GATE CSE 2024 Session 2 Q64: Min and max page-table pages for 2000 pages in a 2-level table

Consider a 32-bit system with 4 KB page size and page table entries of size 4 bytes each. Assume 1 KB = $2^{10}$ bytes. The OS uses a 2-level page table for memory management, with the page table containing an outer page directory and an inner page table. The OS allocates a page for the outer page directory upon process creation. The OS uses demand paging when allocating memory for the inner page table, i.e., a page of the inner page table is allocated only if it contains at least one valid page table entry.

An active process in this system accesses 2000 unique pages during its execution, and none of the pages are swapped out to disk. After it completes the page accesses, let X denote the minimum and Y denote the maximum number of pages across the two levels of the page table of the process.

The value of X+Y is ________