Let's analyze each option in detail:
(A) the court of each other, providing entertainment in return for
Error: The phrase "the court of each other" is problematic. "Each other" typically refers to two entities reciprocating an action. But in this context, there are multiple dance teams and chiefs, so "each other" is not appropriate.
Trick: The use of a modifier that sounds correct but has a subtle error in meaning.
(B) the court of another and provide entertainment in return for
This choice corrects the error in (A) by changing "each other" to "another". The teams represent their chief at the court of another chief.
Trick: Introducing a correct structure that might seem too straightforward.
(C) the court of the other, so as to provide entertainment as a return on
Error: The use of "the other" is incorrect because it implies there are only two tribes or chiefs.
Error: "So as to provide entertainment as a return on" is verbose and awkward.
Trick: Using a verbose structure to make a simple idea sound complex.
(D) each other's court, entertainment being provided in return for
Error: Again, "each other's court" is problematic for the same reason as in (A).
Error: The phrase "entertainment being provided" is passive and unnecessarily wordy.
Trick: Using passive voice to divert attention from the main error.
(E) another's court and provide entertainment as a return on
Error: "As a return on" is awkward phrasing. The more natural expression is "in return for".
Trick: Using an uncommon phrase to test the test-taker's familiarity with idiomatic expressions.
From the above analysis, the correct option is:
(B) the court of another and provide entertainment in return for
This choice is clear, maintains parallel structure, and avoids the pitfalls of the other choices. The GMAT often tests the test-taker's ability to spot subtle errors in meaning and familiarity with idiomatic expressions, both of which are present in this question.