The policeman examined the closed doors of the shops . . . . . . . . a small stick. A. in B. by C. from D. with

The correct answer is D. The policeman examined the closed doors of the shops with a small stick.

The other options are incorrect because:

• A. “in” is not a logical preposition to use in this context. The policeman is not examining the doors “in” a small stick.
• B. “by” is not a logical preposition to use in this context. The policeman is not examining the doors “by” a small stick. He is using the stick as a tool, not as a means of transportation.
• C. “from” is not a logical preposition to use in this context. The policeman is not examining the
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  doors “from” a small stick. He is not looking at the doors from a distance, he is examining
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  them up close.

The preposition “with” is the most logical choice because it indicates that the policeman is using the small stick as a tool to examine the doors.