Today, we’ll take a look at a question from the Official Guide from GMAC dealing with sets! As always, try it on your own, then scroll down for an explanation! 🙂

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 question asks what “x” could be.

150 = B + X

130 = C + X

B + C + X = 170

The MAXIMUM overlap is 130, since the Chemistry circle cannot be GREATER than 130. From there we know the answer must be either (C) or (D).

Plugging in our first two equations:

(150 – X) + (130 – X) + X = 170

150 – X + 130 – X + X = 170

150 – X + 130 = 170

150 – X = 40

– X = 40 – 150

-X = -110

X = 110

The answer is (D).