Official Guide Explanation:
Problem Solving #221

Background

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Solution and Metadata

Question: 221
Page: 184
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Sets > 2 sets
Category 2: Word Problems > Sets >

Explanation: While the number of students majoring in neither chemistry of biology is "at least 30" instead of an absolute number, we can still use the overlapping sets formula: T = G₁ + G₂-B + N. The groups are 130 and 150, the total is 200, and for N, we can use 30, then adjust later to find the range of possible values for B. Plugging in those values:

200 = 130 + 150 - B + 30

200 = 310 - B

B = 110

So, one of the numbers in the correct answer choice must be 110, so it must be (D) or (E). The maximum number of students in both is easier to figure out: there are only 130 students majoring in chemistry, so the maximum number who are studying both can't be more than 130. Thus, the correct range is 110 to 130, choice (D).

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