GATE CS 2024 Set 2 — Question 10
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
In the array shown below, each cell of the first three rows has either a cross (X) or a number.
The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is
Correct answer
(A) 11
Solution
Let the cells in the last row (Row 4) be denoted as . We are given that the last row has no crosses, so all cells in Row 4 contain numbers. A number in a cell represents the count of neighbors (horizontal, vertical, diagonal) that do not contain 'X'.Grid Context:
Row 3:
Row 4: (All are numbers, i.e., not X)Calculating (Corner):
Neighbors: (Not X), , (Not X).
Count of non-X neighbors = 2.
Calculating (Edge):
Neighbors: (Not X), (Not X), , (Not X), (Not X).
Count of non-X neighbors = 4.
Calculating (Edge):
Neighbors: (Not X), , (Not X), , (Not X).
Count of non-X neighbors = 3.
Calculating (Corner):
Neighbors: (Not X), (Not X), .
Count of non-X neighbors = 2.
Sum:
Sum = .
Row 3:
Row 4: (All are numbers, i.e., not X)Calculating (Corner):
Neighbors: (Not X), , (Not X).
Count of non-X neighbors = 2.
Calculating (Edge):
Neighbors: (Not X), (Not X), , (Not X), (Not X).
Count of non-X neighbors = 4.
Calculating (Edge):
Neighbors: (Not X), , (Not X), , (Not X).
Count of non-X neighbors = 3.
Calculating (Corner):
Neighbors: (Not X), (Not X), .
Count of non-X neighbors = 2.
Sum:
Sum = .
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