The Only 20 Quant Formulas You Actually Need for CAT
A categorised, high-yield set of about twenty Quant formulas for CAT, mapped to when each one actually earns you marks under time pressure.
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Why Twenty Is Enough
Most aspirants collect hundreds of formulas and use twenty. The CAT Quant section rewards a small, well-drilled toolkit far more than an encyclopaedic one. Remember the weightage: Arithmetic is roughly 40 percent of QA, Algebra about 35 percent, Geometry around 15 percent, with Number System and Modern Math near 5 percent each. Put differently, Arithmetic and Algebra together account for close to 70 percent of your Quant marks. Your formula effort should follow that distribution, not spread itself thin across topics that rarely appear.
This is not a shortcut list. Every formula below is one you will genuinely reach for in a real paper. What separates a 90-percentiler from a 99-percentiler is rarely a rare identity; it is fluent, instant recall of the common ones so that mental bandwidth stays free for reading the question correctly. The QA section is a two-hour test's final forty minutes, hard-locked, with no chance to borrow time. When the clock is draining, the aspirant who has to reconstruct a formula from scratch has already lost the question. The aspirant who deploys it reflexively is still reading, setting up and verifying.
How To Read The Tables Below
Each table pairs a formula with the exact situation where it earns marks. Do not memorise the formula in isolation; memorise the trigger. When you see equal distances at two speeds, the harmonic-mean speed formula should fire automatically before you have finished reading the sentence. That trigger-to-tool reflex is the entire point of this list.
Arithmetic: The Highest-Yield Bucket
Because Arithmetic dominates the section, these deserve the most drilling. Percentages, ratios, time-speed-distance and time-and-work recur across mocks and the actual test.
| Topic | Formula | When to use |
|---|---|---|
| Percentage change | Change = (New minus Old) divided by Old, times 100 | Profit-loss, data interpretation, growth problems |
| Successive change | Net = a + b + (a times b divided by 100) | Two consecutive percentage changes, discounts on discounts |
| Simple interest | SI = P times R times T divided by 100 | Straightforward interest, flat-rate loans |
| Compound interest | Amount = P times (1 + R over 100) raised to T | Annual compounding, population growth |
| Average speed | Average = 2xy divided by (x + y) | Equal distances at two different speeds |
| Time and work | Work rate adds: 1 over A + 1 over B | Combined work, pipes and cisterns |
| Mixtures (alligation) | Ratio = (High minus Mean) to (Mean minus Low) | Blending two grades or prices to a target |
A Worked Arithmetic Example
Suppose a shopkeeper marks a product up by 40 percent and then offers a 25 percent discount. What is the net effect on the original cost? Reach for successive change with a = 40 and b = minus 25. Net = 40 + (minus 25) + (40 times minus 25 divided by 100) = 15 minus 10 = 5. The net effect is a 5 percent gain. Notice that you never computed a rupee value; the formula collapsed two operations into one line. This is the fluency dividend.
Now a time-and-work case. A can finish a job in 12 days and B in 18 days. Working together, their combined rate is 1 over 12 + 1 over 18. The lowest common denominator is 36, so this becomes 3 over 36 + 2 over 36 = 5 over 36. The pair finishes in 36 over 5, or 7.2 days. Again, one setup, one clean answer, no wasted steps.
Algebra: The Second Pillar
Algebra questions reward pattern recognition. These identities and relationships let you collapse a messy expression into something solvable in seconds.
| Topic | Formula | When to use |
|---|---|---|
| Square identity | (a + b) squared = a squared + 2ab + b squared | Expanding or factoring, simplifying surds |
| Difference of squares | a squared minus b squared = (a + b)(a minus b) | Fast factoring, cancelling terms |
| Sum and product of roots | Sum = minus b over a; Product = c over a | Quadratics without solving fully |
| Discriminant | D = b squared minus 4ac | Judging nature and number of roots |
| Arithmetic progression | Sum = n over 2 times (first + last) | Evenly spaced sequences, series totals |
| Geometric progression | Sum = a times (r to the n minus 1) over (r minus 1) | Constant-ratio sequences, infinite GP when r is less than 1 |
| Logarithm rule | log(mn) = log m + log n | Breaking apart or combining log expressions |
A Worked Algebra Example
A quadratic has roots whose sum is 7 and whose product is 12. You do not need to solve it to answer many questions about it. If asked for the sum of the squares of the roots, use the identity: sum of squares = (sum) squared minus 2 times product = 49 minus 24 = 25. The sum-and-product relationships let you sidestep the quadratic formula entirely. In CAT, that saved minute is often the difference between attempting one more question and not.
