Problem: How does the sentence end?

Christopher was ashamed he broke Logan's lamp, after 
Answer: Logan discovered the broken pieces under the couch.

Problem: How does the sentence end?

Isn't it wiser to buy a reusable filter than a disposable filter? I think the 
Answer: disposable filter is expensive in the long run.

Problem: How does the sentence end?

Rebecca was young when they left home and Monica was older because 
Answer: Rebecca had a bad home life.

Problem: How does the sentence end?

The screw put a deeper scratch in the wall than the nail, because the 
Answer:
nail was duller.