A double-start thread of pitch 1.75 mm is to be cut on the lathe in the figure. The spindle drives the stud shaft through fixed 30T/60T gears in the headstock; change gear A on the stud shaft drives change gear B on the lead screw through an idler (a simple train; the idler only reverses direction). The lead screw is single start with 6 mm pitch. Determine (a) the required change-gear tooth ratio T_{A}/T_{B} (driver teeth ÷ driven teeth) (answer as a ratio, dimensionless) and (b) the number of teeth on driver gear A, chosen from the available set on the figure (answer in teeth).