Quantitative Aptitude is an important section of the CAT exam. The questions in this section are from Algebra, Arithmetic and Geometry. It is crucial for CAT candidates to be well-versed with the basic formulas required for solving these questions with accuracy in the least time. Learning important formulae can help them ace Common Admission Test (CAT).
CAT 2023 Basic Mathematical Formulae: Algebra
- (a + b)² = (a² + b² + 2ab)
- (a – b)² = (a² + b² – 2ab)
- (a + b)(a – b) = (a² – b²)
- (a³ – b³) = (a – b)(a² + ab + b²)
- (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
- (a³ + b³) = (a + b)(a² – ab + b²)
- When a + b + c = 0, then a³ + b³ + c³ = 3abc
- (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
- (a + b)n = an + (nC1)an-1b + (nC2)an-2b² + … + (nCn-1)abn-1 + bn
Basic Formulae: Number System
- (1² + 2² + 3² + ….. + n²) = n ( n + 1 ) (2n + 1) / 6
- 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
- (1³ + 2³ + 3³ + ….. + n³) = (n(n + 1)/ 2)²
- Sum of first n odd numbers = n²
- Sum of first n even numbers = n (n + 1)
Basic Formulae: Percentages
Find what percentage of X is Y: Y/X x 100
- Increase N by S% = N(1+S/100)
- Decrease N by S% = N(1 – S/100)
Basis Averages Formula
Average= Sum of observations/ Number of observations
Basic Formulae: Simple and Compound Interest
- Simple Interest: P x i x n (P= Principle, i= interest rate and n= term of the loan)
- Compound Interest:
- Compound Interest = [P(1+i)n] – P
- Compound Interest = P[(1+i)n-1]
Basic Formulae: Profit, Loss and Discount
- Profit % = Profit/(C P)×100
- Profit/Gain = (S.P.) – (C.P.)
- C P = 100/(100+gain %)×S P
- S P = (100+gain % )/100 ×C P
- Loss % = Loss/(C.P.)×100
- Loss = (C.P.) – (S.P.)
- C P = 100/(100-loss %)×S P
- S P = (100-loss %)/100×C P
Basic Formulae: LCM and HCF
- LCM × HCF = Product of the Numbers
- LCM of Co-prime Numbers = Product Of The Numbers
Important Formulae: Speed, Time and Distance
- Speed= Distance/ Time
- Distance= Speed x Time
- Time= Distance/ Time
Basic Formulae: Time and Work
- If X can do a piece of work in ‘n’ days, then X’s 1 day’s work= 1/n
- If X’s 1 day’s work= 1/n, then X can finish the work in n days.
Basic Fortmulae: Mixtures and Allegations
- If two ingredients are mixed, then
- (Quantity of cheaper / Quantity of dearer) = (C.P. of dearer – Mean Price / Mean price – C.P. of cheaper)
Basic Formulae: Permutation and Combination
- Permutation Formula: A permutation is the choice of r things from a set of n things without replacement. Order matters in permutation.
- Combination Formula: A combination is the choice of r things from a set of n things without replacement. The order does not matter in combination.
