CAT Quantitative Aptitude Shortcut Tricks 2026: Formulas, Calculation Tips & Shortcuts

Why Are CAT Quant Shortcuts Important?

The QA section has 22 questions to be solved in 40 minutes, making efficient calculation important. Shortcuts can help reduce unnecessary steps in familiar question types, but they should be used only after understanding the underlying concept.

• Reduce calculation time
• Simplify lengthy computations
• Improve speed during timed practice
• Help compare answer options quickly
• Leave more time for difficult questions

CAT Number System Shortcut Tricks

Number System concepts are useful for direct questions as well as problems involving Arithmetic and Algebra. The following shortcuts can help reduce calculation time.

Divisibility Rules

For divisibility by $9$, add the digits of the number.

Example: For $N=37895$:

$3+7+8+9+5=32$

Since $32$ is not divisible by $9$, $37895$ is not divisible by $9$.

The $abcabc$ Pattern

A number of the form $abcabc$ can be expressed as a multiple of $1001$.

$abcabc=abc\times1001$

Since $1001=7\times11\times13$, this pattern is useful in divisibility and factorisation questions.

Example:

$325325\div1001=325$

Prime Factorisation

Writing a number using convenient factors can simplify LCM, HCF and factor-related questions.

Example:

$240=16\times15=2^4\times3\times5$

Simplification by Cancellation

Cancelling common factors before multiplication can reduce the number of calculation steps.

Example:

$\frac{50\times35+28\times25}{75\times30+60\times15}=\frac79$

CAT Arithmetic Shortcut Tricks

Arithmetic covers Percentage, Ratio, Average, TSD and Time & Work, making calculation efficiency important in the QA section.

Addition and Subtraction

Using nearby round numbers can make mental calculations faster.

• $28+8=28+10-2=36$

• $36+9=36+10-1=45$

• $57-8=57-10+2=49$

• $87+65=87+60+5=152$

Division Shortcuts

The following conversions can simplify divisions by common numbers.

These shortcuts replace division with simpler multiplication and scaling.

Examples: $523\div5=104.6$, $728\div25=29.12$, and $523\div125=4.184$.

Percentage Shortcuts

These common percentage-fraction conversions are useful for quick calculations.

For example, if B is $30%$ more than A and $A=₹200$, then $B=200\times1.30=₹260$.

Time, Speed and Distance

For a standard late/early problem, the distance can be obtained directly using the following relation.

$D=\frac{S_1S_2\times\text{time difference}}{S_2-S_1}$

For $S_1=7$ km/h, $S_2=8$ km/h and a time difference of $15$ minutes:

$D=\frac{7\times8\times\frac14}{8-7}=14\text{ km}$

Time and Work

The LCM method provides a quick way to calculate combined work rates.

If A takes $8$ days and B takes $14$ days:

$\text{Total work}=\operatorname{LCM}(8,14)=56$

$A=\frac{56}{8}=7$ units/day

$B=\frac{56}{14}=4$ units/day

Together, they complete $11$ units/day.

Therefore, $\text{Time}=\frac{56}{11}$ days.

CAT Algebra Shortcut Tricks

Algebraic identities can reduce lengthy calculations and help with factorisation.

Important Algebraic Identities

The following identities are particularly useful for CAT Quant.

These identities are useful for both simplification and faster numerical calculations.

Example:

$42\times38=(40+2)(40-2)=40^2-2^2=1596$

Quadratic Factorisation

A perfect-square quadratic can often be recognised immediately.

$x^2+6x+9=0$

Therefore:

$(x+3)^2=0$

CAT Geometry Shortcut Tricks

Pythagorean relationships and standard geometric results can help reduce calculation steps in familiar question types.

Pythagorean Triplets

These commonly used triplets can be recalled directly.

For example, when the perpendicular sides are $8$ and $15$, the hypotenuse is $17$.

Equilateral Triangle

The circumradius of an equilateral triangle of side $a$ is given by:

$R=\frac{a}{\sqrt3}$

For $a=6$:

$R=\frac6{\sqrt3}=2\sqrt3$

CAT Mensuration Shortcut Tricks

Knowing standard formulas helps reduce the time spent deriving basic area and volume relationships.

