VENN PS

[GmatKiss]

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

[rijul007]

a+b+c+d = 200

a+b = 130
b+c = 150
d >=30

a+b+b+c+d >= 310
200 + b >= 310
b >= 110

b can't be more than 130


Option D

[CappyAA]

I always like the table setup like this:



Uploaded with ImageShack.us

We know the total of 200, and we know the total chemistry and biology numbers (130 and 150). Since all the columns and rows add up, we can find the numbers of not chemistry and not biology (70 and 50).

The column filled in is the one we are given - At least 30 students are not chemistry or biology. So we know that column must be 30 at the minimum. We also know that it can be a maximum of 50 because there are only 50 students that are not biology majors. So our range for that is between 30 and 50.

Testing out both ends, we can find that if 30 students are neither, 20 students are chemistry majors but not biology majors. Which means that 110 students are are majoring in both.

If 50 students are neither, 0 students are chemistry students but not biology majors. Which means that 130 students are are majoring in both.

Our answer is D

[neelgandham]

Answers :

https://www.beatthegmat.com/og-12-q-221-sets-t51737.html
https://www.beatthegmat.com/og11-239-t2891.html

[saketk]

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

the range cannot go over 130 because in that case the number of student taking ONLY chemistry will become NEGATIVE.

Variables:-

x- chemistry only
y = both
z= bio

we have, x+y = 130
x+y = 130

y+z = 150

and x+y+z = 170

x+y+y+z = 170+y

y = 110.

So we have the minimum range, and the maximum we can go is 130 [ explained earlier]

Answer = D

[vaibhavgupta]

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

D it is!