Which is correct? O A. Many cities had to cut down great numbers of stately old elm trees, when they became infected with Dutch elm disease.
O B. Many cities had to cut down great numbers of stately old elm trees. When they became infected with Dutch elm disease.
O C. Many cities had to cut down great numbers of stately old elm trees when they became infected with Dutch elm disease.

O C. Many cities had to cut down great numbers of stately old elm trees when they became infected with Dutch elm disease.

Explanation:

You usually only use commas in between two independent clauses. An independent clause is a sentence that works on its own. It does not need any  more information to understand. It doesn't depend on anything other than itself.

However, you don't need a comma in between an independent clause and a dependent clause. Dependent clauses are just what they sound like: they depend on independent clauses. Dependent clauses are all the background information that is not entirely necessary, but they add detail.

Let's take a look at the other answers:

O A."Many cities had to cut down great numbers of stately old elm trees" is a dependent clause. You can just slap a period at the end it it works just fine. However, there is also a dependent clause with a comma that follows it: ",when they became infected with Dutch elm disease." Remember, you don't follow an independent clause with a comma and a dependent clause. This is a wrong answer.

O B. "Many cities had to cut down great numbers of stately old elm trees. When they became infected with Dutch elm disease." The first sentence is an independent clause, and it works fine. But, the second sentence is a dangling modifier. It describes something, but doesn't show the thing in that sentence. It doesn't make sense.

O C. "Many cities had to cut down great numbers of stately old elm trees when they became infected with Dutch elm disease." This makes perfect sense. It has an independent clause "Many cities had to cut down great numbers of stately old elm trees" and a dependent clause (which needs the independent clause in a sentence with it to work): when they became infected with Dutch elm disease." It doesn't have a comma in between the independent and dependent clauses, so this is the right answer.

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