Here’s a structured answer to "CAT 2023 QA Slot 3" with sample questions and solutions, focusing on common QA (Quantitative Ability) patterns in the Indian entrance exam:
CAT 2023 QA Slot 3: Key Question Types & Solutions
Focus Areas:
Data Interpretation & Analysis (DIA)
Algebra & Equations
Probability & Combinatorics
Arithmetic (Percentage, Profit/Loss)
1. Data Interpretation (DI) - Set 1
Question:
A bar graph shows sales (in ₹ lakh) of three products (X, Y, Z) over 4 years (2019–2022). Answer:
a) What was the % increase in sales of Product Y from 2019 to 2022?
b) If Product Z’s sales in 2021 were 20% of total sales that year, find total sales in ₹ crore.
Solution:
a) Step 1: Identify sales values (e.g., 2019: ₹50 lakh, 2022: ₹75 lakh).
Step 2: % Increase = [(75−50)/50] × 100 = 50%.
b) Step 1: Let total sales in 2021 = ₹T lakh.
Step 2: Sales of Z = 0.2T.
Step 3: From the graph, sales of X=₹60 lakh, Y=₹80 lakh.
Step 4: T = 60 + 80 + 0.2T → 0.8T = 140 → T = 175 lakh = ₹1.75 crore.
2. Algebra - Linear Equations
Question:
Solve for x:
3(2x + 5) – 2(3x – 4) = 18.
Solution:
Step 1: Expand: 6x + 15 – 6x + 8 = 18.
Step 2: Simplify: 23 = 18 → Contradiction.
Step 3: No solution (invalid equation).
3. Probability
Question:
A box has 5 red, 3 blue, and 2 green balls. What’s the probability of drawing two balls of different colors?
Solution:
Step 1: Total balls = 10.
Step 2: Total ways = C(10,2) = 45.
Step 3: Favorable cases:
Red & Blue: 5×3 = 15
Red & Green: 5×2 = 10
Blue & Green: 3×2 = 6
Step 4: Total favorable = 15 + 10 + 6 = 31.
Step 5: Probability = 31/45 ≈ 0.6889.
4. Arithmetic - Profit/Loss
Question:
A shopkeeper sold a book at 20% profit. If sold at 25% loss, he’d lose ₹50. Find the cost price.
Solution:
Step 1: Let CP = ₹x.
Step 2: SP1 = 1.2x, SP2 = 0.75x.
Step 3: SP1 – SP2 = 50 → 1.2x – 0.75x = 0.45x = 50.
Step 4: x = 50 / 0.45 ≈ ₹111.11.
Key Tips for CAT QA:
Time Management: Allocate 45 mins for 20 DI questions.
Shortcuts: Use options for algebraic equations (e.g., plug-in values).
Probability: Break into cases; avoid overcounting.
DI Tables: Practice constructing quick-reference tables.
Let me know if you need more examples or specific question types! 🚀
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