{"id":10126,"date":"2026-10-23T12:08:25","date_gmt":"2026-10-23T12:08:25","guid":{"rendered":"https:\/\/iimtuniversity.edu.in\/blog\/?p=10126"},"modified":"2026-10-15T12:35:01","modified_gmt":"2026-10-15T12:35:01","slug":"cat-quantitative-aptitude-formulas-pdf","status":"publish","type":"post","link":"https:\/\/iimtuniversity.edu.in\/blog\/cat-quantitative-aptitude-formulas-pdf\/","title":{"rendered":"CAT Quantitative Aptitude Formula Sheet: Free Chapter-Wise Revision Guide PDF"},"content":{"rendered":"

For CAT 2026 aspirants, remembering the right formula can save valuable time during Quantitative Aptitude (QA). However, memorising equations without understanding their applications can lead to avoidable mistakes.<\/span><\/p>\n

This chapter-wise guide covers important <\/span>CAT quantitative aptitude formulas<\/b> for Arithmetic, Algebra, Geometry, Number Systems and Modern Mathematics. Use it while practising questions, analysing mocks or completing your last-minute CAT revision.<\/span><\/p>\n

Free CAT Quant Formula Sheet PDF 2026<\/b><\/h3>\n

Want the essential formulas in one printable reference? Our chapter-wise CAT Quant revision sheet is designed to help you review equations, important conditions and common applications.<\/span><\/p>\n

Download Free CAT Quant Formula Sheet PDF 2026<\/b><\/a><\/p>\n

Free PDF | Chapter-wise formulas | Quick revision reference<\/span><\/i><\/p>\n

What Are the Most Important CAT Quantitative Aptitude Formulas for 2026?<\/b><\/h2>\n

Focus on formulas that help you solve quantitative problems accurately and efficiently.<\/span><\/p>\n\n\n\n\n\n\n\n\n
Topic<\/b><\/td>\nEssential Concepts<\/b><\/td>\n<\/tr>\n
Arithmetic<\/span><\/td>\nPercentages, ratios, averages, profit and loss, interest, time and work<\/span><\/td>\n<\/tr>\n
Algebra<\/span><\/td>\nIdentities, quadratics, exponents, logarithms, progressions<\/span><\/td>\n<\/tr>\n
Geometry<\/span><\/td>\nTriangles, circles, quadrilaterals, mensuration<\/span><\/td>\n<\/tr>\n
Number Systems<\/span><\/td>\nHCF, LCM, divisibility, remainders<\/span><\/td>\n<\/tr>\n
Modern Mathematics<\/span><\/td>\nCounting principles, permutations, combinations, probability<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

This is a preparation reference, not an official CAT 2026 syllabus or a prediction of examination questions.<\/span><\/p>\n

What Are the Important Arithmetic Formulas for CAT Quant Preparation?<\/b><\/h2>\n

Arithmetic formulas simplify calculations involving proportions, rates and changes in value.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n
Concept<\/b><\/td>\nFormula<\/b><\/td>\n<\/tr>\n
Percentage<\/span><\/td>\n(\\frac{\\text{Part}}{\\text{Whole}}\\times100)<\/span><\/td>\n<\/tr>\n
Percentage change<\/span><\/td>\n(\\frac{\\text{New}-\\text{Old}}{\\text{Old}}\\times100)<\/span><\/td>\n<\/tr>\n
Profit percentage<\/span><\/td>\n(\\frac{SP-CP}{CP}\\times100)<\/span><\/td>\n<\/tr>\n
Loss percentage<\/span><\/td>\n(\\frac{CP-SP}{CP}\\times100)<\/span><\/td>\n<\/tr>\n
Average<\/span><\/td>\n(\\frac{\\text{Sum of observations}}{\\text{Number of observations}})<\/span><\/td>\n<\/tr>\n
Simple interest<\/span><\/td>\n(SI=\\frac{PRT}{100})<\/span><\/td>\n<\/tr>\n
Compound amount<\/span><\/td>\n(A=P(1+\\frac{r}{100})^n)<\/span><\/td>\n<\/tr>\n
Speed<\/span><\/td>\n(\\frac{\\text{Distance}}{\\text{Time}})<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Here, (CP) means cost price, (SP) means selling price, (P) is principal, (R) or (r) is the annual interest rate, and (T) or (n) is time in years. The compound amount formula assumes annual compounding at a constant rate.<\/span><\/p>\n

