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Of the 60 students in a class, only the students who had

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Of the 60 students in a class, only the students who had

by BTGmoderatorDC » Sat Aug 03, 2019 7:35 pm

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Of the 60 students in a class, only the students who had obtained Grade A in Science could apply for a scholarship. Only 1 out of every 5 students who applied for a scholarship got it. If the ratio of the number of students who got the scholarship to the number of students who did not get the scholarship is not more than 1:9, what is the maximum possible number of students who applied for but did not get the scholarship? Assume that all the students who were eligible for the scholarship applied for it.

(A) 6
(B) 12
(C) 24
(D) 30
(E) 54

OA C

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by Ian Stewart » Sun Aug 04, 2019 5:14 am
If the ratio of people getting scholarships to people not getting them is not more than 1 to 9, then no more than 1/10 of all people got scholarships. If we have 60 people in total, at most 6 got scholarships. If 6 got scholarships, and that's 1/5 of applicants, 30 people applied in total and 24 did not get them. That's the maximum possible answer to the question, since we'd get a smaller number if we assumed fewer than 6 people got scholarships.
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