48 High-Frequency Quant Formulas to Sprint-Revise Before CAT 2026 Exam Day
A ruthlessly prioritised, last-minute Quant revision sheet for the final two weeks before CAT 2026. It lists 48 high-frequency formulas grouped into arithmetic, algebra and numbers, geometry, and modern math, each with a note on where it appears, plus a 2-week drill plan to convert reading into instant recall.
48 High-Frequency Quant Formulas to Sprint-Revise Before CAT 2026 Exam Day
Two weeks before CAT, no one needs another 200-page Quant book. They need the handful of formulas that actually keep showing up. This is that shortlist: 48 high-frequency Quant formulas for CAT 2026, each drawn from topics that appear on the paper year after year. It is not comprehensive coverage; it is ruthless prioritisation for the final sprint. Print it, screenshot it, and run through it daily, so that on slot day the formula is already in muscle memory and your time goes to thinking, not recalling.
How to Use These 48 Quant Formulas in the Final Sprint
Every formula on this list earns its place by frequency, not by elegance. Each one has surfaced repeatedly across recent CAT papers, either directly or inside a question that hides it one step down. The point of the sprint is recall speed. When you read a question stem, the matching formula should arrive before you finish reading, leaving your working time for the actual reasoning.
Treat the four tables below as a single sheet. Cover the right column, write each formula from memory, then check. The notes tell you where the formula tends to appear so you can connect notation to a real question type. If a particular block feels shaky, that is your signal for where the next focused CAT practice set should go.
The aspirants who clear a high Quant percentile are not the ones who know more formulas. They are the ones who recall the common ones in under two seconds. Speed of recall is a trainable skill: test yourself daily against the clock, not just by reading the sheet.
Arithmetic: The Quant Formulas You Cannot Skip
Arithmetic is the highest-return block in CAT Quant, and it leaks into data interpretation too. Percentages, ratios, averages, time-speed-distance, and interest reappear in disguised forms across the paper. Lock these fifteen first if your sprint time is short.
| Formula | Where it shows up |
|---|---|
| % change = ((New − Old) / Old) × 100 | Growth, profit, data interpretation |
| Successive change = a + b + (ab / 100) | Two back-to-back percentage moves |
| Profit % = (Profit / CP) × 100 | Profit and loss sums |
| SP after discount = MP × (1 − d/100) | Discount and marked-price questions |
| Simple Interest = (P × R × T) / 100 | Interest basics |
| Amount (CI) = P (1 + R/100)ⁿ | Compound interest growth |
| CI − SI (2 yrs) = P (R/100)² | The classic two-year difference trick |
| Average = Sum of terms / n | Averages, weighted means |
| Average speed = 2xy / (x + y) | Equal-distance two-leg journeys |
| Distance = Speed × Time | All time-speed-distance sets |
| Relative speed = S₁ ± S₂ | Trains, boats, opposite or same direction |
| Combined work = 1/a + 1/b | Time and work, pipes and cisterns |
| Alligation = (D − M) / (M − C) | Mixtures and average price |
| Profit share = Capital × Time | Partnership division |
| Combine ratios a:b, b:c into a:b:c | Chained ratio questions |
Algebra and Numbers: The Formulas Behind the Tricky Sets
Algebraic identities save real seconds when a question tries to make you expand or factor the long way. Pair them with the number-system results that decide remainder, factor, and last-digit questions. These seventeen do the heavy lifting in the trickier half of the paper.
