To determine the number of students who took the training course but did not pass the test (represented by [tex]\( A \)[/tex] in the table), follow these steps:
1. First, observe that the total number of students who did not pass the test is given in the table as 35 (in the column labeled "Total" and the row labeled "Did Not Pass").
2. From the same row and in the "No Training Course" column, we see that 20 students who did not pass the test did not take the training course.
3. To find how many students who did not pass actually took the training course, we need to subtract the number of students who did not pass and did not take the training course from the total number of students who did not pass. Mathematically:
[tex]\[
A = \text{Total students who did not pass} - \text{Students who did not pass and didn't take the training course}
\][/tex]
4. Substitute the known values:
[tex]\[
A = 35 - 20
\][/tex]
5. Calculate the result:
[tex]\[
A = 15
\][/tex]
Thus, the number of students who took the training course but did not pass the test is 15.
