Even besides the syntactic errors your code won't compile. You will get the following error:
Type 'MyNamespace.ABC' already defines a member called 'GetAge' with the same parameter types
This is because the compiler will merge all parts of a partial class into a single class as
Section 10.2 of the C# Language Specification explains:
With the exception of partial methods (§10.2.7), the set of members of a type declared in multiple parts is simply the union of the set of members declared in each part. The bodies of all parts of the type declaration share the same declaration space (§3.3), and the scope of each member (§3.7) extends to the bodies of all the parts.
C# won't allow to have to methods with the same names and with the same number and types of arguments within one single class. This is stated in section 1.6.6 of the specification:
The signature of a method must be unique in the class in which the method is declared. The signature of a method consists of the name of the method, the number of type parameters and the number, modifiers, and types of its parameters. The signature of a method does not include the return type.
There is one option though to add the declaration of a method into one part of a partial class and the implementation into another: Partial Methods. You can read more about them in Eric Lippert's blog post on that topic:
What's the difference between a partial method and a partial class?