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by src_saurav » Fri Jun 19, 2015 8:04 am
222. 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

I got 110 but got stuck with the second part.
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by GMATGuruNY » Fri Jun 19, 2015 8:07 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
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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by Matt@VeritasPrep » Tue Jun 23, 2015 6:20 pm
In general, you have the MOST overlap when everybody in the smaller group is also in the larger group, and you have the LEAST overlap when everybody is in *one* of the two groups (i.e. there is NOBODY outside of the two groups).

In this case, that means the most overlap is when everyone in chemistry is also in biology, and the least overlap is when everyone is majoring in one of the two subjects. (This particular problem then stipulates that this is impossible, but I figured it was worth mentioning for the general case.)
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