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by rahul.s » Fri Feb 05, 2010 4:54 am
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) 20 to 50
(B) 40 to 70
(C) 50 to 130
(D) 110 to 130
(E) 110 to 150

OA: D

I got the minimum as 110, but how do I determine the maximum?

200 = 130 + 150 + 30 - x
x = 110
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by ajith » Fri Feb 05, 2010 5:00 am
rahul.s wrote: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) 20 to 50
(B) 40 to 70
(C) 50 to 130
(D) 110 to 130
(E) 110 to 150

OA: D

I got the minimum as 110, but how do I determine the maximum?

200 = 130 + 150 + 30 - x
x = 110
Of the 200 students 30 are not majoring in chemistry or Biology
The population majoring in either chem or biology is at most 170

Now you got the minimum by your method
Maximum is when all 130 majoring in chemistry majors in Biology also.
That will make The population majoring in either chem or biology 150
But at most is 170, so it is not violating any conditions
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by thephoenix » Fri Feb 05, 2010 5:28 am
tot=200
neither>=30
chemistry=130
bio=130

maximum common=minimum of the two=130

if neither=30
then common=150+130+30-200=110

hence the range is 110-130
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by harsh.champ » Fri Feb 05, 2010 5:31 am
rahul.s wrote: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) 20 to 50
(B) 40 to 70
(C) 50 to 130
(D) 110 to 130
(E) 110 to 150

OA: D

I got the minimum as 110, but how do I determine the maximum?

200 = 130 + 150 + 30 - x
x = 110
_________
The question may seem easy if you try to solve it through Venn Diagram.
For minimum,as you had done
200 = 130 + 150 + 30 - x
x = 110

For the maximum,one circle in Venn diagram should be inside or equal to the other circle.
Hence,130.

Alternatively,for the maximum case all the 130 majoring in chemistry can major in biology.
Hence,total no. of the students are not majoring in either chemistry or biology = 50
Hence,Answer is 110 and 130.
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