The protest was effective, but not without cost: sixteen people died.

First I should mention that this sentence was in the section specifically for testing colons. Later in the chapter an example is given where a colon or semicolon could be used correctly in a sentence. The example is:
Bill was tormented; the Packers lost again.
Bill was tormented: the Packers lost again.
The examples are followed by a brief note that says that the colon would be preferred because the colon explains the cause of Bill's torment, whereas the semicolon doesn't do as clear of a job at explaining how the sentences are related. I think the example question I originally posted follows this train of thought as well. A semicolon could be used correctly in this sentence, but the colon further clarifies the cost of the protest.

Since the clause just before colon doesn't have an independent clause , you are either left with the choice to introduce a semicolon or to make it an independent clause . The protest was effective, but it wasn't without a cost : sixteen people died.
Am I on the right track ?

Not quite. Initially when I posed this question I thought that the structure of the sentence was independent clause + coordinating conjunction + (some phrase that wasn't an independent clause) : explanation.

Then I realized that the but is not a coordinating conjunction in this case. The but is a preposition introducing a prepositional phrase, so you really have an independent clause + prepositional phrase : explanation. I believe the prepositional phrase in this instance is acting as an adverbial phrase, quantifying the extent of the effectiveness, that is modifying the adjective effective.

Overall we have (I couldn't get this to line up correctly, so I just used line breaks instead.)
The protest was effective,
(Ind. Clause)

but not without cost
(Prep Phrase)

: sixteen people died.
(Explanation)


Does that clear things up?

That seems correct to me now. How did you decide it was no more than a prepositional phrase. I mean , if 'but' is not a coordinating conjunction , then then one of the clause must be subordinating. But without any pre-context , how can we assume that ' The protest was without a cost' is a supporting idea ?

But is a preposition when it is being used to mean except. The sentence in question can be thought of this way

The protest was effective, EXCEPT not without cost: sixteen people died.

In my head I think of the except with extra emphasis and the sentence makes sense. This is how I realize that the but is being used as a preposition and not a conjunction.

Your statement, "if but is not a coordinating conjunction, then one of the clauses must be subordinating." is not correct. You are still talking about a subordinating CLAUSE. "but not without cost" is not a subordinating clause. This is a preposition PHRASE. You end up having an independent clause + preposition phrase (+ colon + explanation) which is a perfectly allowable grammatical structure.

A more accurate line of reasoning might be, "If but is not a coordinating conjunction, then it is probably being used as a preposition and introducing a prepositional phrase." Here I am saying "probably" with the assumption that the but is being used correctly, and not being purposefully used where another grammatical structure would be correct.

The sentence actually looks fine, so the OA and the reasoning used need to be looked at first.

This sentence is listed as Correct in our Foundations of Verbal book. The portion before the colon is an independent clause. It's not necessary that each portion of the clause (set off by commas) be an independent clause in its own right. We could write "The protest was effective, but not without cost" as a complete sentence on its own, so it's an independent clause and the sentence is correct as written.

It is acceptable to say that structurally this sentence is passable as what you have before the colon is no more than a simple sentence with two descriptive elements. The spoilsport, however, is the use of a comma before 'but' giving the feeling that a clause is likely to follow. The second bigger problem is the use of a comma to connect just two items in the list. The serial comma is used as a matter of style only in lists containing more than two items.
However, what about the problem of logic? If the death of sixteen people tries to explain an effective protest, how can it be logical? If some 50 people had died due to the protest, can we call it a very effective protest? Maybe the colon is explaining the costly part of the description but not the effective part. To that extent, the use of the colon is delinquent.
Another point is to whether 'but' is used as part of a preposition? I think otherwise. If it is used as a preposition, there should be a noun after 'but'. What is the noun after 'but'? There is only an adverbial phrase.

Let me clarify a few of these concerns:

*"But" is used as a conjunction here. There is no way to read this as a prepositional phrase.

*Many people will find the comma unnecessary here, but remember that while a comma can be a great structural clue, there aren't as many hard and fast comma rules as most people suspect. For instance, there are many cases in which the GMAT will separate subject and predicate with a comma (usually for clarity), even though that is frowned upon. That doesn't mean that we treat these two terms as a list, so we don't need to think about the serial comma.

*The material after the colon does not have to refer beack to *everything* in the preceding clause. The deaths are a description of the cost, not the effectiveness.