At least 15 percent of the students registered for Professor Tyler’s

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.