Usage of second sentence posed as a question [closed]

Solution 1:

It's fine. One can omit repeated material that is implied or understood. Unnecessary repetition is tedious and annoys the reader.

He might wait till Christmas to gorge on rum cake. Why should you [wait till Christmas to gorge on rum cake]?

He asked me if I liked music. Did he ask you?

More elaborate example:

I like eating chocolate at night while wearing a hat and coat. Do you?