Common Mensuration Formulas

The following formulas cover several frequently used shapes.

These formulas can be used directly when the required dimensions are given.

Regular Hexagon

For a regular hexagon of side $a$, the standard formulas are:

$A=\frac{3\sqrt3}{2}a^2$

$R=a$

For $a=8$:

$A=96\sqrt3\text{ sq. units}$

$R=8\text{ units}$

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CAT Trigonometry Shortcut Tricks

Basic trigonometric ratios and identities are useful when geometry questions involve angles.

Basic Trigonometric Ratios

For a right triangle:

$\sin\theta=\frac{P}{H}$

$\cos\theta=\frac{B}{H}$

$\tan\theta=\frac{P}{B}$

Important Identities

These identities are useful for simplifying trigonometric expressions.

$\sin^2\theta+\cos^2\theta=1$

$\sec^2\theta-\tan^2\theta=1$

For the area of a triangle:

$A=\frac12ab\sin C$

For $a=10$, $b=7$ and $C=30^\circ$:

$A=\frac12(10)(7)\sin30^\circ=17.5\text{ cm}^2$

CAT Shortcut Tricks for Probability and P&C

Basic outcome-counting formulas can simplify straightforward Probability and P&C questions.

Probability

The basic probability formula is:

$P(E)=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}$

For $n$ coin tosses:

$\text{Total outcomes}=2^n$

For $n$ dice:

$\text{Total outcomes}=6^n$

Permutation and Combination

When each of $n$ distinct objects can independently be placed in any of $r$ boxes, the number of ways is:

$\text{Number of ways}=r^n$

For 5 letters and 3 boxes:

$3^5=243$

CAT Quant Shortcut Quick Revision

The following table summarises the main shortcut areas covered in the article.

Use these shortcuts as a revision checklist after completing the underlying concepts and practising CAT-level questions.

How to Use CAT Quant Shortcuts

Shortcuts are most effective when applied to familiar concepts under timed conditions.

• Learn the underlying concept first.

• Practise each shortcut with different question types.

• Apply shortcuts to CAT previous-year questions.

• Use timed sectional tests to improve speed.

• Maintain an error log for calculation mistakes.

• Avoid a shortcut if it increases the possibility of an incorrect answer.

CAT Quantitative Aptitude Shortcut Method: Trick to Find the Number of Factors of Any Factorial

To find the number of factors of a factorial, like n!, follow these steps:

1. Prime Factorization: First, find the prime factorization of n!. For this, you need to determine the highest power of each prime number that divides n!. For a prime p, this power can be calculated using the formula:
   Highest power of p in n! = (n/p) + (n/p²) + (n/p³) + …, where you stop when p^k > n.

2. Number of Factors: Once you have the prime factorization of n!, express it in the form p₁a₁ × p₂a₂ × … × pₖaₖ. To find the total number of factors, use the formula:
   Number of factors = (a₁ + 1) × (a₂ + 1) × … × (aₖ + 1).
   Here, a₁, a₂, …, aₖ are the powers of the prime factors.

CAT Quantitative Aptitude Shortcut Method: Assumption Technique

The assumption technique is a method used in quantitative aptitude problems, especially in algebra and statistics, to simplify complex problems by making reasonable assumptions. Here’s how to use it:

1. Identify the Variables: Understand the variables involved in the problem and what you need to find.

2. Make an Assumption: Choose a reasonable value for one of the variables to simplify calculations. For example, assume a specific value for an unknown or a common value to test the feasibility of different options.

3. Solve the Simplified Problem: Use the assumed value to solve the problem and derive a solution or pattern. This helps in making the problem more manageable and often leads to insights about the real values.

4. Validate the Assumption: Check if the solution obtained with the assumption fits all conditions of the problem. Adjust the assumption if necessary and repeat the process.

