Sentence completion: the sentence given below has a blank. Choose the phrasal verb that best completes the sentence. How did you __________ this rare book?

Introduction / Context:
This question tests your knowledge of phrasal verbs formed with come. Phrasal verbs are combinations of a verb and a particle such as by, with, to, or at, and they often have meanings that are different from the simple verb alone.

Given Data / Assumptions:

• Sentence: How did you __________ this rare book.
• Options: come with, come to, come by, come at.
• The context suggests someone is asking how another person obtained or managed to get a rare book.

Concept / Approach:
Come by as a phrasal verb means to obtain or acquire something, especially something rare or hard to get. For example, It is difficult to come by honest friends or How did you come by so much money so quickly. This fits perfectly when we speak about a rare book.

Step-by-Step Solution:
Step 1: Identify the idea implied by the sentence: the speaker wants to know how the person obtained the book. Step 2: Recall that come by means obtain or get, especially something rare. Step 3: Test the options in the sentence: How did you come with this rare book, How did you come to this rare book, How did you come by this rare book, How did you come at this rare book. Step 4: Conclude that only come by gives a natural and correct meaning.

Verification / Alternative check:
Check dictionary usage or examples: to come by something equals to get something, often by chance or effort. When speaking about a rare item, we commonly ask How did you come by it. None of the other phrasal combinations are used in this sense, which confirms come by as the correct answer.

Why Other Options Are Wrong:

• come with: Means to accompany or to be included with something, as in This phone does not come with a charger.
• come to: Can mean regain consciousness or reach a total amount, not obtain a rare book.
• come at: Means to move towards or attack, as in The dog came at him aggressively.

Common Pitfalls:
Learners often try to guess from literal meanings of the prepositions and may choose come with or come to. Phrasal verbs, however, are idiomatic and must be learned as fixed expressions. Exposure through reading and listening is the best way to master them for exam use.

Final Answer:
Correct option: come by.