BTGmoderatorDC wrote: ↑Tue Mar 31, 2020 6:50 pm
The student-professor ratio at a certain university was 25:4, but when the university expelled eighty students for acts of civil disobedience, seventeen professors quit in protest. Which of the following could be the new student-professor ratio at the university?
A. 63:12
B. 95:17
C. 33:5
D. 55:6
E. 55:3
OA
C
Source: Veritas Prep
Given that the student-professor ratio at a certain university was 25 : 4, let's assume that there were 25x students and 4x professors, where x is a positive integer.
Thus, currently, there are (25x – 80) students and (4x – 17) professors.
New student-professor ratio = (25x – 80)/(4x – 17)
Note that there can be multiple answers to this question. This is a 'Could be true' type of question.
Also, note that the student-professor ratio was 25 : 4 = 6.25 : 1. And the ratio of expelled students to quit professors = 80 : 17 = 4.7 : 1. Since 6.25 > 4.7, it means that relatively fewer students were expelled than the professors who quit. This means that the new student-professor ratio would be greater than 6.25 : 1. Thus, Option A (63 : 12 = 5.2..: 1) and Option B (95 : 17 = 5. 5...: 1) cannot be answers.
Also, note that the denominator of the revised ratio 25x – 80)/(4x – 17) is (4x – 17), which is always odd; thus, Option D is ruled out. Thus, we have two options to choose from: Option C and E.
• Option C: (25x – 80)/(4x – 17) = 33/25; upon solving, we get x = 23. Since x = 23, a positive integer, this is one of the correct answers.
Though we got the answer, let's check Option E, too.
• Option E: (25x – 80)/(4x – 17) = 55/3; upon solving, we get x = 23. Since x = 4.75.., not a positive integer, this cannot be a correct answer.
The correct answer:
C
Hope this helps!
-Jay
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