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posted by math student .
In a survey of 150 students, 90 were taking algebra, and 30 taking biology.
a. what is the least number of students who could have been taking both classes?
b. what is the greatest number of students who could be taking both courses?
c. what is the greatest number of student who could have been taking neither courses?
Please explain.

(a) 0, since there are still 30 students in neither class. Only if the two classes sum to more than 150 does it mean that someone is taking both.
(b) 30, since that would mean that ALL the biology students are also taking algebra
(c) 60, since if all 30 biology students were taking algebra, that only uses up 90 of the 150 students.
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