Official Guide Explanation:
Problem Solving #193




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Solution and Metadata

Question: 193
Page: 179
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Sets > 2 sets
Category 2: Word Problems > Sets >

Explanation: This is a perfect scenario for the equation T = G1 + G2-B + N. G1 = 75 (the percent of students who answered the first question correctly), G2 = 55 (the percent who answered the second question correctly), and N = 20 (the percent who answered neither correctly). T = 100, since we're working with percents--the total is 100, regardless of the number of students. To solve for those who answered both correctly (B):

100 = 75 + 55 - B + 20

100 = 150 - B

B = 50, choice (D).

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