Why did Miss Perumal encourage Reynie to take the advertised test?

Miss Perumal encouraged Reynie to take the advertised test because she recognized his intelligence and potential. Her belief in his capabilities stemmed from her observations of Reynie’s critical thinking skills and problem-solving abilities. By suggesting he participate, she was essentially offering him an opportunity that aligned with his strengths, knowing that he was likely to pass the test.

The other choices do not accurately reflect her motivations. For instance, Reynie's availability as the only student did not influence her decision; rather, she was more concerned with his abilities than a lack of other candidates. Additionally, the encouragement was not due to parental insistence, which would suggest an external pressure rather than a supportive initiative. Finally, the ease of the test was not a factor in her encouragement; she believed in Reynie’s competence and thought he would thrive, regardless of the test's difficulty. Thus, Reynie's intelligence was central to Miss Perumal's support of him taking the test.