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GATE CSE 2025 Session 1 Q21: Effect of inserting 23 into a full B+ tree

Question

Consider the following B+B^+ tree with 5 nodes, in which a node can store at most 3 key values. The value 23 is now inserted in the B+B^+ tree. Which of the following option(s) is/are CORRECT?

B+ tree: root with keys 6, 12, 19 and four leaves with keys (1, 4, 3), (7, 9, 10), (13, 15, 17) and (20, 21, 22)
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Answer: B, D (official GATE 2025 final answer key)

Concept used: B+ tree insertion: a full leaf splits and pushes a key up; a full parent splits in turn.

First step: 23 goes into the last leaf (20, 21, 22), which is already full, so it splits and sends a key to the root, which is also full.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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