gmatruler wrote:The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?
(A) 5
(B) 8
(C) 10
(D) 12
(E) 15
We can plug in the answers, which represent the number of teachers.
Since all of the numbers in the problem are multiples of 5, the correct answer also is likely to be a multiple of 5.
Answer choice C: 10 teachers.
30:1 = 300:10, implying 300 students.
Students increased by 50 = 300+50 = 350.
Teachers increased by 5 = 10+5 = 15.
350:15 = 70:3.
The needed ratio is 25:1 = 75:3.
Since 75:3 > 70:3 -- implying more distance between the number of students and the number of teachers -- the correct answer must be bigger.
Answer choice E: 15 teachers.
30:1 = 450:15, implying 450 students.
Students increased by 50 = 450+50 = 500.
Teachers increased by 5 = 15+5 = 20.
500:20 = 25:1.
Success!
The correct answer is
E.
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