Quick Example: Successive Percentage Changes<\/b><\/h3>\n

If a price increases by 20% and then decreases by 10%, the net percentage change is:<\/span><\/p>\n

[<\/span>
\n<\/span>20-10+\\frac{20(-10)}{100}=8%<\/span>
\n<\/span>]<\/span><\/p>\n

The final price is 8% higher than the original price\u2014not 10% higher.<\/span><\/p>\n

\"CAT<\/a><\/p>\n

What Are the Important Algebra Formulas for the CAT Exam?<\/b><\/h2>\n

Algebra questions often require simplifying expressions, identifying patterns and solving equations.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n
Concept<\/b><\/td>\nFormula<\/b><\/td>\n<\/tr>\n
Square identity<\/span><\/td>\n((a+b)^2=a^2+2ab+b^2)<\/span><\/td>\n<\/tr>\n
Difference of squares<\/span><\/td>\n(a^2-b^2=(a-b)(a+b))<\/span><\/td>\n<\/tr>\n
Cube identity<\/span><\/td>\n((a+b)^3=a^3+3a^2b+3ab^2+b^3)<\/span><\/td>\n<\/tr>\n
Quadratic roots<\/span><\/td>\n(x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a})<\/span><\/td>\n<\/tr>\n
Arithmetic progression<\/span><\/td>\n(a_n=a+(n-1)d)<\/span><\/td>\n<\/tr>\n
AP sum<\/span><\/td>\n(S_n=\\frac{n}{2}[2a+(n-1)d])<\/span><\/td>\n<\/tr>\n
Geometric progression<\/span><\/td>\n(a_n=ar^{n-1})<\/span><\/td>\n<\/tr>\n
Exponent rule<\/span><\/td>\n(a^ma^n=a^{m+n})<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

For quadratic roots, (a\\ne0). Real roots exist when (b^2-4ac\\ge0).<\/span><\/p>\n

The logarithm rule (\\log_b(xy)=\\log_bx+\\log_by) requires (x,y>0), (b>0) and (b\\ne1).<\/span><\/p>\n

What Are the Important Geometry Formulas for CAT Quantitative Aptitude?<\/b><\/h2>\n

Recognise the relevant shape and its properties before substituting values.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
Shape<\/b><\/td>\nFormula<\/b><\/td>\n<\/tr>\n
Triangle area<\/span><\/td>\n(\\frac12 bh)<\/span><\/td>\n<\/tr>\n
Pythagoras<\/span><\/td>\n(a^2+b^2=c^2)<\/span><\/td>\n<\/tr>\n
Circle area<\/span><\/td>\n(\\pi r^2)<\/span><\/td>\n<\/tr>\n
Circle circumference<\/span><\/td>\n(2\\pi r)<\/span><\/td>\n<\/tr>\n
Rectangle area<\/span><\/td>\n(lb)<\/span><\/td>\n<\/tr>\n
Trapezium area<\/span><\/td>\n(\\frac12(a+b)h)<\/span><\/td>\n<\/tr>\n
Cylinder volume<\/span><\/td>\n(\\pi r^2h)<\/span><\/td>\n<\/tr>\n
Cone volume<\/span><\/td>\n(\\frac13\\pi r^2h)<\/span><\/td>\n<\/tr>\n
Sphere volume<\/span><\/td>\n(\\frac43\\pi r^3)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The Pythagorean theorem applies to right-angled triangles, with (c) representing the hypotenuse. In area formulas, (h) represents perpendicular height.<\/span><\/p>\n

Which Number System Formulas Should You Memorise for CAT?<\/b><\/h2>\n

Number Systems require understanding factors, multiples and divisibility alongside formulas.<\/span><\/p>\n

For two positive integers:<\/span><\/p>\n

[<\/span>
\n<\/span>HCF\\times LCM=\\text{Product of the two numbers}<\/span>
\n<\/span>]<\/span><\/p>\n

Other useful results include:<\/span><\/p>\n