOT go under the people that have done Data Management Calculus Advanced Functions. Am I right or wrong?

If you add them together and subtract, (158-144) = 14 students are doing none.

Can anyone confirm?

Last edited:

#### Ackbach

##### Indicium Physicus
Staff member
I've attempted a solution that might work.

Because of the wording of the question,

Code:
              * * *       x x x
*     D     x     A     x
*           x   *           x
*           x     *           x
14
*           x       *           x
*   52     x       *  38  x
*           x o o o *           x
o           o
*      o    x  8  *    o      x
*    o  18  x   *   11 o    x
*           x           x
o * * *       x x x o
o                   o
o                   o
3
o                 o
o               o
o     C     o
o o o
The people that were exclusively taking for example Data Management and Calculus, DO NOT go under the people that have done Data Management Calculus Advanced Functions. Am I right or wrong?

If you add them together and subtract, (158-144) = 14 students are doing none.

Can anyone confirm?
This looks right to me. I think you are correct in your surmise that those taking A and D are not in the group taking all three.