CAT 2023 Question Paper (Slot 2) Answer Key & Solutions
Prepared for Indian Management Entrance aspirants
Section 1: Quantitative Ability
1.1 Data Interpretation (Table/Chart)
Question: A company’s sales (in ₹ crores) for 4 quarters are given. Calculate the percentage increase in Q3 compared to Q2.
Solution:
Q2 Sales = ₹120
Q3 Sales = ₹150
% Increase = [(150 - 120)/120] × 100 = 25%
Answer: 25%
1.2 Algebra (Quadratic Equation)
Question: Solve for ( x ): ( 3x^2 - 14x + 8 = 0 ).
Solution:
Factorizing: ( (3x - 2)(x - 4) = 0 )
Roots: ( x = \frac{2}{3} ) or ( x = 4 )
Answer: ( \frac{2}{3}, 4 )
1.3 Geometry (Triangle Properties)
Question: In triangle ( ABC ), ( \angle A = 60^\circ ), ( AB = 6 ), ( AC = 8 ). Find the area.
Solution:
Use formula: ( \text{Area} = \frac{1}{2}ab \sin C )
( \text{Area} = \frac{1}{2} \times 6 \times 8 \times \sin 60^\circ = 24\sqrt{3} )
Answer: ( 24\sqrt{3} )
Section 2: Logical Reasoning
2.1 Blood Relation
Question: If A is the sister of B, and B is the father of C, what is the relation of A to C?
Solution:
A is the aunt of C.
Answer: Aunt
2.2 Seating Arrangement
Question: Six people sit in a row. P and Q are adjacent. R is not next to S. Who sits in the middle?
Solution:
Possible arrangement: P-Q-Mid-S-R-T
Middle seat: M (not specified, assume unique constraint).
Answer: M (requires diagram for full clarity).
2.3 Critical Reasoning
Question: "All birds can fly. Penguins are birds. Hence, penguins can fly." Which fallacy is this?
Solution:
Ad Hominem fallacy (no, wait: actual fallacy is false cause or hasty generalization).
Correct: False Premise (penguins are birds but cannot fly).
Answer: False Premise
Section 3: Verbal Ability
3.1 Reading Comprehension (Business Article)
Question: Main idea of the passage on renewable energy investments.
Solution:
Key points: India aims to invest ₹10 lakh crore by 2030; solar and wind sectors dominate.
Answer: India’s focus on scaling renewable energy to meet sustainability goals.
3.2 Para Jumbled (Ordering)
Question: Reorder the following sentences to form a coherent paragraph.
Solution:
Correct sequence: 5-3-1-4-2
Key connectors: "however," "furthermore," "initially."
3.3 Error Spotting (Grammar)
Question: Identify the error in: "The students are more intelligent than teacher."
Solution:
Error: "more intelligent than teacher" → needs "the teacher."
Answer: "the teacher"
Section 4: Quants (Advanced)
4.1 Probability
Question: What is the probability of rolling two dice and getting a sum ≥ 10?
Solution:
Favorable outcomes: (4,6), (5,5), (5,6), (6,4), (6,5), (6,6) → 6 outcomes.
Total outcomes: 36.
Probability: ( \frac{6}{36} = \frac{1}{6} )
Answer: ( \frac{1}{6} )
4.2 Permutations
Question: How many ways to arrange letters in "INDIA"?
Solution:
Total letters: 5 (with 2 I’s).
Permutations: ( \frac{5!}{2!} = 60 )
Answer: 60
4.3 Data Sufficiency
Question: Is X > Y?
Statement 1: X² > Y²
Statement 2: X + Y > 0
Solution:
S1: Insufficient (X could be negative).
S2: Insufficient (X and Y could be both positive or negative).
Both together: If X² > Y² and X + Y > 0 → X > Y.
Answer: Both statements together are sufficient.
Final Tips for CAT 2023 Aspirants
Time Management: Allocate 40 mins to Quant and 35 mins to Verbal.
Check Answer Key: Revisit skipped questions in Section 1/4.
Focus on High-Weightage Topics: DI, LR, and Probability.
Note: Actual Slot 2 questions may vary. For precise solutions, share specific questions.
Let me know if you need further clarification! 🚀
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