CAT Quantitative Aptitude Shortcut Method: To Find the Squares of Numbers from 30 to 70

For numbers between 30 and 70, you can use the following shortcuts to quickly find their squares:

1. Use the Formula: For numbers near 50, use the formula: (50 ± d)² = 2500 ± 2 × 50 × d + d². Here, d is the difference from 50. For example, to find 53², use:
   53² = (50 + 3)² = 50² + 2 × 50 × 3 + 3² = 2500 + 300 + 9 = 2809.

2. Break Down Larger Numbers: For numbers further from 50, break them into simpler parts. For instance, to find 68², use:
   68² = (70 - 2)² = 70² - 2 × 70 × 2 + 2² = 4900 - 280 + 4 = 4624.

3. Direct Multiplication: For exact squares, use direct multiplication if you’re comfortable. For example, 34² = 34 × 34 = 1156.

4. Estimate and Adjust: For quicker estimates, find the nearest base (like 50 or 100), calculate the square, and adjust for the difference.

Using these tricks and techniques will help you tackle problems related to factorials, assumptions, and squares more efficiently.

Additional CAT Quantitative Aptitude Shortcut Methods

Percentages: To quickly find 15% of a number, calculate 10% and 5% separately and add them together. For example, 15% of 240 is 24 (10% of 240) + 12 (5% of 240) = 36.

Squaring Numbers Close to 50: For numbers close to 50, use (a+b)² = a² + 2ab + b². For example, to find 48², use (50 - 2)² = 50² - 2 × 50 × 2 + 2² = 2500 - 200 + 4 = 2304.

Multiplying Numbers Close to 100: For numbers like 97 and 98, use (100 - a) × (100 - b) = 10000 - 100(a + b) + ab. So, 97 × 98 = 10000 - 100(97 + 98) + (97 × 98) = 9506.

Percentage Increase/Decrease: To find a percentage increase, use (New Value - Old Value) / Old Value × 100%. For a decrease, the formula is (Old Value - New Value) / Old Value × 100%.

Finding the Average: To quickly find the average of a set of numbers, sum them up and divide by the number of items. For example, the average of 8, 12, and 15 is (8 + 12 + 15) / 3 = 35 / 3 = 11.67.

Simple Interest Calculation: Use the formula SI = (P × R × T) / 100, where P is the principal, R is the rate of interest, and T is the time in years.

Compound Interest Approximation: For compound interest, use the formula A = P × (1 + R/100)ⁿ, where P is the principal, R is the rate, and n is the number of periods. For quick approximation, use 1 + (R/100)ⁿ.

Ratios: To simplify ratios, divide all terms by their greatest common divisor. For example, 30:45 simplifies to 2:3 (since both 30 and 45 can be divided by 15).

Time and Work: If A can complete a job in x days and B in y days, their combined work rate is 1/x + 1/y. For example, if A can finish in 6 days and B in 12 days, their combined rate is 1/6 + 1/12 = 1/4, so they finish in 4 days.

Finding Percentages of Large Numbers: To find 8% of 1250, calculate 10% of 1250 (which is 125), and then subtract 2% (which is 25). Thus, 8% of 1250 = 125 - 25 = 100.

How to Practise CAT Quant Shortcuts?

Shortcuts become useful through repeated application. After learning a technique, practise it with CAT-level questions and previous-year questions to check whether it actually saves time.

• Learn the concept first
• Practise the shortcut with different question types
• Solve CAT PYQs from 2021–2025
• Take timed QA sectional tests
• Record recurring calculation mistakes
• Avoid a shortcut if it increases the chance of an error

CAT 2026 Quant ebooks and recommended resources

CAT 2026 Quant Ebooks and Recommended Resources

The following CAT 2026 Quant ebooks and resources cover key concepts, formulas, shortcuts, practice questions, PYQs and sectional tests to support focused Quantitative Aptitude preparation.

These resources cover concept building, formulas, topic-wise practice, PYQs, sectional tests and high-frequency Quant topics for CAT 2026.

Download Free Practice Questions with Detailed Solutions for CAT Exam - MCQ PDFs

Access free CAT practice questions in MCQ format with detailed solutions to strengthen concepts, improve accuracy and practise exam-level Quant questions.