One sentence is true

One sentence is true

Talking to the physics teacher at the faculty science party, he told me the following:

A) I have more than 10 brothers.
B) I have less than 10 brothers.
C) I have at least 1 brother.

If only one of these 3 sentences is true: How many brothers do I have?


There are two possible solutions:

I have 10 brothers and the only correct phrase is C.
I have no brother and the only correct phrase is B.