Title: CAT 2021 Slot 1 Quantitative Ability Solutions
Question: What is the sum of the first 100 natural numbers?
Answer: The sum of the first 100 natural numbers can be calculated using the formula for the sum of an arithmetic series:
Sum = n/2 * (first number + last number)
Here, n = 100, first number = 1, and last number = 100.
Sum = 100/2 * (1 + 100) = 50 * 101 = 5050
Question: If x + y = 15 and x - y = 5, what is the value of x?
Answer: To find the value of x, we can add the two equations:
x + y = 15
x - y = 5
Adding them, we get:
2x = 20
x = 20/2
x = 10
Question: A train 120 meters long passes a pole in 8 seconds. What is the speed of the train?
Answer: The speed of the train can be calculated using the formula:
Speed = Distance / Time
Here, Distance = Length of the train = 120 meters, Time = 8 seconds.
Speed = 120 / 8 = 15 meters per second.
Question: A certain number increased by 25% gives 750. Find the original number.
Answer: Let the original number be x. An increase of 25% means the number becomes 125% of the original.
So, 125% of x = 750
125/100 * x = 750
x = 750 * 100 / 125
x = 600
Question: A box contains 5 red, 6 blue, and 3 green balls. If 4 balls are drawn at random, what is the probability of getting exactly 2 red balls?
Answer: The total number of ways to draw 4 balls out of 14 (5 red + 6 blue + 3 green) is given by the combination formula:
Total ways = C(14, 4) = 14! / (4! * (14 - 4)!)
To get exactly 2 red balls, we need to choose 2 out of 5 red balls and 2 out of the remaining 9 balls (6 blue + 3 green).
Ways to choose 2 red balls = C(5, 2) = 5! / (2! * (5 - 2)!)
Ways to choose 2 balls from the remaining 9 = C(9, 2) = 9! / (2! * (9 - 2)!)
The probability is then:
Probability = (Ways to choose 2 red balls * Ways to choose 2 balls from 9) / Total ways
Probability = (C(5, 2) * C(9, 2)) / C(14, 4)
Probability = (10 * 36) / 1001
Probability = 360 / 1001
Note: The exact probability should be simplified further if required.
CAT 2021 Slot 1 Quantitative Ability: Strategies and Solutions for Indian Students
The Common Admission Test (CAT) 2021 Slot 1 Quantitative Ability section posed challenging questions across diverse topics. Indian aspirants preparing for IIM entrances must focus on mastering problem-solving strategies tailored to the exam’s unique format. Below is a breakdown of key themes, common pitfalls, and effective approaches to tackle this section.
1. Key Topics Tested in CAT 2021 Slot 1 Quant
Data Interpretation (DI):
Caselets with 2-3 tables/charts (e.g., sales data, demographics).
Questions required multi-step calculations (e.g., percentage changes, ratios).
Number Theory:
Divisibility rules, LCM/GCF, modular arithmetic.
Problems involving remainders and digit manipulation.
Algebra & Functions:
Quadratic equations, inequalities, and polynomial properties.
Sequence and series (e.g., arithmetic progression word problems).
Geometry:
Coordinate geometry (distance, slope, equations of lines).
mensuration (volume, surface area, profit/loss in 3D shapes).
Logical Reasoning:
Permutations/combinations with constraints.
Set theory and Venn diagrams.
2. Common Mistakes to Avoid
Overcomplicating Calculations:
CAT often includes questions solvable via approximation or mental math (e.g., estimating roots or percentages).
Fix: Practice simplifying expressions and using shortcuts (e.g., 70% of 80 = 56 → 7×8 = 56).
Ignoring Units and Context:
Questions often hide traps in units (e.g., km vs. meters) or misinterpretation of "what is asked."
Fix: Double-check units and rephrase questions in your own words.
Time Management:
DI and Algebra questions can eat into time if not prioritized.
Fix: Allocate 30-40 minutes to DI and 20-25 minutes to Algebra/Geometry.
3. Proven Strategies for Success
A. DI & LR
Skim First, Process Later:
Read the entire caselet once to grasp the context before solving questions.
Create tables or flowcharts to map relationships (e.g., profit/loss chains).
Practice Visual Thinking:
Use plug-in values for charts (e.g., assume 100 as base for population questions).
B. Number Theory
Leverage Modular Arithmetic:
For questions like "What is the remainder when 7^15 is divided by 5?"
Step 1: Observe the cycle of 7^n mod 5: 7, 4, 3, 1, repeating every 4.
Step 2: 15 ÷ 4 = 3 remainder 3 → Third term in cycle is 3.
Prime Factorization:
Break down large numbers (e.g., 2021 = 43 × 47) for GCF/LCM problems.
C. Algebra
Quadratic Equations:
If x^2 + ax + b = 0 has roots α and β, then α + β = -a and αβ = b.
Use this to solve questions like "If α and β are roots, find α^2 + β^2."
Solution: α^2 + β^2 = (α + β)^2 - 2αβ = a^2 - 2b.
Inequalities:
Test boundary cases (e.g., equality holds when x = 0).
D. Geometry
Coordinate Geometry:
Use distance formula: d = √[(x2 - x1)^2 + (y2 - y1)^2].
For questions on lines: "Find the slope of the line perpendicular to y = 2x + 3."
Answer: Slope = -1/2 (negative reciprocal).
Mensuration:
Visualize 3D objects (e.g., cubes inside a cuboid) to avoid surface area errors.
4. Sample Question Breakdown
Question 1 (DI):
A company’s sales in 2020 were ₹120 crores. In 2021, sales increased by 15% in Q1, decreased by 10% in Q2, and then grew by 20% in Q3. What was the net sales in 2021?
Solution:
Q1: 120 × 1.15 = ₹138
Q2: 138 × 0.90 = ₹124.2
Q3: 124.2 × 1.20 = ₹148.64 crores.
Question 2 (Number Theory):
Find the smallest positive integer N such that N ≡ 3 mod 7 and N ≡ 5 mod 11.
Solution:
N = 7k + 3.
Substitute into second equation: 7k + 3 ≡ 5 mod 11 → 7k ≡ 2 mod 11.
Multiplicative inverse of 7 mod 11 is 8 (since 7×8=56≡1 mod11).
k ≡ 2×8 ≡ 16 ≡ 5 mod11 → k=11m+5.
N=7(11m+5)+3=77m+38. Smallest N=38.
5. Final Tips for CAT 2021 Aspirants
Mock Tests: Simulate Slot 1 conditions (time constraints, question order).
Focus on High-Weightage Topics: DI, Algebra, and Number Theory account for ~60% of marks.
Review Errors: Maintain a mistake log to identify recurring weaknesses.
Stay Calm: Manage anxiety with breathing exercises and timed practice.
By integrating these strategies, Indian students can tackle CAT 2021 Slot 1 Quant with confidence. Remember: Speed and accuracy depend on consistent practice and smart preparation.
Prep smarter, not harder. Good luck! 🚀
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