(6$4)#(5$3)=2.5
In the equation above, # and $ represent two distinct operations chosen from the set (+. -. *. /). What is the value of (6#2)$4 ?
If $ = +, then (6+4)#(5+3)=2.5; 10#8=2.5, this would not work.
If $ = -, then (6-4)#(5-3)=2.5; 2#2=2.5, this would not work.
If $ = /, then (6/4)#(5/3)=2.5; 1.5#1.67=2.5, this would work if # = *.
Thus, we know that $ = / and # = . This means that (6#2)$4 = (62)/4=12/4=3.
For problems like these, it’s helpful to try setting one of the symbols to an operation and seeing it’s possible for the equation to be true with any of the other operations. Unfortunately, there’s no easy way afaik but trial and error.