Answer:
B. Decrepit
Step-by-step explanation:
Well, they're asking you for a negative connotation, correct?
If you don't know what a connotation is, it's basically the feeling involved with a word. For example, two words that technically mean the same thing are: stench and aroma. They both mean a smell, but stench has a negative connotation (like you wouldn't say "Her perfume had a gorgeous stench.") and aroma has a positive connotation ("Her perfume had a gorgeous aroma." fits much better).
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So, using inferencing, you want to find a sentence that sounds negative. Let's go through each answer choice together:
-A. Aging
Well, aging is actually a word that has a neutral connotation. It could be used perfectly well in both "Her aging skin sagged" and "Her aging skin still shone". Even if you're not sure about the connotation of aging (it is the only answer choice that doesn't show up in the passage after all), you can skip this one and go look at the others.
-B. Decrepit
Now, this is where we can look at the sentences before and after the word to see if they're being used positively or negatively. We can see that the passage tells us that decrepit is being used by someone who wants to demolish the library. If this isn't enough evidence, the following sentence states that "'It detracts from the downtown.'" Doesn't sound like this guy likes the library very much, huh. Therefore we can rule decrepit as having a negative connotation. We'll still go through the other ones to see why they aren't the answer.
-C. Venerable
Let's look at the sentence venerable is being used in. "'That venerable edifice had many distinguished guests, including a U.S. president.'" They also tell you that the man saying this believes the library should be saved. That's why venerable can be ruled as having a positive or maybe even neutral connotation.
-D. Vintage
Vintage is used in the sentence. "'The library is a historic treasure. It has elements of vintage architecture.'" Calling the library a historic treasure sounds positive, no? That is why vintage will also have a positive/neutral connotation.
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That's all for explanations! I hope your understanding of why the answer is correct has improved after reading my lengthy explanation!