Q.The average translational kinetic energy of gas molecules depends on

Step 1. Kinetic theory gives two related but distinct quantities: the average kinetic energy of a SINGLE molecule, $\overline{KE}=\tfrac32kT$, which depends only on $T$; and the total kinetic energy (internal energy) of the WHOLE gas sample, $U=N\overline{KE}=\tfrac32NkT=\tfrac32\mu RT$, which depends on both $T$ and the amount of gas present.

Step 2. This question asks about 'the average translational kinetic energy of gas molecules' as a property of the sample -- i.e. the total kinetic energy content carried collectively by the gas molecules present -- which scales directly with $\mu$ (more moles means more molecules, each still carrying $\tfrac32kT$, so the total is proportionally larger) as well as with $T$. …

Distinguish the per-molecule average KE (depends only on T) from the sample's total kinetic energy cont …

• Answering 'only on T', which is true for the PER-MOLECULE average KE but not for the total KE content of a given sample of gas. …