The first day of this month is not Tuesday. So may be first Tuesday is 3^rd. We let's try: 

Tuesday: 3              10              17              24              31

but 31^st is last day of a month has 31days => Unsatisfactory

So first Tuesday of this month is 2^nd

We let's try too.

Tuesday: 2               9               16               23               30

So the last Tuesday of this month is 30^th may be last day of this month. But the topic talk last day isn't Tuesday. Angain have in a year will has 7 months have 31 days.

So the last day of the month is 31 

The last day of the month is 31.

Please for me! 

I'd add the answer more from Dao Trong Luan's answer:

Because 30 is Tuesday (1) => The month has 31 days. (2)

From (1) and (2) => The last day of the month is Wednesday.

Answer is: I don't know