GATE ME 2023 Set 1 — Question 5

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MCQ+1 / -0.33MediumDeduction & InductionAnalytical AptitudeGeneral Aptitude

General Aptitude → Analytical Aptitude → Deduction & Induction

Last updated 5 September 2026

Question

The symbols O, *, Δ, and □ are to be filled, one in each box, as shown below. The rules for filling in the four symbols are as follows. 1) Every row and every column must contain each of the four symbols. 2) Every 2\times2 square delineated by bold lines must contain each of the four symbols. Which symbol will occupy the box marked with ‘?’ in the partially filled figure?

Correct answer (B) Solution Let's analyze the constraints on the symbol in the cell marked with '?' based on the provided rules and the partially filled grid. The grid can be interpreted from the image as follows (let G(row, col) be the cell content): G(1,3) = Δ G(2,2) = O G(2,3) = G(3,1) = G(3,4) = □ G(4,2) = Δ G(4,3) = O This question is known to be flawed as any logical deduction from the given state leads to a contradiction. For example: From Column 3, which contains Δ, *, and O, the missing symbol is □. So, G(3,3) must be □. Now, consider the Bottom-Right 2x2 square (cells G(3,3), G(3,4), G(4,3), G(4,4)). We have G(3,4)=□ and G(4,3)=O. Our deduction gives G(3,3)=□. This means the 2x2 square contains two □ symbols, which violates Rule 2. Due to this flaw, there is no valid solution. However, if we attempt a direct elimination for the '?' cell, a different conclusion is reached: 1. Row Constraint: The '?' is in Row 1, which contains Δ. So, ? \neq Δ. 2. Column Constraint: The '?' is in Column 1, which contains at G(3,1). So, ? \neq . 3. 2x2 Square Constraint: The '?' is in the top-left 2x2 square, which contains O at G(2,2). So, ? \neq O. 4. Following this direct logic, the only remaining symbol is □. This contradicts the official answer key. The official answer is '*', which can only be reached if one of the premises above is incorrect (i.e., there is a typo in the grid diagram). For instance, if the symbol at G(3,1) was not '*' but '□', the logic would lead to '?' being '*'. Given the ambiguity, the question is considered flawed, but the intended answer was B. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (B) Solution Let's analyze the constraints on the symbol in the cell marked with '?' based on the provided rules and the partially filled grid. The grid can be interpreted from the image as follows (let G(row, col) be the cell content): G(1,3) = Δ G(2,2) = O G(2,3) = G(3,1) = G(3,4) = □ G(4,2) = Δ G(4,3) = O This question is known to be flawed as any logical deduction from the given state leads to a contradiction. For example: From Column 3, which contains Δ, *, and O, the missing symbol is □. So, G(3,3) must be □. Now, consider the Bottom-Right 2x2 square (cells G(3,3), G(3,4), G(4,3), G(4,4)). We have G(3,4)=□ and G(4,3)=O. Our deduction gives G(3,3)=□. This means the 2x2 square contains two □ symbols, which violates Rule 2. Due to this flaw, there is no valid solution. However, if we attempt a direct elimination for the '?' cell, a different conclusion is reached: 1. Row Constraint: The '?' is in Row 1, which contains Δ. So, ? \neq Δ. 2. Column Constraint: The '?' is in Column 1, which contains at G(3,1). So, ? \neq . 3. 2x2 Square Constraint: The '?' is in the top-left 2x2 square, which contains O at G(2,2). So, ? \neq O. 4. Following this direct logic, the only remaining symbol is □. This contradicts the official answer key. The official answer is '*', which can only be reached if one of the premises above is incorrect (i.e., there is a typo in the grid diagram). For instance, if the symbol at G(3,1) was not '*' but '□', the logic would lead to '?' being '*'. Given the ambiguity, the question is considered flawed, but the intended answer was B.

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GATE ME 2023 Set 1 — Question 5

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