Solution

LRU page replacement works by replacing the page that has not been used for the longest time. For the reference string 4, 2, 4, 1, 5, 2, 3, 4 with 3 frames, the page faults occur as follows: • Insert 4 (fault), Insert 2 (fault), Access 4 (hit), Insert 1 (fault), Insert 5 (fault, replace 4), Access 2 (hit), Insert 3 (fault, replace 1), Access 4 (fault, replace 5). Thus, there are 6 page faults in total. LRU minimizes page faults compared to other algorithms by always keeping the most recently used pages in memory. Why other options are wrong: A) 3 faults would require the reference string to contain repeated pages with no replacements. B) 5 faults underestimate the replacements required after the first few frames fill up. D) 7 faults occur in algorithms with more aggressive replacements like FIFO. E) 8 faults assume no page hits at all, which is incorrect since some pages are reused before replacement.