Basic Formulae: Logarithm
- If n and a are positive real numbers, and a is not equal to 1, then If ax = n, then log a n = x
- log of 1 to any base is 0 (log b 1 = 0)
- log of any number to base as itself is 1, log a a = 1
- Logarithm of a Product (log a pq = log a p + loga q)
- The logarithm of a Fraction (log a (p/q) = log a p – log a q)
- log a pn = n log a p
- a(log a p) = p
- Base Change Rule of Logarithms: (log a n = log b n × log a b)
Basic Formulae : Coordinate Geometry
Distance Between two Points A and B:
- AB² = (Bx – Ax)² + (By – Ay)²
The Midpoint of a Line Joining Two Points
The midpoint of the line joining the points (x1, y1) and (x2, y2) is:
- [½(x1 + x2), ½(y1 + y2)]
The Equation of a Line Using One Point and the Gradient
The equation of a line which has gradient m and which passes through the point (x1, y1) is:
- y – y1 = m(x – x1)
Basic Formulae: Mensuration
- Rectangle
- Area = lb
- Perimeter = 2(l+b)
- Square
- Perimeter = 4a
- Area = a×a
- Triangle
- Area =b×h/2 or √s(s-a)(s-b)(s-c)___where s=a+b+c/2
- Cube
- Volume: V = l3
- Surface Area: S = 6s2
- Diagonal (d) = √3l
- Lateral surface area = 4a2
- Circle
- Circumference = 2πr or πd
- Area = πr² or πd²/4
- Area of a sector of a circle = (θπr² )/360
- Cuboid
- Total surface area = 2 (lb + bh + hl) or 6l2
- Volume of cuboid: lbh
- Length of diagonal =√(l²+b²+h²)
Basic Formulae: Trigonometry
Trigonometric Identities |
Sine = Opposite/Hypotenuse |
Secant = Hypotenuse/Adjacent |
Cosine = Adjacent/Hypotenuse |
Tangent = Opposite/Adjacent |
Co−Secant = Hypotenuse/Opposite |
Co−Tangent = Adjacent/Opposite |
Reciprocal identities |
cosec θ = 1/sin θ |
sec θ = 1/ cos θ |
cot θ = 1/tan θ |
sin θ = 1/cosec θ |
cos θ = 1/sec θ |
tan θ = 1/cot θ |
Reference Books For Quant Preparation – CAT 2023
Quantitative Ability:
How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (8th Edition)
Quantitative Aptitude Quantum by Sarvesh Kumar (2020)
Quantitative Aptitude for CAT by Nishit Sinha (2020)
Verbal Ability:
How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)
The Pearson Guide to Verbal Ability and Reading Comprehension for CAT by Nishit Sinha (2020)
Word Power Made Easy by Norman Lewis
Data Interpretation & Logical Reasoning:
A Modern Approach to Logical Reasoning by R.S.Agarwal
How to Prepare for Logical Reasoning and Data Interpretation for CAT by Arun Sharma (2011)
Logical Reasoning and Data Interpretation by Nishit Sinha (2020)
Youtube Channel For CAT Quant Prep: CAT 2023
In addition to the books available for CAT quantitative aptitude preparation, there are also several YouTube channels dedicated to this topic that can be helpful. These channels offer detailed content on each topic covered under quant and provide step-by-step explanations for the solutions. By referring to these videos, you can better understand the concepts and techniques involved in CAT quant preparation. Furthermore, watching video tutorials can be a more engaging way to learn and make learning more enjoyable. Some of the popular YouTube channels for CAT quant preparation include;
Strategy For CAT Quant Preparation In 2023
When studying for the CAT quant, having a strategy is essential because it allows you to handle the preparation in a systematic and ordered way. A plan offers a clear roadmap of what you must do, how you must do it, and by when you must do it. It also aids in keeping you concentrated and determined during the preparation process. So here is a 5-step plan for you on page five.
Step 1: Assess your knowledge and identify areas for improvement.
Take a diagnostic test to assess your current level of proficiency in quant. Analyse the test results to identify your strengths and weaknesses. This will help you focus on the topics that need improvement.
Step 2: Build a strong foundation
Focus on building a strong foundation in the basics of mathematics. This will help you understand the more complex topics better. Revise your fundamentals by referring to textbooks, online courses, or YouTube videos.
Step 3: Practice regularly.
Practice is crucial for CAT quant preparation. Regularly practice questions from various sources such as previous years’ question papers, mock tests, online quizzes, and textbooks. Ensure that you solve questions from a variety of difficulty levels to develop problem-solving skills.
Step 4: Analyze your performance.
After practising, analyse your performance to identify areas where you’re making mistakes. Try to understand why you’re making mistakes and work on rectifying them. Keep track of your progress to see if you’re improving.
Step 5: Take mock tests and assess your progress.
Mock tests are a great way to assess your progress and identify areas that need more attention. Take mock tests regularly, preferably once every two weeks, and analyse your performance. This will help you identify your strengths and weaknesses and improve your overall performance.
