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Not all extant versions of the Book of Genesis say that Methuselah died the year of the Flood. Wikipedia gives the following:
Of these, only the Masoretic text and the Samaritan text have Methuselah die in the year of the Flood. I believe the Samaritan text is not original, because neither his age when his son was born (67 years) nor his age at death is divisible by the 'magic' number 17, whereas in the Masoretic they are.
The Septuagint (Vaticanus) can be ruled out because there is no mention of Methuselah on the ark, and he could not have survived otherwise. This seems a pious attempt to avoid the appearance that a righteous man died in the Flood. The Septuagint (Alexandrinus) is technically possible, but is more likely another pious attempt to avoid the appearance that a righteous man died in the Flood. So, the Masoretic text is probably original.
Wilfred Shuchat explains in The Creation According to the Midrash Rabbah, page 124, that according to this midrash, the Flood was delayed by seven days to allow a period of mourning for Methuselah. Midrashim are a Jewish method of interpreting biblical stories, and were written down in the early centuries CE.