Official Solution: At a university orientation, attendance was recorded for two optional activities: a campus tour and a study-skills workshop. Among 180 students, how many attended the campus tour but not the study-skills workshop? We need \(\{\text{Tour only}\}\).
(1) 126 students attended neither activity.
So:
\(\{\text{Tour or Workshop}\} = 180 - 126 = 54\)
But we do not know how many of these 54 attended the workshop, so we cannot determine \(\{\text{Tour only}\}\).
Not sufficient.
(2) 18 students attended the study-skills workshop.
This gives the total number of workshop attendees, but it gives no information about how many students attended neither activity or how many attended the campus tour.
Not sufficient.
(1)+(2) From statement (1):
\(\{\text{Tour or Workshop}\} = 54\)
From statement (2):
\(\{\text{Workshop}\} = 18\)
Since everyone in \(\{\text{Tour or Workshop}\}\) either attended the workshop or attended the tour but not the workshop:
\(\{\text{Tour only}\} = \{\text{Tour or Workshop}\} - \{\text{Workshop}\}\)
\(\{\text{Tour only}\} = 54 - 18 = 36\)
Sufficient.
Answer: C