Help with performance and speed-up question related to number of cores and their areas
The problem in an exam is that you need the answer that is expected from you - something I’d have a real problem with. So keep this solution to yourself. 

Speed up is always hard to calculate - calculating execution time avoids lots of fractions and is equivalent. Assume your task would take one second on one processor X. 

Since S is serial, you need at least S seconds. In that time, your 15 remaining cores can do 15S worth of work. If 15S >= 1-S or S >= 1/16 then all work is done after S. if S &lt;= 1/16 then all cores can work on the task simultaneously, so the work takes 1/16 time. So time = max(S, 1/16) and speed up = min (1/S, 16). Speed up = 4 when S = 1/4. 

You can have four processors of type Y at twice the speed or 1 of type Z at four times the speed. The work takes half of max(S, 1/4), that is max (S/2, 1/8) on 4 processors of type Y and it takes 1/4 on one processor of type Z. 

X is fastest when S &lt;= 1/8. Y is fastest for 1/8 &lt;= S &lt;= 1/2, and Z is fastest for S >= 1/2.