I am following the transmission check.
Shift the lever into the "P" (Parking) position.
Start the engine, and wait until the engine rpm has reduced to normal level (650 - 850 rpm).
With your foot holding down the brake pedal, shift to the "R" (Reverse) position. After only a short delay (0.3 - 0.8 seconds), the transmission should engage (you feel smooth push towards the back) very smoothly, without a jerk. Shift to "N" (Neutral), and the transmission should release. Then shift to the "D" (Drive) position. After the same short delay (0.3 - 0.8 seconds), the vehicle should twitch smoothly forward, also without a jerk. Now, still holding the brake pedal down, try to shift from D to R and vice versa.
! If there is any strong jerk or noise while shifting, avoid buying such a car.
! If there is a long delay (more than 1 - 1.5 seconds) between the moment you shift the lever and the moment the the transmission engages , such a transmission is either too worn or has some defect, avoid buying such a car.