Breaking down the statement: "Her only brother's mother is the only child of my grandmother."
Let's identify "the only child of my grandmother":
- Ajay's grandmother has only one child
- This only child must be Ajay's mother (or father, but one parent must be the only child)
- So "the only child of my grandmother" = Ajay's mother
Now identifying "her only brother's mother":
- The girl has only one brother
- Her brother's mother = the girl's mother
- So "her only brother's mother" = the girl's mother
Combining both parts:
The girl's mother = Ajay's mother
Since Ajay and the girl share the same mother, they are siblings.
Therefore, Ajay is the girl's brother.
The answer is Option 1: Brother.