There were 50 faculty members comprising 30 males and the rest females. No male faculty member knew music, but many of the female faculty members did. The Head of the institution invited six faculty members to a tea party by draw of lots. At the party it was discovered that no member knew music. The conclusion is that :
- (a) the party comprised male faculty members only
- (b) the party comprised only those female faculty members who could not give renderings in music
- (c) the party comprised both male and female faculty members
- (d) nothing can be said about the gender composition of the party ✓ UPSC's answer
Why the answer is (d)
["- The problem states that no male faculty member knew music, but only 'many' (not all) female faculty members did, implying some females also did not know music.", "- The condition that 'no member knew music' at the party means every invited person must be from the group of non-musicians.", '- The group of non-musicians consists of all 30 males and the subset of females who do not know music.', '- Since the draw of lots was random, the six selected members could have been all males, all non-musician females, or a mix of both.', '- Because multiple gender compositions are possible under the given constraints, no definitive conclusion can be drawn about the specific gender mix.', '- Therefore, option (d) is correct as it accurately reflects the uncertainty regarding the gender composition.']
Why the other options are wrong
- (a) the party comprised male faculty members only
- The party could have included female faculty members who did not know music, so it is not necessarily comprised of males only.
- (b) the party comprised only those female faculty members who could not give renderings in…
- The party could have included male faculty members, so it is not necessarily comprised only of non-musician females.
- (c) the party comprised both male and female faculty members
- The party could have been comprised entirely of males or entirely of non-musician females, so it is not necessarily a mix of both genders.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.