Is it permissible for a Muslim to talk about his good performance on an exam, or should he remain silent out of consideration for his colleagues who were not successful?

The general rule concerning informing about good performance or remaining silent about it is permissibility. Therefore, it is permissible to inform as a way of acknowledging God's blessings and praising Him, not out of pride. It is also permissible to remain silent to avoid envy and breaking the hearts of colleagues.