B-MAT(ビーマット) | ２つの「考える」で学力センスを鍛えるためのシステムです。

It is a typical item to build up the logical thinking ability and hypothesis think ability through game play.
Although it is OK to make a figure and think just for solving a question, here, since, addition to a high level of the logical thinking ability and the hypothesis think ability, it also works as training to enhance imaginary ability, let participants solve questions without making a figure.

If the purpose of the training is to solve a problem with speculative computation, to think while drawing a figure is all right, but as long as the training is to enhance the imagination ability as well as high-level logical & hypothetical thinking, you should become able to solve problems without drawing figures whatsoever.
However, when you found the problem too hard to solve or got wrong answer, you can draw a figure to confirm correct answer.
By doing this training, you can build the basis for your ability to solve intricate problem at which you will worry in the future and which are so difficult that "even if you wanted to draw a figure, there is no way of drawing!"

Logical thinking abilities
Hypothetical abilities
Imaginary ability