Correct Option
The problem states that no male faculty member knew music. It also states that many female faculty members knew music, which implies that some female faculty members did not know music. Six faculty members were invited to a tea party, and it was discovered that none of them knew music.
This condition means the six attendees must have been drawn from the pool of faculty members who do not possess musical knowledge. This pool includes:
- All 30 male faculty members (as none of them knew music).
- Some female faculty members (specifically, those who did not know music).
Since the six members could have been selected from either the male faculty (all of whom qualify) or the non-music-knowing female faculty, or a combination of both, there are multiple possible gender compositions for the party. Therefore, based on the given information, it is not possible to definitively conclude the gender composition of the party.
Incorrect Options
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Option 1: the party comprised male faculty members only. This is a possible scenario since all male faculty members did not know music. However, it is not a certainty, as female faculty members who did not know music could also have been included.
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Option 2: the party comprised only those female faculty members who could not give renderings in music. This is also a possible scenario, as some female faculty members did not know music. However, it is not a certainty, as male faculty members could also have been included.
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Option 3: the party comprised both male and female faculty members. This is a possible scenario, provided the female members selected were among those who did not know music. However, it is not a certainty, as the party could have been composed entirely of males or entirely of females who did not know music.
Each of these options describes a potential composition, but none can be concluded as the sole definitive outcome. The only certain conclusion is that the gender composition remains indeterminate.