If I were you, I'd look up the electrode potential values and when you've found them report back here with your conclusion and we'll confirm your thoughts.
I have the values myself, but it will be a much better learning exercise if you take an active role in it.
Manganate(assumeVII) is a really rather strong oxidising agent. MnO4− + 8 H+ + 5 e− <-> Mn2++ 4 H2O E = +1.51 V Zinc metal isa pretty good reducing agent. Zn2+ + 2 e− <-> Zn(s) E = −0.76 V