There are 1000 students in a class. 200 passed algebra, 100 passed statistics, and 150 passed mathematics. Only 40 passed the three courses, while equal number of students passed exactly two courses. If 6 students were absent for the examination, what are the number of students that passed exactly two courses?. And the number that failed each of the courses?
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Inclusion-exclusion: Total number of non-absent students equals number passing algebra plus number passing statistics plus number passing mathematics, minus (number passing algebra and stats plus number passing algebra and math plus number passing stats and math), plus number passing all three. Number passing algebra and stats is the 40 who passed all three, plus the $x$ who passed just algebra and stats. You get an equation for $x$.
That stats class must have been a nightmare!
EDIT: This seems to be quite wrong. As others note, it appears there isn't enough information to solve the problem.
Let me answer this question with a question, because Gerry's answer does not look like a correct one to me (or I am just confused by the original post).
Denote the total number of non-absent students that pass at least one course with a, the number of students passing Algebra as $|A|$, the number of students passing Stat as $|S|$ and the number of students passing Mathematics as $|M|$.
We know $|A \cap M| = |A \cap S| = |S \cap M| = x$.
$a = |A| + |M| + |S| - 3x + |A \cap S \cap M| = 490 - 3x$
Now we are stuck because we have no information about students failing? Or did I misinterpret the original problem?