Final answer:
It is false that the Psalms are rarely quoted in the New Testament, as they are frequently referenced. Early Methodists were indeed methodical, making that statement true. The myth of Quetzalcoatl does not rely on sources contemporaneous with the Aztec conquest, making that statement false.
Step-by-step explanation:
The statement 'The Psalms are rarely quoted in the New Testament' is false. The Psalms are one of the most frequently quoted books in the New Testament, serving as a key bridge between the Jewish scriptures and Christian writings, reflecting the common heritage of Christianity with Judaism.
For the second question, Early Methodists were indeed called Methodists because they were methodically and systematically applying their religious practices and beliefs. Thus, the statement 'Early Methodists were called that because they were so methodical' is true.
Last but not least, the myth of Quetzalcoatl does not rely solely on contemporaneous sources with the conquest of the Aztec; much of it comes from oral traditions and accounts written after the conquest. Therefore, the statement 'The myth of Quetzalcoatl relies on sources that are contemporaneous with the conquest of the Aztec' is false.