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# Of the 200 students at college T majoring in one or more of

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Manager
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Of the 200 students at college T majoring in one or more of [#permalink]  25 Jan 2008, 11:52
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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 atleast 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 20 to 50
B 40 to 70
C 50 to 130
D 110 to 130
E 110 to 150
Manager
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Re: students [#permalink]  25 Jan 2008, 12:11
d
200-30 = 170

170-150=20
130-20=110

130
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Re: students [#permalink]  25 Jan 2008, 12:12
d.
Set rule/formula
Ch + Bio+neither-both(Ch and Bio)=Total
130+150+30-x=200 x=110 min
X max=130 because Chemistry members could be at the same time members of Biology class but not vice versa.
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Re: students [#permalink]  25 Jan 2008, 12:13
D: 110-130
A - students who major in chemistry, B - students who major in biology.

P(A+B) = P(A) + P(B) - P(A*B)

Since P(A+B) <= 200-30 = 170, then

P(A) + P(B) - P(A*B) <= 170, P(A*B) >= P(A)+P(B) - 170 = 130+150-170 = 110, 110 - possible 30 students major in neither bio or chem, 20 major only in chem, 110 in both chem and bio, 40 - in bio only

P(A*B) <= min(P(A), P(B)) = 130 - possible when all students who major in chemistry also major in biology
Re: students   [#permalink] 25 Jan 2008, 12:13
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