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)

• No male knew music, and only 'many' (not all) of the 20 female members knew music, so some women also did not know music.

• Since nobody at the party knew music, all six guests came from the non-musicians: the 30 men plus the women who did not know music.

• Six such guests could be all men, all non-musician women, or a mix of both.

• So nothing definite can be said about the gender composition of the party.

• Hence option (d).

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.