First, if this is exactly the sentence on the exam and not your translation, it's ambiguous. It could mean that OOD is one possible way to create and use ADT, or that creating and using ADTs requires OOD.
Furthermore, ADT can mean two things: abstract data type or algebraic data type. The two concepts are completely different but are often confused. An algebraic data type is a type that is defined by its recursive structure, or equivalently by the ways to build an object of that type. An abstract data type is a type that is defined by its properties, with the way to build objects remaining hidden.
The second interpretation — that you need OOD for ADTs — is definitely false. There are programming languages which have no object orientation whatsoever but have ADTs in one sense or the other or both. Standard ML is a prime example: record and sum type definitions provide algebraic data types, while the module system provides abstract data types.
The first interpretation — that ADTs can be implemented with OOD — is contentious, because it depends on terminology that isn't standard. In typical languages that provide objects, you can build algebraic data types: define several implementations of a class to make a sum type, and put multiple fields in a class to make a product type. However this is not intrinsic to object-oriented programming. Regarding abstract data types, most object-oriented languages provide some kind of abstraction facility by hiding the implementation of a class under some interface. However, this isn't intrinsic to OOP: the key feature of objects is inheritance, and you can have inheritance without any abstraction whatsoever.
The question may be making a difference between object-oriented design and object-oriented programming construct, but OOD isn't really on the same plane as ADTs.
All in all this is a poorly-worded exam question. The connection between OOD and ADTs is an interesting subject, but the question is not phrased in a meaningful way.