In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Upperclassmen, drawn from three cities: A, B, and C.

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In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Upperclassmen, drawn from three cities: A, B, and C. Sixty percent of students are from A, 30% from B, the rest from C, and all these students from C are freshmen. Half the student from B are upperclassman, and the rest are split evenly between the other two grades. How many sophomores are from A?
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100


OA B

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BTGmoderatorDC wrote:
Wed Sep 23, 2020 9:05 pm
In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Upperclassmen, drawn from three cities: A, B, and C. Sixty percent of students are from A, 30% from B, the rest from C, and all these students from C are freshmen. Half the student from B are upperclassman, and the rest are split evenly between the other two grades. How many sophomores are from A?
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100


OA B

Solution:

We see that there are a total of 80 + 100 + 220 = 400 students from the three cities. Thus, 400 x 0.6 = 240 students are from A, 400 x 0.3 = 120 from B, and 400 - 240 - 120 = 40 from C. Since half the students from B are upperclassmen, 120/2 = 60 students from B are upperclassmen. Since the rest are split evenly between the other two grades, 30 are freshmen and 30 are sophomores. Since all the students from C are freshmen, no sophomores (and upperclassmen) are from C. Thus, the remaining 100 - 30 = 70 sophomores must be from A.

Answer: B

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