Fill in the missing value.
The pattern is a network/tree of circles connected by lines where the numbers follow an arithmetic relationship. The values shown are:
Top node: 8
Second level left: 2, right: 4
Third level: 1, _, 2, 5
(The missing value is at position indicated by the blank)
The missing value is: ___
GATE 2015 · General Aptitude · Number Relations · medium
Answer: 3
Determine the pattern rule: From the figure: the top node (8) connects to second-level nodes. Second-level node values 2 and 4 are direct branches from a middle connector or sub-trees. Checking: 1 + ? = 4 (left sub-tree) and 2 + 5 = 7... The network actually shows: each node equals the sum of the two nodes below it. Node with value 4: its children are ? and something. Node with value 8 at top: structured such that 8 can be traced to 1, ?, 2, 5 at the bottom. The official answer is 3, consistent with: if the pattern groups into (1+?) and (2+5)=7 feeding into middle nodes, and those feed into 8: top node 8 = left branch + right branch where left = 1 + ? and right uses 2 and 5, and left branch value = 2+? feeds to give 8 total.
Apply rule to the unknown branch: The node above the missing value has value 4. Its two children are 1 and the missing value. So: 4 = 1 + missing => missing = 4 - 1 = 3.