Hey GaYoon! 

Thank you for the GREAT question. 

And no worries about sending me questions outside of the course material—I got you! 

You can send me ANY grammar questions at ANY time. 

This is a good one! Here's the foundational English knowledge you need to never get these questions wrong again. 

The reason A), B), and C) are wrong is because of the same reason: they all include two "main verbs" that are not properly formed. 

Let me explain with a simple example to make the point clear: 

"Jack is smart, gets good grades." 

This sounds RIDICULOUS, right? You can say, "Jack is smart" as one sentence. You can say "Jack gets good grades" as another sentence. But you can't say "Jack is smart, gets good grades" because you can't have two main verbs ("is" and "gets") written this way to form a proper sentence. 

You could say, "Jack is smart AND gets good grades," but you need a connecting word like "and" to properly form this sentence. 

SO, taking this foundational knowledge piece and applying it to YOUR question, "The chapter was the subject of a profile appeared in the Navajo Times" makes the SAME mistake. Can you see it? You can say, "The chapter was the subject of a profile" as one sentence. You can also say "The chapter appeared (or "has appeared" or "appears") in the Navajo times" as another sentence. BUT you can't combine the two because if you do, you have TWO MAIN VERBS (A, B, and C) THAT ARE NOT PROPERLY FORMED. 

This is why you need a verb FORM (not a main verb, which is called a verb TENSE) like "appearing." 

-ing verbs are known as a present participle FORM. By itself, an -ing verb (like running, playing, appearing, etc...) is NOT a verb. It may LOOK like a verb, but it does not ACT like a verb. -ing verbs only become main verbs when they get help from other verbs (called "helping verbs") like "is/are/was/were" or "has been/have been/had been." 

For example, 

If I said, "The boy eating pizza." This is NOT a complete sentence because it is missing a MAIN VERB. "Eating" (-ing verb) is by itself, which again, means that it does not ACT like a verb. It only LOOKS like a verb. 

"The boy eating pizza" only becomes a complete sentence when we add a verb like "is" or "has been"

For example, 

The boy IS eating pizza. (COMPLETE SENTENCE because of the verb "is")

The boy HAS BEEN eating pizza (COMPLETE SENTENCE because of the verb "has been").

When -ing verbs are by themselves, they act like modifiers (adjectives), which means they describe nouns. 

For example, 

"The boy eating pizza"

Which boy are we talking about? Are we talking about the boy STUDYING FOR HIS TEST? Nope. Are we talking about the boy DOING HIS HOMEWORK? Nope, not that boy either. We are talking about the boy EATING PIZZA. That is the boy we are referring to. 

Thus, you could form a complete sentence in two ways: 

You could say, "The boy IS eating pizza" (subject = the boy; verb = is)

OR

You could say "The boy eating pizza looks happy" (subject = the boy eating pizza; verb = looks). 

Do you see the difference? =) 

SO, to bring it back to YOUR question, "The chapter was the subject of a profile APPEARING IN THE NAVAJO TIMES" is correct. Can you see how the -ing verb "appearing" describes which profile we are referring to? 

So now, we only have ONE main verb in the sentence when we plug in D (verb = was) and the other verb (appearing) is just a verb form that describes the noun "profile." 

Hope this helps! 

Keep moving forward! You Got This! 

Jin