Final answer:
The most suitable word to fill in the blank is 'elicit,' as it specifically means to draw out a response, which matches the action of Tom coaxing and questioning his sister to reveal a secret.
Step-by-step explanation:
The correct word to fill in the blank is 'elicit.' The sentence given implies that Tom is trying to gently and persistently draw out a secret from his sister. '
The word extract can mean to remove or take out something forcibly, which doesn't suit the context of the sentence as it suggests a more gentle action. The word acquire means to buy or obtain something for oneself, and obtain similarly means to get or gain something, but both these words lack the nuance of drawing out something through coaxing or questioning.
Therefore, 'elicit' is the right choice here. 'Elicit' means to draw out a response, answer or fact from someone in reaction to one's own actions or questions, which perfectly matches the scenario described within the sentence.