Bunuel wrote:
At least 15 percent of the students registered for Professor Tyler’s course dropped out before the end of the course. The drop-out rate for Professor Quin’s course was 20 percent greater than that for Professor Tyler’s course. If 120 students remained on the last day of Professor Quin’s class, which of the following could be the number of students who signed up for Professor Quin’s class?
I. 147
II. 162
III. 185
A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III
20% greater than 15% = 15% + 2(1.5) = 18% = \(\frac{18}{100}\) = \(\frac{9}{50}\)
Since the dropout rate for Tyler's course is at least 15%, the dropout rate for Quin's course must be greater than or equal to \(\frac{9}{50}\).
I: 147
Since 120 students remain in the course, 27 students drop out, implying the following dropout rate:
\(\frac{27}{147} = \frac{9}{49}\)
Since \(\frac{9}{49} > \frac{9}{50}\), option I is possible.
Eliminate C.
II: 162
Since 120 students remain in the course, 42 students drop out, implying the following dropout rate:
\(\frac{42}{162} ≈ \frac{40}{160} = \frac{1}{4}\)
Since \(\frac{1}{4} > \frac{9}{50}\), option II is possible.
Eliminate A and D.
III: 185
Since 120 students remain in the course, 65 students drop out, implying the following dropout rate:
\(\frac{65}{185} ≈ \frac{60}{180} = \frac{1}{3}\)
Since \(\frac{1}{3} > \frac{9}{50}\), option III is possible.
Eliminate B.
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