题目

There are at least 10 freshmen in a room. The ratio of freshmen to sophomores to juniors in the room is 3 to 5 to 12. 40 percent of the freshman in the room are taking history, 60 percent of the sophomores in the room are taking history, and 36 percent of the total number of freshman, sophomores, and juniors in the room are taking history.


Quantity A

The percent of the juniors in the room taking history


Quantity B

30%

选项

A.

The quantity in Column A is greater.

B.

The quantity in Column B is greater.

C.

The two quantities are equal.

D.

The relationship cannot be determined from the information given.

解析

房间里至少有10名大一新生。房间里大一新生、大二学生和大三学生的比例为3:5:12。房间里40%的大一新生在学习历史,60%的大二学生在学习历史,大一新生、大二学生和大三学生总数中有36%在学习历史。设大一新生、大二学生和大三学生的人数分别为\(3x\)、\(5x\)和\(12x\)(\(x\)为正整数),那么总人数为\(3x + 5x+12x=20x\)。 已知\(40\%\)的大一新生学历史,那么大一新生中学习历史的人数为\(0.4\times3x = 1.2x\);\(60\%\)的大二学生学历史,大二学生中学习历史的人数为\(0.6\times5x=3x\);设大三学生中学习历史的比例为\(y\),则大三学生中学习历史的人数为\(12xy\)。 因为大一、大二、大三学生总数中有\(36\%\)在学习历史,所以可得方程: \(\frac{1.2x + 3x+12xy}{20x}=0.36\) 解得\(y = 0.25 = 25\%\)大三学生中学习历史的比例为\(25\%\),而\(25\%<30\%\),所以Quantity B更大,答案是B。
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