Why Do Some Students Appear to Be Double-Counted in Math Enrollment Figures?

[Dethrone]

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. (?)

+++++

Additional Info:

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.

 

[soroban]

Hello, Rido12!

There are 158 students at FLC High School.
92 in Data Management (D).
71 in Advanced Functions (A).
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.

              * * *       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.

 

[Dethrone]

Hello, Rido12!


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

              * * *       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,

              * * *       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?

 

[Ackbach]

I've attempted a solution that might work.

Because of the wording of the question,

              * * *       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.

 

[CellCoree]

I would suggest taking a closer look at the data and the diagram to see if there are any discrepancies or errors. It is highly unlikely that there are more students enrolled in math courses than there are in the entire school. It is possible that some students are taking multiple math courses, but it is also possible that there are some errors in the data or the diagram.

One potential explanation for the negative number is that the numbers in the diagram do not add up correctly. For example, if there are actually 90 students taking Data Management and 70 students taking Advanced Functions, the numbers in the diagram would add up to 160 instead of 158, which could result in a negative number when trying to calculate the students not enrolled in any math course.

Another possibility is that there are some students who are not included in the data or the diagram. It is important to make sure that all students are accounted for and that there are no missing data points.

In any case, it would be helpful to double check the data and the diagram to ensure accuracy and to find the correct number of students not enrolled in any math course.