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

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Of the 200 students at College T majoring in one or more of [#permalink] New post 29 Dec 2012, 05:57
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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 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
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Re: Of the 200 students at College T majoring in one or more of [#permalink] New post 29 Dec 2012, 06:03
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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 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


{Total} = {Chemistry } + {Biology} - {Both} + {Neither}

200 = 130 + 150 - {Both} + {Neither} --> {Neither} = {Both} - 80.

Since given that {Neither}>=30, then {Both} - 80>=30 --> {Both}>=110.

Now, as the number of students majoring in both chemistry and biology cannot possibly be more than the number of students majoring in either of sciences, then 110<={Both}<=130.

Answer: D.
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Re: Of the 200 students at College T majoring in one or more of [#permalink] New post 18 Aug 2013, 04:22
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Let X be the number majoring in Both Chemistry and Biology .

Then

130-X+X+150-X+GT30 = 200

X= GT110 ( Here GT=Greater than )

X>= 110

And as one of the set consists of only 130 , the maximum value cannot exceed 130.

110<=X<=130
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Re: Of the 200 students at College T majoring in one or more of   [#permalink] 18 Aug 2013, 04:22
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