Question

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

• A. 2020 to $50$
• B. $40$ to $70$
• C. $50$ to $130$
• D. $110$ to $130$
• E. 110 to 150

Answer 1

Answer: (D)

$110$ to $130$

At maximum there are 170 students majoring in at least one of the sciences and a minimum of 150 majoring in at least one of the sciences.

$n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

$=150+130-170=110$ This is minimum no. of people majoring in both chemistry and biology.

$=150+130-150=130$ This is maximum no. of people majoring in both chemistry and biology.