Using "qué tan" vs. "qué" or "hasta qué" in questions

Question

I have a question about asking questions :)

When asking questions about the degree of an adjective, such as "how far is it?," what is the difference between the following:

1. ¿Qué tan lejos está?
2. ¿Hasta qué lejos está?
3. ¿Qué lejos está?
4. ¿Cuán lejos está?

Is #3 OK, informal, or is it completely incorrect?

I have heard native spanish speakers say questions like #3 before (qué alta, qué bonita, qué barato, etc), but I have started to notice that #1 seems more common in writing.

If #1 and #3 are both OK, is there a slight difference in meaning that is provided by adding "tan?"

Am I correct in believing that #4 sounds overly formal or maybe archaic?

Answer 1

From the point of view of a Spain Spanish speaker:

1. ¿Qué tan lejos está?: Correct, but it sounds kind of Latin American to me. See qué 4,g.
2. ¿Hasta qué lejos está?: Plainly incorrect. I don't even use this form orally. If you want to use a structure with "hasta", you can maybe try:

¿Hasta qué punto está lejos? (to which degree is it far?)

3. ¿Qué lejos está?: I believe this is incorrect, it doesn't sound right to me in an interrogative sentence. However the DPD says that cuán (the actual adjective to use, see #4) tends to be replaced with qué in exclamative sentences:

[...] hoy es más normal, en estos casos, el empleo de qué (→ qué, 1.3). [...]

4. ¿Cuán lejos está?: Correct, but very formal, I've seen it only in the written form or in very formal discourse, I would never use it in a conversation. Although, technically, this is the correct interrogative adjective when trying to measure the degree of an adjective.

 

However, instead of all the forms that you propose, I would use the following:

¿Cómo de lejos está?

This is correct and at least in Spain it sounds normal, neither formal nor informal.

Alternatively, you can rephrase the sentence in order to avoid this kind of structure:

¿Está muy lejos?

Answer 2

Now, from a Colombian speaker

2 and 3 are totally incorrect, as @Alicia says, so we have the other choices

4 is used in formal and literary, but is not forbiden in spoken ways

1 is the natural way (in Latin America)

In the 1st case tan is a short way of tanto in its 19th significance, when is used to compare. You could heard sentences like 3, not as questions but as affirmations (que alta esa jirafa, que bonita esa mujer, que barato ese celular)

The option suggested by Alicia, I only see some question like that reciently in a website and i belive that was a mistake from an automatic translator... ('How to' = 'Cómo de' without '¿') but now i know that is the usual way in Spain...