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  3. In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students

In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students

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问题 In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry? ______students
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答案121
解析 This is the type of problem for which drawing a Venn diagram is usually helpful. The Venn diagram below is one you could draw to represent the information given in the question.

    Note that the algebra and chemistry numbers given do not separate out the number of students who took both algebra and chemistry, and that this question asks for the greatest possible number of such students. It is a good idea, therefore, to redraw the Venn diagram with the number of students who took both algebra and chemistry separated out. The revised Venn diagram looks like the one below.

    To solve this problem you want the greatest possible value of x. It is clear from the diagram that x cannot be greater than 142 nor greater than 121, otherwise 142 -x or 121 — x would be negative. Hence, x must be less than or equal to 121. Since there is no information to exclude x = 121, the correct answer is 121.
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