As already stated above, an abstract class in C++ is, by definition, a class which has at least one pure virtual function. The class being abstract means that you can't make instances of it (only of "concrete" classes derived from it), which protects you from calling the "unexistent" pure virtual functions (although technically you can still call them from base class constructor/destructor and get a nasty runtime crash).
There are no explicit "interface" kind of classes in C++, so you are free to provide implementation for some functions in any classes as you wish, regardless of whether the class is already abstract due to some other function being pure virtual.
On a side note, I'd still like to point out one way to make your class abstract without actually making any "real" methods pure virtual. It is enough to make the class destructor pure virtual (note that it is generally a good idea for the destructor of any polymorphic class to be virtual anyway). A minor gotcha here is that in this particular case (only for destructor), you will still have to provide an implementation for it for the linker to be happy. It may look like this:
class A // abstract class
{
public:
virtual ~A() = 0 {} // destructor is pure virtual, but still needs a body
};
class B : public A {}; // concrete class deriving from an abstract class
Also note that in this particular case, class B does not have to explicitly implement its own destructor to become concrete, so, if you'd like it to be abstract too, you'll have to repeat the same trick again (or add some other pure virtual methods to B).