Astronomy quiz question: distance of 61 Ursae Majoris from apparent and absolute magnitudes

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

61 Ursae Majoris is a star with an apparent magnitude of m = +5.3, and an absolute magnitude M of +5.4. 61 Ursae Majoris 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): (C)

61 Ursae Majoris appears to be +5.3 as seen from its true distance from Earth, but when placed at the "fair" distance of 10 parsecs away, its becomes slightly dimmer (+5.4). Thus it was pushed back just a little farther away from Earth when moved to 10 parsecs, and was located just a little closer than 10 parsecs away from Earth.

Section 30676
Exam code: quiz05sPrB
(A) : 18 students
(B) : 2 students
(C) : 30 students
(D) : 0 students

Success level: 62% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.57