CAT 2022 Slot 1 Quantitative Ability Solutions
Here are detailed solutions for common question types encountered in CAT 2022 Slot 1 Quantitative Ability. Each problem includes a step-by-step breakdown to ensure clarity and alignment with CAT's scoring standards.
1. Data Interpretation (DI) – Bar Graph Analysis
Question:
A bar graph shows the number of students in five schools (A, B, C, D, E). What is the ratio of students in School A to School C?
Solution:
Extract Data: Assume values from the graph (if not provided, use standard DI formats).
School A: 200 students
School C: 300 students
Calculate Ratio:
[
\text{Ratio} = \frac{200}{300} = \frac{2}{3}
]
Answer: ( \boxed{\frac{2}{3}} )
2. Algebra – Quadratic Equation
Question:
Solve ( 4x^2 - 12x + 9 = 0 ).
Solution:
Factorize:
[
(2x - 3)^2 = 0 \quad \Rightarrow \quad x = \frac{3}{2}
]
Verify:
Substitute ( x = \frac{3}{2} ):
( 4(\frac{9}{4}) - 12(\frac{3}{2}) + 9 = 9 - 18 + 9 = 0 ).
Answer: ( \boxed{\frac{3}{2}} ) (Double root)
3. Geometry – Circle Sector Area
Question:
Find the area of a sector with radius 7 cm and central angle ( 60^\circ ).
Solution:
Convert Angle to Radians:
( 60^\circ = \frac{\pi}{3} ) radians.
Apply Sector Area Formula:
[
\text{Area} = \frac{1}{2} r^2 \theta = \frac{1}{2} \times 7^2 \times \frac{\pi}{3} = \frac{49\pi}{6} , \text{cm}^2
]
Answer: ( \boxed{\frac{49\pi}{6}} )
4. Permutations – Arranging Books with Constraints
Question:
How many ways can 5 books be arranged if two specific books must be adjacent?
Solution:
Treat Pair as a Single Unit:
Total units = 4 (pair + 3 books).
Arrange Units:
( 4! = 24 ).
Arrange Within Pair:
( 2! = 2 ).
Total Arrangements:
( 24 \times 2 = 48 ).
Answer: ( \boxed{48} )
5. Probability – Coin Tosses
Question:
What is the probability of getting exactly 3 heads in 5 fair coin tosses?
Solution:
Total Outcomes: ( 2^5 = 32 ).
Favorable Outcomes:
Choose 3 positions out of 5:
[
\binom{5}{3} = 10
]
Probability:
[
\frac{10}{32} = \frac{5}{16}
]
Answer: ( \boxed{\frac{5}{16}} )
Key Tips for CAT 2022 Quant
Time Management: Prioritize questions with higher marks (e.g., DI and Algebra often hold 3 marks).
Formula Mastery: Memorize critical formulas (e.g., quadratic roots, sector area, permutations).
Check Units: Ensure consistency in units (e.g., cm vs. meters).
Avoid Overcomplication: Simplify fractions early (e.g., reduce ( \frac{6}{36} ) to ( \frac{1}{6} )).
For practice, refer to official CAT 2022 papers and mock tests. Best of luck! 🚀
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