Exam Pattern: CAT 2023
To develop a foolproof strategy for CAT 2023, it is essential to have a thorough understanding of the CAT 2023 exam format. The exam consists of three sections, each lasting 40 minutes, resulting in a total duration of two hours. The test pattern has remained the same as in previous years.
Exam Details – CAT 2023 |
Exam Mode – Offline |
Official Website – iimcat.ac.in |
Test Duration |
The total duration of the CAT exam is 120 minutes (2 hours) – CAT exam comprises three sections – Quantitative Ability (QA) section lasts for 40 minutes – Verbal Ability & Reading Comprehension (VARC) section lasts for 40 minutes – Logical Reasoning & Data Interpretation (LRDI) section also lasts for 40 minutes. |
Type of Section |
The CAT exam consists of three sections, namely Quantitative Ability (QA), Verbal Ability & Reading Comprehension (VARC), and Logical Reasoning & Data Interpretation (LRDI) – Each section of the CAT exam lasts for 40 minutes – Quantitative Ability (QA) section assesses the candidate’s mathematical and problem-solving abilities – Verbal Ability & Reading Comprehension (VARC) section evaluates the candidate’s English language proficiency and reading comprehension skills – Logical Reasoning & Data Interpretation (LRDI) section assesses the candidate’s analytical and logical reasoning abilities. |
Number of Questions for CAT 2023 |
The CAT exam consists of three sections, namely Quantitative Ability, Verbal Ability & Reading Comprehension, and Logical Reasoning & Data Interpretation – Quantitative Ability section carries a weightage of 22 marks out of a total of 100 marks – Verbal Ability & Reading Comprehension section carries a weightage of 24 marks – Logical Reasoning & Data Interpretation section carries a weightage of 20 marks – Total marks for the CAT exam are 100, with each section contributing to the final score – Weightage assigned to each section reflects the importance of each area in evaluating a candidate’s aptitude and skills. |
Maximum Marks Alloted – 198 |
Marking System For CAT 2023 |
The CAT exam uses a scoring system that awards points for correct answers and deducts points for incorrect answers. – Each correct answer is given a score of +3. – For every incorrect answer, a penalty of -1 mark is applied. – The scoring system is designed to encourage accuracy and minimise guesswork. – Candidates must carefully consider their answers to avoid losing points due to incorrect responses. |
Important Dates to Keep in Mind for CAT 2023
Keeping track of important dates for the CAT exam is essential for effective preparation and timely completion of the application process. Here are some reasons why it’s important to keep track of these dates:
CAT 2023 notification will be released in the 4th week of July 2023.
The application process for CAT 2023 will commence in the 1st week of August 2023.
The last date to fill out the CAT 2023 application form is the 2nd week of September 2023.
The last date to submit the CAT 2023 application fee is also the 2nd week of September 2023.
CAT 2023 admit card will be released in the 4th week of October 2023.
CAT 2023 exam is scheduled for the 4th week of November 2023.
The result for CAT 2023 will be declared in the 1st week of January 2024.
These tantative dates are essential for candidates who wish to appear for the CAT 2023 exam, kindly refer to the official website for CAT 2023 or stay tube on Pagalguy for recent CAT 2023 updates.
Eligibility for CAT 2023
To be eligible for the CAT exam, candidates must have completed their graduation in any stream with a minimum of 50% in aggregate (45% for SC/ST/PwD candidates) or equivalent from a recognised university. Additionally, final-year bachelor’s degree candidates or those awaiting their results are also eligible to apply for the CAT exam. Candidates who possess professional qualifications such as CA/CS/ICWA can also appear in the CAT exam.
It is important for candidates to note that fulfilling the eligibility criteria does not guarantee admission into the management programmes offered by IIMs and other participating institutes. The selection process also considers the candidate’s performance in the CAT exam, past academic record, work experience, and other factors. Candidates are advised to carefully read the information brochure and follow the application process as per the guidelines provided to avoid any discrepancies or disqualifications.
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