Work done in an irreversible process

I was given a problem to identify whether the given statement is true or false.

And the statement was:

"Consider an ideal gas which is expanded from $$(P_{1},V_{1},T_{1})$$ to $$(P_{2},V_{2},T_{2}).$$ Then, the work done on the gas is maximum when it is compressed back irreversibly from $$(P_{2},V_{2})$$ to $$(P_{1},V_{1})$$ against a constant pressure $$P_1$$".

I concluded that the statement is false, as:

1. It is nowhere mentioned what is greater $$P_1$$ or $$P_2$$ as there is no information on how the expansion process was done.

2. Even if I assume that $$P_1 > P_2$$, still during irreversible compression I can vary the pressure such that the pressure goes beyond $$P_1$$ in the middle of the process but finally returns to the required final state $$(P_{1},V_{1})$$ , which would mean that I am doing more work than what I would be doing if I keep the pressure constant.

However the answer says that the statement is true.

Where am I wrong?

• In my judgment, this problem is woefully underspecified. Feb 14 '19 at 14:53