Temperature of ideal gas in a cylinder 
12 An ideal gas is contained in an insulating cylinder fitted with a piston, as shown.

The piston is suddenly moved inwards so that the volume of the gas is reduced. What happens to the temperature of the gas?
A It increases because the gas molecules bounce off the piston at higher speeds.
B It increases because the gas molecules collide with each other more often.
C It stays constant because $\mathrm{pressure \times volume}$ is constant for an ideal gas.
D It stays constant because the cylinder is an insulator.

Why is option A and C wrong or correct?
My attempted answer: A: is plausible as if the piston is suddenly moved inwards, the gas molecules bounce off the piston at higher speeds. Since temperature is proportional to rms speed, temperature increases.
Or, based on 1st law of thermodynamics, the piston suddenly moved in. So means $Q = 0$ because there is no time for the heat transfer. Since compression, $W$ is +ve, so $U$ is +ve. That implies $T$ increases.
C: as $P$ increases, $V$ decreases.
Please help to correct my understanding!
A: When the piston is moved suddenly, then the pressure on the piston is greater than the average pressure in the chamber: the process is not reversible and some energy is lost to fluid as opposed to an adiabatic reversible process.
According to the first principle, and because the heat transfer to the system is 0 (insulating cylinder) the internal energy of the system increases. It implies that the temperature of the gas increases over time.
What do you think about the other answers ?
A: The answer is B.
Pushing the piston is doing work against the pressure exerted by the gas. By doing so, it increases the internal energy within the system and part of it transfers into KE and thus increases the temperature.
