On the one hand, some Muslims might agree with this statement because they believe that the Qur'an contains a complete and accurate record of Allah's message to mankind, told to Muhammad through the angel Jibril. If it is the totality of Allah's message, then there is no reason for them to need any other authority, because Allah is the ultimate authority in Islam.
On the other hand, the fourth Shia article of faith is Imamah: belief in the authority of Imams. This suggests that Muslims need other authority, aside from the Qur'an. Sunni Muslims also believe in the authority of Caliphs.
There are also several other holy books as well as the Qur'an. There is the Tawrat (Torah) given to Musa that contains "guidance and light" (Qur'an). There is also the Zabur (Psalms) given to Dawud; "to David we gave the book of Pslams," and the Injil. If Allah gave all of these to mankind, then they must have needed them, not just the Qur'an.
Additionally, Muslims follow the Hadith and Sunnah because Muhammad is a role model to them, so they read the details of his practices to learn how to be good Muslims.
In conclusion, I believe that Muslims need multiple sources of authority, otherwise why would Allah have provided them? Together the teachings of all the holy books and the Imams or Caliphs provides suitable authority for Muslims.
Complete question:
'The Qur'an is the only authority a Muslim needs in life.'
Evaluate this statement [12 marks]