GATE 2024 Chemical Engineering, Q9 · General Aptitude
The correct answer is C, 2.
Question
In the array shown, each cell of the first three columns has either a cross (X) or a number, as per the given rule: the number in a cell represents the count of crosses among its immediate neighboring cells (left, right, top, bottom, diagonals). The grid (rows 1–4, columns 1–3) reads: Row1: 1, 1, 2; Row2: 2, X, 3; Row3: 2, X, 4; Row4: 1, 2, X. As per this rule, the maximum number of crosses possible in the empty (4th) column is
- A. 0
- B. 1
- C. 2
- D. 3
Official answer: 2
Why
GATE 2024 official key: (C). Let column-4 cells be a,b,c,d (rows 1–4). The constraints from cells (1,3)=2, (2,3)=3, (3,3)=4 (counting already-known crosses at (2,2),(3,2),(4,3)) reduce to: a+b=1, c=0, b+d=1. Maximizing a+b+c+d gives a=1,b=0,c=0,d=1, i.e., 2 crosses.
Explanation cross-checked for consistency. Final answer matches the official IIT answer key.