Example 1
Uds quieren saber mi país.
If concur is substituted for saber in this sentence, the meaning switch from knowing exactly what the country is to things about the country.
Example 2
Conozco los servicios que ofrece aquella oficina.
If saber is used instead, then I know what exactly what service they offer.
PS THE EXAMPLES ARE WHAT ARE SAID TO BE CORRECT BY MY TEACHER.
Saber and conocer are not always perfectly interchangeable.
Saber is used when we want to convey knowledge or mastery of skills. Conocer conveys a meaning more like "be familiar with" or "to know".
First example is incorrect. It needs a preposition
Uds. quieren saber de mi país.
Which conveys, "you want to gather information about my country", rather than "you want to know my country" (like, visit for the first time), which would be
Uds. quieren conocer mi país. (you want to visit the country, or learn about it)
For the second example, you could use either saber or conocer and meaning would not change much. Saber would imply that you know the services, but conocer would convey that you have a deeper understanding of them.
When used with nouns, the distinction is actually deceptively simple. With saber, we refer to concrete data about something. In essence, we refer to the attributes of some thing. Let's say we want to talk about a book:
All of these attributes fit nicely in questions in the format ¿Cuál es el/la ______ del libro?. But in this same context, we can't say sé el libro. The book isn't an attribute of something else1.
When we want to refer to the thing itself, rather than the individual facts/data about it, we use conocer which instead of fitting a question like ¿Cuál es el/la ______ de ______? instead answers ¿Cómo es _____? This then expresses knowledge of all the attributes of the thing simultaneously.
For an example of how this plays out in some of the cases where their usage seems to overlap:
¿Sabes el precio de las manzanas?
Here, the thing in question are the apples, and we want to know if you know a literal fact about them — their price. The answer would be a single datum, like $2/kg.
¿Conoces el precio de las manzanas?
Here we want to know if you know cómo es el precio. While that could indeed include the current price, it also includes things like its normal variation, whether that price is higher or lower than normal.
¿Sabes (el nombre de) la capital de Canadá?
Topic: Canada. Just give me the answer. Sí, sé (el nombre de) la capital. Notice the possibility for an implied el nombre de, though its not strictly required.
¿Conoces la capital de Canadá?
Topic: Ottawa. Are you familiar with the city of Ottawa?
This is why with people you almost always use conocer (besides its to meet meaning) with people — people are inevitably asking if you know the person and their corresponding attributes. Rarely is the person himself an attribute of something else, but it's not impossible and then we switch to saber: ¿Sabes el presidente de Guatemala? Es el Gen. Pérez Molino.
1. Note that I refer to this context. The book maybe indeed be an attribute of something else in a different context, for example, the first book published by an author (in which case it becomes an attribute of the author).
Although they are usually words that can not be replaced each other, I think that in the following examples are equivalent sentences.
Quisiera conocer tu nombre.
Quisiera saber tu nombre.
Ya conoces las reglas del juego.
Ya sabes las reglas del juego.
Conozco algunos datos que te pueden interesar.
Sé algunos datos que te pueden interesar.
Él sabe los precios.
Él conoce los precios.
I feel any difference as a user of the language, but I can not specifically recognize it. In the first instance I think the words are interchangeable when informed "abstract data".
