The symbol (said to have been adopted as being the initial letter of the German Quelle, source) for that material common to both Matthew and Luke of about 230 verses, mostly sayings of Jesus, which is not from Mark. It is assumed that there was a stock of Jesus' teaching which was preserved in an early community. Some modern advocates of the Q hypothesis suggest that it shows Jesus to have been a teacher of aphoristic, quasi-Gnostic, quasi-Cynic wisdom, but that, when edited into the gospels of Matt. and Luke, it was given a change of direction and emphasis. Even so, many of the sayings in Q do resemble some ancient Near Eastern Wisdom writings. In due course Q had become available to these two evangelists and each incorporated it (in different ways) into their gospels. The classical exposition of this solution to the ‘synoptic problem’ by the English scholar B. H. Streeter (1924) held that Q was a now lost written document. There is, however, a small group of NT scholars who reject the ever-burgeoning complexity of the Q hypothesis altogether on the ground that, where the three gospels run in parallel, Luke sometimes follows Matt. rather than Mark. This suggests the possibility that Luke knew and used Matt. to supplement his use of Mark, rather than the hypothetical, non-existing Q. Another theory is that Matthew, after first writing up Jesus' sayings in Aramaic, then (having seen Mark) revised his existing Matt. into Greek; finally Luke wrote the third gospel with Mark available to him and Matt. had been previously read.
Defenders of the Q hypothesis argue, for example, that Matt. 3: 7–10 and Luke 3: 7–9 is a Q passage. Matt. has deliberately introduced the Pharisees and Sadducees in verse 7 (omitted by Luke) to provide a polarized audience; Luke is less polemic: but opponents of the Q hypothesis suggest that Luke has omitted the opposition simply because he is less hostile to those groups than Matt., and preferred to introduce ‘the crowds’ (verse 7) because, in his theology, the Baptist was preparing the whole nation for the coming of Jesus. And so, on this view, Luke knew and altered Matt.