SOLUTION: The numbers 1, 3, 4, 6 and 8 are placed in boxes A, B, C, D, and E so that the resulting product of the 2- and 3-digit numbers below is between 23000 and 25000. What is the largest

Since we are trying to make AB large as possible, 
we first see if A can be 8.  So let's see what
happens when we assume A = 8.

   

But 





Then  and 
      and 
      and 

That's not possible.  

So A cannot be 8.

So we try A=6
    
We see if it is possible to make AB as large as possible
by making B=8

Then 
     

We can do that only by making CDE = 341

Answer:  , so the largest possible 
         value for AB is 68.

Edwin