Important CAT Quant Formulas for Scoring 99.99 Percentile

Important CAT Quant Formulas: Attaining a 99.99 percentile in the Quantitative Ability section of the Common Admission Test (CAT) is an impressive accomplishment. It requires not only smart preparation but also a solid understanding of important mathematical formulas.

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What is the CAT Quant section in the CAT 2024 Exam?

Important CAT Quant Formulas for Scoring 99.99 Percentile

• Percentage Change: Percentage Change = ((New Value – Old Value) / Old Value) × 100
• Simple Interest: Simple Interest (SI) = (Principal × Rate × Time) / 100
• Compound Interest: Compound Interest (CI) = P(1 + R/n)^(nt)
• Profit and Loss: Profit = Selling Price – Cost Price, Loss = Cost Price – Selling Price
• Average: Average = (Sum of all terms) / (Number of terms)
• Ratio and Proportion: If a : b = c : d, then (a/b) = (c/d)
• Quadratic Equation: For ax² + bx + c = 0, x = (-b ± √(b² – 4ac)) / 2a
• Arithmetic Progression (AP) Sum: Sum = n/2 * (First Term + Last Term)
• Geometric Progression (GP) Sum: Sum = a * (1 – r^n) / (1 – r)
• Distance Traveled when speed and time are given: Distance = Speed × Time
• Time taken to cover a certain distance at different speeds: Time = Speed × Distance

Arithmetic Formulas:

1. Percentage Change: Percentage Change = ((New Value - Old Value) / Old Value) × 100
2. Simple Interest: Simple Interest (SI) = (Principal × Rate × Time) / 100
3. Compound Interest: Compound Interest (CI) = P(1 + R/n)^(nt) (where P is principal, R is rate, n is number of times compounded annually, t is time in years)
4. Profit and Loss: Profit = Selling Price - Cost Price Loss = Cost Price - Selling Price
5. Average: Average = (Sum of all terms) / (Number of terms)
6. Ratio and Proportion: If a : b = c : d, then (a/b) = (c/d)
7. Partnership: Ratio of investment × Time = Share in Profit or Loss

Algebra Formulas:

1. Quadratic Equation: For ax² + bx + c = 0, x = (-b ± √(b² - 4ac)) / 2a
2. Arithmetic Progression (AP) Sum: Sum = n/2 * (First Term + Last Term)
3. Geometric Progression (GP) Sum: Sum = a * (1 - r^n) / (1 - r), where a is the first term and r is the common ratio
4. Binomial Theorem: (a + b)^n = nC0 * a^n + nC1 * a^(n-1)b + ... + nCn * b^n
5. Factorization: a² - b² = (a + b)(a - b) (a + b)² = a² + 2ab + b²
6. Linear Equations: ax + by = c Solve for x: x = (c - by) / a Solve for y: y = (c - ax) / b
7. Inequalities: If a > b, then a + c > b + c and ac > bc (for positive c)

Geometry Formulas:

1. Area of Triangle: Area = 0.5 * Base * Height
2. Perimeter of Rectangle: Perimeter = 2(Length + Width)
3. Circumference of Circle: Circumference = 2πr (r is the radius)
4. Area of Circle: Area = πr²
5. Volume of Cylinder: Volume = πr²h (h is the height)
6. Pythagorean Theorem: In a right triangle, a² + b² = c²
7. Area of Trapezoid: Area = 0.5 * (Sum of parallel sides) * Height

Number System Formulas:

1. Divisibility Rule by 2: A number is divisible by 2 if its units digit is even (0, 2, 4, 6, 8).
2. Divisibility Rule by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
3. Divisibility Rule by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
4. Prime Factorization: Expressing a number as a product of prime numbers.
5. LCM (Least Common Multiple): LCM of a and b = (a * b) / GCD(a, b)
6. HCF (Highest Common Factor): HCF of a and b = Greatest common divisor of a and b.
7. Prime Numbers: Natural numbers greater than 1 that have no positive divisors other than 1 and themselves.

Time, Speed, and Distance Formulas:

1. Speed: Speed = Distance / Time
2. Relative Speed: Speed of A + Speed of B
3. Time taken to cover a distance at average speed: Time = Total Distance / Average Speed
4. Distance Travelled when speed and time are given: Distance = Speed × Time
5. Time taken to cover a certain distance at different speeds: Time = Distance / Speed
6. Time taken to meet when moving towards each other: Time = Distance / Relative Speed
7. Time taken to meet when moving in the same direction: Time = Relative Distance / Relative Speed

Also Read: Best online coaching for CAT MBA Entrance Exam

What topics are covered in the CAT Quant Section?

1. Algebra: This includes things like equations, inequalities, polynomials, functions, and quadratic equations. Understanding algebra is really important for solving problems and using logical reasoning.
2. Arithmetic: This covers basic operations like percentages, ratios, averages, and proportions. It's the starting point for lots of quantitative problems.
3. Number System: This involves integers, fractions, decimals, prime numbers, LCM, and HCF. Knowing number properties is super important for solving problems about divisibility and factors.
4. Modern Math: This part includes set theory, permutations, combinations, and probability. You'll use these ideas when dealing with data interpretation and logical reasoning.
5. Geometry & Mensuration: This deals with shapes, sizes, properties of space, areas, volumes, and angles. Your ability to understand space is tested through geometry problems in CAT.
6. Trigonometry: This focuses on the relationships between angles and sides of triangles. Trigonometry is used when solving problems about heights, distances, and geometry.
7. Permutation & Combination: This involves arranging and selecting objects without thinking about order. These ideas come in handy when dealing with counting problems and probability scenarios.
8. Probability: This deals with how likely events are to happen and includes probability distributions, conditional probability, and Bayes' theorem. It's crucial for solving problems that involve chance and uncertainty.

What is the difference between problem-solving and data sufficiency in the CAT Quant Section?

1. Problem-Solving:
   • These questions are structured similarly to CAT but are generally at a slightly easier level. Candidates need to directly solve mathematical problems.
   • The focus here is on accuracy, and candidates can check their answers before submitting.
   • Problem-solving questions test mathematical abilities without the need to evaluate data sufficiency.
2. Data Sufficiency:
   • On the other hand, data sufficiency questions are unique to GMAT.
   • Candidates are given two statements and must decide if the information provided is enough to solve a problem.
   • This type of question evaluates critical thinking and reasoning skills by assessing the sufficiency of information, rather than requiring direct problem-solving.

What are some common mistakes to avoid in data sufficiency questions?

1. Assuming Extra Information: Don't guess or think about information that isn't given in the question. Stick to the details provided and don't add any extra assumptions.
2. Ignoring Statements: Every statement in a Data Sufficiency question is important. If you ignore or don't think carefully about any statement, you might come to the wrong conclusion. Take the time to assess all the information given.
3. Focusing Only on the Answer: In Data Sufficiency questions, the goal isn't to solve the problem but to figure out if the given information is enough to solve it. Don't get stuck trying to find the answer; instead, focus on checking if the provided information is sufficient.
4. Not Checking Both Statements: It's a common mistake to think one statement alone is enough without looking at both. Always check if each statement by itself has enough information before making a decision.

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