Another surprising result:

>>> open('temp.txt', 'w').write('ABCDE\nFGHIJ\nKLMNO\nPQRST\nUVWXY\nZ\n')
32
>>> f = open('temp.txt', 'r+')
>>> f.write('test')
4
>>> f.close()
>>> open('temp.txt').read()
'testE\nFGHIJ\nKLMNO\nPQRST\nUVWXY\nZ\n'

>>> open('temp.txt', 'w').write('ABCDE\nFGHIJ\nKLMNO\nPQRST\nUVWXY\nZ\n')
32
>>> f = open('temp.txt', 'r+')
>>> f.write('test')
4
>>> f.read(1)
'A'
>>> f.close()
>>> open('temp.txt').read()
'ABCDE\nFGHIJ\nKLMNO\nPQRST\nUVWXY\nZ\ntest'

The position of the write in the file depends on whether or not there is a subsequent read.