In a survey of 150 students,90 were taking algebra and 30 were
taking biology.
A. What is the least number of students who could have been
taking both courses?We see if it could be 0, none at all. Then none of the 90 algebra
students were taking biology and none of the biology students were
taking algebra. That's possible with 90 taking only algebra, 30
taking only biology, and the other 30 taking neither.
Answer: 0, none at all.
B. What is the greatest number of students who could be taking both
courses?We see if it could be 30, with all of the biology students taking
algebra. That's possible with 30 taking both, 60 taking only
algebra, and the other 60 taking neither.
Answer: 30
C. What is the greatest number of students who could have been
taking neither?That's the same case as part B, since to have the greatest number
taking neither would be the case with the least number were taking
one or the other, which would be the case when there were no
biology-only students.
Answer: 60
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Note: there was no part D, but if there had been it would have been:
D. What is the least number of students who could have been
taking neither?That would have been the same case as part A, with no students taking
both.
Answer: 30
Edwin
