In this vocabulary analogy, Careful is to Cautious as Boastful is to which describing word that best matches its meaning?

Introduction / Context:
This verbal analogy tests understanding of relationships between adjectives, especially synonym and meaning based connections. The pair Careful and Cautious is given as a model relationship. You must decide which describing word has a meaning that matches Boastful in a similar way, using standard English usage and exam level vocabulary.

Given Data / Assumptions:
1) Careful and Cautious both describe someone who acts with attention and avoids risk.
2) Boastful describes a person who talks too much about personal achievements or qualities in a proud way.
3) The options are Surprisingly, Happily, Arrogant, and Humble.
4) The correct option must be a word whose meaning stands in a similar relationship with Boastful as Cautious stands with Careful, that is a close meaning match.

Concept / Approach:
The key concept is that the first pair is a synonym based pair. Careful and Cautious are not opposites, but rather very close in meaning. Therefore, the second blank must also be filled with a near synonym of Boastful. People who are boastful are often described as arrogant, proud, or conceited because they exaggerate their importance. So we must search for a word that captures this proud and self important behaviour.

Step-by-Step Solution:
Step 1: Confirm that Careful and Cautious are near synonyms. Both words describe behaviour where a person takes care to avoid mistakes or danger. Step 2: Identify the main idea of Boastful. It refers to someone who brags and talks too proudly about self or achievements. Step 3: Examine each option. Surprisingly is an adverb about how unexpected something is. Happily is an adverb about doing something with happiness. Step 4: Arrogant describes a person who has an exaggerated sense of self importance, very close to the attitude of someone who is constantly boastful. Step 5: Humble describes a person with a modest view of self. That is more opposite to Boastful and therefore does not follow the synonym pattern of the first pair. Step 6: Since the first pair uses similar meaning, the second pair should also be based on similarity, so Boastful goes with Arrogant.

Verification / Alternative check:
Rephrase the analogy as synonyms. Careful is similar to Cautious. Boastful is similar to Arrogant. This is natural English usage and appears in many example sentences. None of the adverbs Surprisingly or Happily describe character in the same way. Humble is almost an antonym, so it would create a different relationship type and break the pattern that the question models.

Why Other Options Are Wrong:
Surprisingly just describes an unexpected manner and has no link to pride or self praise. Happily is related to emotional state, not boasting. Humble is the opposite personality, someone with low or moderate opinion of self, not one who brags. Since Careful and Cautious are not opposites, choosing an opposite for Boastful would make the analogy inconsistent.

Common Pitfalls:
A common pitfall is to think that analogies always use opposites, and therefore pick Humble. However, many analogies use synonym pairs instead. Always check the relationship in the first pair carefully before deciding the nature of the second pair. Here, that check clearly shows that the first pair are near synonyms.

Final Answer:
The best describing word that completes the analogy is Arrogant. Therefore, Careful is to Cautious as Boastful is to Arrogant.