GATE CS 2015 Set 2 Q6 — File Organization and Indexing (B and B+ Trees)

To satisfy the query "greater than or equal to $7$ and less than $15$" (i.e., $7 \le \text{key} < 15$), we first search for the key $7$ from the root and then traverse the leaf nodes sequentially using sibling pointers.

The step-by-step node access is as follows:

1. Root Node (contains 9): Since $7 < 9$, we follow the left pointer to the child node.
2. Internal Node (contains 5): Since $7 \ge 5$, we follow the right pointer to the leaf node.
3. First Leaf Node (contains 5, 7, 8): We retrieve the key $7$ and follow the leaf sibling pointer.
4. Second Leaf Node (contains 9, 11): We retrieve the keys $9$ and $11$, then follow the sibling pointer.
5. Third Leaf Node (contains 13, 15): We retrieve the key $13$ (since $13 < 15$). Since $15$ is not strictly less than $15$, the search terminates here.

Thus, the minimum number of nodes that must be fetched is 5.