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OG 12 221-How to solve this

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by [email protected] » Mon Apr 15, 2013 8:48 pm
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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by vipulgoyal » Mon Apr 15, 2013 8:56 pm
my take D
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by Anju@Gurome » Mon Apr 15, 2013 8:56 pm
[email protected] 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
As total number of students is 200 and 150 are majoring in Biology, the maximum number of students who are not majoring in either chemistry or biology is (200 - 150) = 50

Total = Biology + Chemistry - Both + None
Hence, None = (Total - Biology - Chemistry + Both) = (200 - 130 - 150 + Both) = (Both - 80)

Now, 30 ≤ None ≤ 50
---> 30 ≤ (Both - 80) ≤ 50
---> (30 + 80) ≤ Both ≤ (50 + 80)
---> 110 ≤ Both ≤ 130

The correct answer is D.
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by srcc25anu » Mon Apr 15, 2013 9:05 pm
Bio - 150
Chem - 130
Total = 200
None >= 30

suppose # students majoring in none is minimum 30, then MINIMUM # students who took BOTH is 150 + 130 - 170 = 110

Maximum all students who took Chem can also take Bio that is 130 students at maximum can take both subjects

thus 110 < both subjects < 130
Hence D
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by GMATGuruNY » Mon Apr 15, 2013 9:20 pm
[email protected] 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
Chemistry = 130 and Biology = 150.
Since 130+150 = 280 -- exceeding the total number of students by 80 -- at least 80 students must major in both subjects.
Eliminate A, B and C.

Since only 130 students major in chemistry, the number of students majoring in both subjects cannot exceed 130.
Eliminate E.

The correct answer is D.
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