Is there a word or term to describe a statement that implies a question so sufficiently that the question is not actually included?

Solution 1:

Wikipedia uses the term declarative questions, splicing form and function:

Languages may use both syntax and prosody to distinguish interrogative sentences (which pose questions) from declarative sentences (which state propositions). Syntax refers to grammatical changes, such as moving words around or adding question words; prosody refers here to changes in intonation while speaking.

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Intonation patterns characteristic of questions often involve a raised pitch near the end of the sentence. In English this occurs especially for yes–no questions; it may also be used for sentences that do not have the grammatical form of questions, but are nonetheless intended to elicit information (declarative questions), as in "You're not using this?"

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The use of intonation to mark yes–no questions is often combined with the grammatical question marking described in the previous section. For example, in the English sentence "Are you coming?", rising intonation would be expected in addition to the inversion of subject and verb. However it is also possible to indicate a question by intonation alone. For example:

You're coming. (statement, typically spoken with falling intonation) You're coming? (question, typically spoken with rising intonation)

A question like this, which has the same form (except for intonation) as a declarative sentence, is called a declarative question.

Solution 2:

I would say that they are 'implied questions' and quite correctly end with question marks. It is a normal way of speaking, and yours is the normal way of reproducing that speech in written form.

Solution 3:

I agree with WS2's label of implied questions, but these are often conveyed even when the context alone does not dictate that they are questions. Rather the tone of the response marks them as interrogatories. Consider this spoken dialog:

John: You are mean to me.

Peter: I'm the bad guy?

The response is not interrogatory in form, but when spoken, there would be a heavy emphasis on I'm and a rising inflection on guy, which together would suggest both a question and a likely negation implied by the speaker.

In written form, the question mark guides the reader as to what is really being said. Without the spoken inflection or the written question mark, the sentence would be a declaratory admission rather than an implied interrogatory denial.