Using the Occam's Razor rationale, the Q theory just doesn't hold up under any kind of logical analysis. The early Church fathers were certainly not all of one accord of what manuscripts should be included as authentic in what we now have as the "New Testament", and finally agreed on those that could be tied to a) somebody who was there and who had first hand contact with Jesus of Nazareth or b) somebody who was an immediate disciple to one who had first hand contact with Jesus of Nazareth. It just isn't reasonable that at least one of these would not have objected to extra curricular or erroneous accounts given by others and would have questioned the so-called Q theory that would not have met the basic test.
The Gospels are not intended to be chronological history and they leave a lot to the imagination for us more than 2000 years later--the writers no doubt saw no reason to elaborate on what was common knowledge at the time. They were certainly pulled together from multiple sources and edited into a coherent form to be read in the newly forming Christian congregations. And, as is the case in the Old Testament, the 'editors' almost certainly used some editorial license in how the information was put together.
Mark was the earliest of the three synoptic gospels written, the shortest, and the most succinct. Matthew and Luke almost certainly were familiar with Mark and used it as their starting point as both contain material from Mark, some of it essentially verbatim. There is nothing in Mark that is not also included in some way in Matthew and Luke. But both had more to say than Mark said. There is a lot of material in Matthew that is unique to Matthew, and material in Luke that is unique to Luke, and both very occasionally disagree with Mark and/or each other. But there is no place that Matthew and Luke agree with each other against Mark.
John, also considered one of the four Gospels, was the among the oldest documents contained in the New Testament and is so different from the others, it is usually considered by itself.
Most theologians view the Beatitudes as pericopes (per - ick' - oh - pees) or short sayings or teachings of Jesus that people could hold onto and commit to memory. The odds are good that they were not restricted to one sermon or Mark and Luke would have more likely included them in that way.
Interesting stuff if you are a 'theology nerd' and like to get into the nitty gritty of theological studies.
