Official Guide Explanation:
Problem Solving #200




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Solution and Metadata

Question: 200
Page: 181
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Sets > 2 sets
Category 2: Word Problems > Sets >
Category 3: Arithmetic > Percents > other

Explanation: First, convert all the percents into numbers, which is straightforward when the total number of researchers is 50. 50(0.4) = 20 will be assigned to team A and 50(0.6) = 30 will be assigned to team B. 50(0.7) = 35 prefer team A while 50(0.3) = 15 prefer team B. To limit the number of researchers who aren't assigned to the team they would like, assign 20 of the 35 researchers who would prefer team A to team A, leaving 15 researchers who prefer team A but can't be assigned to it. That leaves those 15 unlucky researchers along with the 15 who preferred team B to be assigned to team B. That's a total of 15 researchers who weren't assigned to the team they preferred, choice (A).

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