For an infinite geometric progression where the first term is 8 and the common ratio is one-half, the sum tends to a over (1 minus r) = 8 over (1 minus 0.5) = 16. Recognising when r is less than 1, so the series converges, is the trigger; the formula is the tool.
Fluency beats coverage. A 99-percentiler recalls these instantly and spends their forty minutes reading questions correctly, not hunting for the right identity.
Geometry and Mensuration
Geometry is a smaller slice but a reliable one. A handful of relationships handle most triangle, circle and solid problems.
| Topic | Formula | When to use |
|---|---|---|
| Pythagoras | hypotenuse squared = base squared + height squared | Right triangles, distances, diagonals |
| Area of triangle | Area = half times base times height | Any triangle with a known base and height |
| Circle | Area = pi r squared; Circumference = 2 pi r | Circles, sectors, rolling-wheel problems |
| Cone or cylinder volume | Cylinder = pi r squared h; Cone = one-third of that | Solids, capacity, melting-and-recasting |
Common Pythagorean Triples Worth Memorising
Geometry speed often comes not from the formula but from recognising a triple on sight, so you skip the arithmetic entirely. Keep these instantly available.
| Triple | Ratio family | Where it shows up |
|---|---|---|
| 3, 4, 5 | Also 6-8-10, 9-12-15 | The default right triangle in most problems |
| 5, 12, 13 | Also 10-24-26 | Ladder, distance and diagonal setups |
| 8, 15, 17 | Standalone | Less common but a frequent CAT trap |
| 7, 24, 25 | Standalone | Circle chords and coordinate geometry |
When a right triangle shows two of these numbers, the third is instant. Recognising 5 and 12 tells you the hypotenuse is 13 without touching Pythagoras. That is seconds saved on a question you might otherwise grind through.
Number System and Modern Math
These topics are small in weightage but appear often enough to matter, and they cluster around a few counting and divisibility ideas.
| Topic | Formula | When to use |
|---|---|---|
| Number of factors | If N = p to the a times q to the b, factors = (a + 1)(b + 1) | Counting divisors from prime factorisation |
| Combinations | nCr = n factorial over (r factorial times (n minus r) factorial) | Selecting without order, probability setups |
| Permutations | nPr = n factorial over (n minus r) factorial | Arranging where order matters |
A Worked Counting Example
How many factors does 360 have? First factorise: 360 = 2 cubed times 3 squared times 5. Add one to each exponent and multiply: (3 + 1)(2 + 1)(1 + 1) = 4 times 3 times 2 = 24 factors. No listing, no guesswork. The moment you see "how many factors", the trigger fires and the prime factorisation does the rest.
Common Mistakes That Waste These Formulas
Knowing a formula and misapplying it under pressure is more common than not knowing it. Watch for these recurring errors, each of which shows up in mock error logs again and again.
- Confusing permutations and combinations. If order matters, it is nPr; if not, nCr. Rushed candidates default to the wrong one and never re-check.
- Using the arithmetic mean of two speeds instead of the harmonic mean. For equal distances, the average speed is 2xy over (x + y), never (x + y) over 2. The simple average always overstates it.
- Forgetting the cross term in successive percentage change. Adding 40 and minus 25 to get 15 ignores the interaction term and gives the wrong answer on non-trivial numbers.
- Mishandling the sign in sum of roots. It is minus b over a, not b over a. A dropped negative sign silently corrupts the whole solution.
- Applying simple interest logic to a compound interest question, or vice versa, because the problem was read too quickly.
Every one of these is a selection or reading error, not a knowledge gap. That is precisely why the fix is drilling and verification, not more theory.
How to Actually Own These
Reading a formula is not owning it. Write each one from memory, then solve five varied problems per formula until you no longer pause to recall it. Build a single index card per topic and cycle through the deck until every trigger fires without hesitation. Speed on CAT Quant is mostly the absence of hesitation, not faster arithmetic.
When you take full-length mocks and analyse them on MBA CATalyst, tag every Quant error by which of these tools you failed to reach for. A pattern will emerge fast, usually in Arithmetic, and that is exactly where a few focused hours move your percentile the most.
The Takeaway
The goal is not to know more formulas than the next aspirant; it is to deploy these twenty without thinking, so your scarce forty minutes go to reading, setting up and verifying rather than remembering. A candidate fluent in twenty formulas will out-score one who half-remembers two hundred, every single time. Master the trigger for each, drill until recall is instant, and let your error log tell you which of these still costs you marks. That focused loop, not endless formula collection, is what turns Quant from a scramble into a section you finish with time to spare.
Reading is step one. Mocks are where scores move.
Put this into practice on a full-length, exam-realistic mock, then let MBA CATalyst's analytics tell you exactly which topics and time-traps to fix next.