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  3. Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the students in

Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the students in

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问题 Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the students in the school are in the band but are not in the science club, what percent of the students who are in the science club are not in the band?
选项 A、5%
B、20%
C、25%
D、60%
E、75%
答案E
解析 You are given that 20% of the students are in the science club, 30% are in the band, and 25% are in the band but are not in the science club. You need to determine what percent of the students who are in the science club are not in the band. The information can be represented in a Venn diagram as follows.

From the Venn Diagram, you can see that the 30% who are in the band consists of 25% who are in the band but not in the science club, and 5% who are in both the band and the science club. Then you can see that the 20% who are in the science club consists of 5% who are in both the science club and the band, and 15% who are in the science club but not in the band, as shown in the revised Venn diagram below.

Thus(100%), or 75%, of the students in the science club are not in the band. The correct answer is Choice E.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 2: Translate from Words to a Figure or Diagram
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