| Formula | Where it shows up |
|---|---|
| (a + b)² = a² + 2ab + b² | Expansion and simplification |
| (a − b)² = a² − 2ab + b² | Expansion and simplification |
| a² − b² = (a + b)(a − b) | Quick factoring |
| a³ + b³ = (a + b)(a² − ab + b²) | Cubes and surds |
| a³ − b³ = (a − b)(a² + ab + b²) | Cubes and surds |
| (a+b+c)² = a²+b²+c²+2(ab+bc+ca) | Three-variable identities |
| Sum of first n naturals = n(n+1)/2 | Series and counting |
| Sum of squares = n(n+1)(2n+1)/6 | Series sums |
| AP: Tₙ = a + (n−1)d | Arithmetic progression |
| AP sum = n/2 [2a + (n−1)d] | Arithmetic progression |
| GP: Tₙ = arⁿ⁻¹, Sum = a(rⁿ−1)/(r−1) | Geometric progression |
| Roots = (−b ± √(b²−4ac)) / 2a | Quadratic equations |
| Sum = −b/a, Product = c/a | Quadratic roots without solving |
| logₐ(mn) = logₐm + logₐn | Logarithm questions |
| Factors of N = (p+1)(q+1)... | Number of divisors |
| HCF × LCM = product of two numbers | HCF and LCM problems |
| Zeros in n! = ⌊n/5⌋ + ⌊n/25⌋ + ... | Factorial trailing zeros |
The temptation in the last fortnight is to keep adding rare identities you saw in one mock. Resist it. A bloated sheet you half-remember is worse than a tight sheet you recall instantly. If a formula has not appeared in your recent mocks, it does not belong in your sprint.
Track Which Formulas You Still Forget
Optima Learn flags the exact Quant sub-topics where your recall slips, so your final-sprint revision targets the gaps instead of the whole syllabus.
Build a Targeted Revision PlanGeometry and Mensuration: High-Frequency Formulas
Geometry questions look intimidating but lean on a small, stable set of area, volume, and coordinate results. Reproduce these twelve cleanly and most figures become arithmetic. Keep a rough diagram habit so you map the formula to the shape instantly.
| Formula | Where it shows up |
|---|---|
| Triangle area = ½ × base × height | Basic triangles |
| Heron's = √(s(s−a)(s−b)(s−c)) | Triangle with three sides |
| a² + b² = c² (Pythagoras) | Right triangles, distances |
| Equilateral area = (√3/4) a² | Equilateral triangle |
| Circle: area = πr², circumference = 2πr | All circle questions |
| Sector area = (θ/360) × πr² | Sectors and arcs |
| Square diagonal = a√2 | Squares and rectangles |
| Cuboid volume = l × b × h | Boxes and tanks |
| Cylinder volume = πr²h, CSA = 2πrh | Cylinders |
| Cone volume = ⅓πr²h, l = √(r²+h²) | Cones and slant height |
| Sphere volume = (4/3)πr³, area = 4πr² | Spheres and hemispheres |
| Distance = √((x₂−x₁)² + (y₂−y₁)²) | Coordinate geometry |
Modern Math: The Last Few Formulas Worth Memorising
Modern math is a smaller slice of the paper, but its four core results are pure recall once you know them. They decide the counting and probability questions that aspirants otherwise reason out slowly and incorrectly.
| Formula | Where it shows up |
|---|---|
| Permutations: nPr = n! / (n−r)! | Ordered arrangements |
| Combinations: nCr = n! / (r!(n−r)!) | Selections and groups |
| P(A∪B) = P(A) + P(B) − P(A∩B) | Probability of either event |
| n(A∪B) = n(A) + n(B) − n(A∩B) | Two-set Venn questions |
An aspirant who recalls all 48 instantly typically saves fifteen to twenty seconds per Quant question. Across a 22-question section, that is roughly seven extra minutes, enough to attempt two or three more questions cleanly. Recall speed, not formula count, is where those marks come from.
Your Two-Week Revision Plan for These CAT Formulas
A formula sheet only works if you drill it on a schedule. Use the final fortnight to convert reading into instant recall, while keeping a thin layer of problem practice so the formulas stay tied to real questions rather than floating as notation.
- Days 1 to 4: write out each table from memory once a day; mark every formula you miss.
- Days 5 to 9: drill only the missed formulas, and solve five mixed problems daily that force you to pick the right one.
- Days 10 to 12: time yourself reproducing the whole sheet in under six minutes.
- Final 2 days: one calm read-through, no new formulas, and trust the recall you built.
Want this drill sequenced against your mock calendar? The CAT 2026 waitlist opens a plan that adapts to your weak sub-topics. The wider CAT 2026 preparation library keeps your strategy aligned. Curious how a sharper Quant section moves your overall number? Run a quick estimate on the CAT score predictor. Then revisit the full CAT preparation roadmap as exam day nears.
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Turn This Sheet Into a Daily Drill
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