Bunuel
Close to its African roots,
Frank Manning introduced the Savoy-style Lindy Hop dance form in the mid-1930s to the Savoy Ballroom and was readily accepted by people due to less rigidity in its movements than the original Lindy Hop.
Right from the jump, the thing to notice is that this sentence begins with an Opening Modifier. This is one of the three common ways that Modifiers show up when they're being tested, and the process is always the same: ask yourself the Modifier as a question ("What is close to its African roots?") and keep only answers that place the answer to that question (in this case, probably the Lindy Hop) after the comma.
(A)
Frank Manning introduced the Savoy-style Lindy Hop dance form in the mid-1930s to the Savoy Ballroom and was readily accepted by people due to less rigidity
Starting with Frank Manning won't work because it would imply that Frank Manning was close to its African roots, and, well, no. If nothing else, you can't use the pronoun it to refer to a person unless that person is actually a robot bent on your destruction, and even then, robots are people too. Eliminate this one.(B) the Savoy-style Lindy Hop dance form was introduced by Frank Manning to the Savoy Ballroom
in the mid-1930s and was readily accepted by people
because it was less rigid(C) the Savoy-style Lindy Hop dance form was introduced by Frank Manning to the Savoy Ballroom and was readily accepted by people
in the mid-1930s because of less rigidityI've highlighted above the two major differences between (B) and (C): the positioning of in the mid-1930s and the phrasing of because... at the end. When a word or phrase is changing position from answer choice to answer choice, it's usually another sign that Modifiers are being tested. Consider what different meanings are conveyed by the different positions of in the mid-1930s by looking at what the phrase shows up next to: in (B), it's next to introduced by Frank Manning to the Savoy Ballroom; in (C), it's next to readily accepted by people. Which actually happened in the mid-1930s? Probably the introduction, but if it's hard to say, look to the other split (the because phrase). You might just prefer one way to the other, but if you don't automatically feel this one, the phrasing in (B) makes the meaning more clear: the Savoy-style Lindy Hop was less rigid than the original Lindy Hop. More importantly, it also creates a more logical Comparison with the non-underlined portion at the end of the sentence. The than implies that you need to be comparing something to the original Lindy Hop,, and (C) simply doesn't provide that something. (B) is the correct answer.(D) Frank Manning’s
introduction of the Savoy-style Lindy Hop dance form to the Savoy Ballroom in the mid-1930s was readily accepted by people because it was less rigid
(E) the Savoy-style Lindy Hop dance form’s
introduction by Frank Manning to the Savoy Ballroom in the mid-1930s was readily accepted by people because it was less rigid
Both of these make the same mistake as (A), albeit in a more subtle way. When Opening Modifiers are involved, answers often try to trick you by putting the right noun after the comma but then adding a cheeky apostrophe-S to it. This means that even though (E) appears to start with the Savoy-style Lindy Hop dance form, the apostrophe-S on form's turns that whole phrase into a Modifier itself. This in turn means that introduction is serving as the subject in (D) and (E), and introduction isn't a great target for the Opening Modifier (that is, the introduction isn't what's close to its African roots). Good riddance, (D) and (E).