Broadly, an Online Exam or Institute management solution can be divided into two major components, Software and Server Environment. But it is not just a Software or a Server in isolation...the solution depends on an optimal mixture of several parameters.
Software capability and Environment capability are 2 different things. The same Online Exam Software can handle 10 or 10000 candidates if it is supported by a suitably capable Application Server having proportionate resources, appropriate Data Transfer Bandwidth at Server and good internet bandwidth at user end.
Besides buying the same software, the type of need determines the server infrastructure. If you have a low-end requirement with minimum budget, like a coaching center distributing free tests, so accordingly cloud deployment with basic bandwidth that support 0-10 concurrent users should be opted. Increasing bandwidth to keep provision for entertaining higher number of simultaneous 25-50 users will be a wastage of resources in anticipation of maximum load. It is better to plan workload by time sharing.
However, if your tests are of critical importance even for 25 students, you must buy surplus bandwidth at the server level and ensure candidates appear in a Lab, or have a broadband connection at home or 3G/4G connection in smart device.
If you plan to conduct tests of more number of candidates like 50-100, then you should opt for an in-house server in the lab, eliminating all dependency on internet and bandwidth. Because if server is on cloud and users in lab, that lab must have consistent internet with high bandwidth is the range of 10+ MBPS. If the server is on cloud and the users are distributed in their homes, cyber café or using their smart devices with mobile internet, they will have different experiences depending on their internet.