This paper investigates and considers factors that affect success in solving a stand-alone geometrical problem by 182 students of the 7th and 8th grades of elementary school. The starting point for consideration is a geometrical task from the National Secondary School Leaving Exam in Croatia (State Matura), utilising elementary-level geometry concepts. The task was presented as a textual problem with an appropriate drawing and a task within a given context. After data processing, the key factors affecting the process of problem solving were singled out: visualisation skills, detection and connection of concepts, symbolic notations, and problem-solving culture. The obtained results are the basis of suggestions for changes in the geometry teaching-learning process.