To truly test a statements sufficiency, shouldn I try to solve the problem for the specific value asked?
No. You don’t get extra points on the GMAT for performing needless calculations. Knowing that the information is sufficient is enough. For example, if you have the equation 2x+12y=1,220 and are asked “What is the value of y,” you don’t actually need to solve for y — just find out if you CAN solve for y. If statement 1 says that x=32, then you know you CAN plug x into the equation to find y. You don’t need the exact value of y. This will work in many different ways on the GMAT, but the idea is the same in all cases: do only the calculations that are necessary.