The solution given here is incorrect. The expert chose the smaller of the two options for minimum diameter. While this will ensure the max shear stress is not exceeded, it will fail the angle of twist test. A diamter of $17$mm would allow an angle of twist of $8\mathrm{.}83$ degrees which exceeds the allowable $5$degrees. The correct answer for diameter should be $19\mathrm{.}6$ mm$.$ This provides an angle of twist of $5$ degrees, and a shear stress of $70\mathrm{.}55$ Mpa, which does not exceed the allowable of $165$ MPa.