I also like this type of questiion. It tests several levels of understanding.
The explanation is also well constructed, however I think it also contains a couple of typos where the 200,000 pages becomes 20,000 part way through.
For level 1 (the lowest intermediate level), one entry is needed for each of the 200,000 pages; these 20,000 entries need 470 pages total.
and
That works out to a total of 20,000 leaf pages, 472 intermediate pages, 1 root page, and 1 IAM page = 20,474 pages.
Dave