Astronomy quiz question: distance of Arcturus from apparent and absolute magnitudes

Astronomy 210 Quiz 5, spring semester 2016
Cuesta College, San Luis Obispo, CA

Arcturus is a star with an apparent magnitude of m = –0.05, and an absolute magnitude M of –0.30. Arcturus is located __________ 10 parsecs from Earth.
(A) farther than 10 parsecs.
(B) exactly 10 parsecs.
(C) closer than 10 parsecs.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

Arcturus appears to be –0.05 as seen from its true distance from Earth, but when placed at the "fair" distance of 10 parsecs away, its becomes slightly brighter (–0.30). Thus it was brought just a little closer to Earth when moved to 10 parsecs, and was located just a little farther than 10 parsecs away from Earth.

Section 30674
Exam code: quiz05nUL7
(A) : 10 students
(B) : 0 students
(C) : 8 students
(D) : 1 student

Success level: 48% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80