Logical Reasoning and Constraint Deduction Previous Year Questions (PYQs) for GATE DA: 2+ Solved Questions with Step-by-Step Solutions

Solve 2+ Logical Reasoning and Constraint Deduction previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

Chapter Roadmap: Logical Reasoning and Constraint Deduction

Chapter Journey: Logical Reasoning and Constraint Deduction

Step 1: Monotonicity-Based Logical Deduction

Understanding Strict vs. Non-Strict Monotonicity
Reversing Inequalities (Output trends to Input bounds)
The Single Peak and Single Valley Patterns

Step 2: Constraint-Based Sequencing and Elimination

Building Ordering Chains (A is before B, B is after C)
The Elimination Grid Method
Handling "Not" and "Either-Or" Constraints

The Core of Monotonicity

What is Monotonicity?
A function

f (x)

is monotonic if it preserves or reverses the order of its inputs. It never changes direction.

1. Monotonically Increasing

x

gets larger,

f (x)

gets larger (or stays same).

2. Monotonically Decreasing

x

gets larger,

f (x)

gets smaller (or stays same).

The Logical Superpower:
If a function is strictly increasing, it creates a perfect two-way mirror between inputs and outputs.

x_{1} < x_{2} ⟺ f (x_{1}) < f (x_{2})

This means if you are given an inequality about the outputs, you can instantly translate it into an inequality about the inputs.

Logical Reasoning and Constraint Deduction: Solved Questions with Step-by-Step Explanations (2 Problems)

Question 1 · Analytical Aptitude MCQ

Rishi and Swathi are students of Class 5. Pavan and Tanvi are students of Class 4. Rishi and Pavan are boys. Swathi and Tanvi are girls. The four students played a total of three games of chess. The games were played one after another. A player who lost a game did not participate in any more games. It was observed that:
(i) the first game was the only game where two students of the same class played against each other,
(ii) the students of Class 5 won more games than the students of Class 4, and
(iii) the boys won two games and the girls won one game.
The student who did not lose any game is __________.

A.
Pavan
B.
Rishi
C.
Swathi
D.
Tanvi

Correct Answer:

Step-by-Step Solution

Key idea: This is a constraint-based sequencing and elimination question, recognizable by the sequential games, elimination rules, and conditions on wins/classes.

Step 1: Understand the game format. There are 4 students and 3 games. A loser is eliminated. For all 4 students to play, the format must be: Game 1 (A vs B), Game 2 (Winner of G1 vs C), Game 3 (Winner of G2 vs D).

Step 2: Use condition (i). Game 1 is the ONLY game where two students of the same class played. The same-class pairs are (Rishi, Swathi) in Class 5 and (Pavan, Tanvi) in Class 4. Thus, Game 1 must be either (R, S) or (P, T).

Step 3: Test if Game 1 is (P, T). If Class 4 plays each other in G1, Class 4 wins G1. Condition (ii) states Class 5 won more games than Class 4. Since there are 3 games total, Class 5 must win 2 and Class 4 must win exactly 1. This means Class 5 must win G2 and G3. If Class 5 wins G2, the winner is R or S. Then Game 3 would be (R or S) vs the remaining (S or R), which is a same-class game. This violates condition (i). Thus, Game 1 cannot be (P, T).

Step 4: Test if Game 1 is (R, S). Game 1 is R vs S. Class 5 wins G1. To satisfy the quotas (Class 5 wins 2, Class 4 wins 1; Boys win 2, Girls win 1), Rishi (Boy) must win G1. If Swathi won, we would need 2 Boy wins from the remaining games, forcing Class 4 to win 2 games, violating (ii). So Rishi wins G1.

Step 5: Determine Game 2 and 3. Rishi plays Game 2 against Pavan or Tanvi. If Rishi loses G2, the Class 4 student wins, and Class 4 would end up winning 2 games total (violating ii). Thus, Rishi must win G2.

Step 6: Now Rishi has won G1 and G2 (2 Boy wins, 2 Class 5 wins). The quotas for Boys and Class 5 are fully met. Therefore, Game 3 must be won by a Girl from Class 4 to satisfy the remaining quotas (1 Girl win, 1 Class 4 win).

Step 7: Game 3 is Rishi vs Tanvi. Tanvi must win. Since Tanvi won her only game and didn't play before, she never lost any game.

Answer: D

Question 2 · Analytical Aptitude MCQ

Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of

50

years and then it monotonically decreases. Let

a_{1}

and

a_{2}

(in years) denote the ages of the brothers and

a_{1} < a_{2}

.
Which one of the following statements is correct about their age on the day when they attain the same weight?

A.
$a_{1} < a_{2} < 50$
B.
$a_{1} < 50 < a_{2}$
C.
$50 < a_{1} < a_{2}$
D.
Either $a_{1} = 50$ or $a_{2} = 50$

Correct Answer:

Step-by-Step Solution

Key idea: This is a monotonicity-based logical deduction question, recognizable by the function's trend (increasing then decreasing) and the equality of outputs for two different inputs.

Step 1: Understand the function's behavior. The weight function $W (a)$ monotonically increases for $a \leq 50$ and monotonically decreases for $a > 50$ . This creates a single peak at $a = 50$ .

Step 2: Analyze the condition $W (a_{1}) = W (a_{2})$ with $a_{1} < a_{2}$ .

Step 3: Evaluate the positions of $a_{1}$ and $a_{2}$ relative to the peak.

If both $a_{1} < a_{2} \leq 50$ , they lie on the monotonically increasing segment. For a strictly monotonic function, $W (a_{1}) < W (a_{2})$ , so they cannot be equal.

If both $50 \leq a_{1} < a_{2}$ , they lie on the monotonically decreasing segment. Similarly, $W (a_{1}) > W (a_{2})$ , so they cannot be equal.

Step 4: The only way for $W (a_{1}) = W (a_{2})$ with $a_{1} \neq = a_{2}$ is if one age is on the increasing slope and the other is on the decreasing slope.

Step 5: Since $a_{1} < a_{2}$ , it must be that $a_{1} < 50$ and $a_{2} > 50$ .

Step 6: This matches the condition $a_{1} < 50 < a_{2}$ .

Answer: B

A question from this chapter

Question 1

Rishi and Swathi are students of Class 5. Pavan and Tanvi are students of Class 4. Rishi and Pavan are boys. Swathi and Tanvi are girls. The four students played a total of three games of chess. The games were played one after another. A player who lost a game did not participate in any more games. It was observed that: (i) the first game was the only game where two students of the same class played against each other, (ii) the students of Class 5 won more games than the students of Class 4, and (iii) the boys won two games and the girls won one game. The student who did not lose any game is __________.

Question 2

Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of 50 years and then it monotonically decreases. Let a_{1} and a_{2} (in years) denote the ages of the brothers and a_{1} < a_{2} . Which one of the following statements is correct about their age on the day when they attain the same weight?

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Logical Reasoning and Constraint Deduction Previous Year Questions (PYQs) for GATE DA: 2+ Solved Questions with Step-by-Step Solutions

Chapter Roadmap: Logical Reasoning and Constraint Deduction

Chapter Journey: Logical Reasoning and Constraint Deduction

The Core of Monotonicity

Logical Reasoning and Constraint Deduction: Solved Questions with Step-by-Step Explanations (2 Problems)

Step-by-Step Solution

Step-by-Step Solution

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