CAT Quant: 50 Must-Know Formulas (With Traps)
- MBA Entrance Exam Expert
- Jul 5
- 10 min read
CAT Quant is a tricky beast. It's not the kind of funny that makes you laugh, more like the kind that leaves you bewildered when you think you've mastered a formula, only to have the answer options quietly mock you.
This section is essentially a compilation of formulas that you should have at your fingertips. But it's not just about knowing the clean version of these formulas. I'm also including the typical traps that tend to appear in CAT style questions. The reality is, most people don't falter in Quant due to a lack of knowledge about formulas.
They stumble because they apply the right formula in an inappropriate context. Or they rush through the problem, make assumptions, and forget that CAT loves to throw curveballs with statements like “unless stated otherwise”.
So how do you make this list work for you?
First, take a moment to jot down the formulas that don't immediately come to mind onto a single sheet. Next, for each “trap”, write a brief explanation in your own words. Finally, challenge yourself by solving 10 mixed questions and ensure you mention the relevant formula before diving into the solution.
Now, let's delve into some key areas.
A) Arithmetic: percentages, ratios, averages, mixtures (1 to 18)
1) Percentage change
Formula: % change = (\frac{New - Old}{Old} \times 100) Trap: A common mistake is dividing by New. Remember, always divide by Old.
2) Successive percentage change
Formula: Net % change = (a + b + \frac{ab}{100}) Trap: This formula works for two changes only. For three changes, tackle it step by step.
3) If price increases by x%, consumption decreases by y% to keep expenditure same
Formula: (y = \frac{x}{100+x} \times 100) Trap: Many people mistakenly assume y = x. This is a classic error.
For those preparing for competitive exams like GMAT or CAT, mastering these quant concepts can significantly improve your performance. You might want to check out this GMAT Focus Edition course which could be beneficial in grasping these quant concepts better.
Additionally, understanding how CAT percentiles work can also play a crucial role in your preparation strategy. For insights on CAT percentiles and their impact on IIM interview calls, be sure to explore the linked article.
4) Profit
Formula: Profit = SP − CP Trap: If marked price, discount, tax etc are there, CP and SP get messy. Define them clearly first.
5) Profit percent
Formula: Profit% = (\frac{Profit}{CP} \times 100) Trap: Loss% also divides by CP, not SP.
6) Discount percent
Formula: Discount% = (\frac{MP - SP}{MP} \times 100) Trap: Two discounts. Don’t add them. Multiply: SP = MP(1−d1)(1−d2)
7) Simple Interest
Formula: SI = (\frac{PRT}{100}) Trap: T in years. Months need conversion. CAT loves 9 months, 15 months.
8) Amount in SI
Formula: A = P + SI Trap: If rate changes in between, do piecewise.
9) Compound Interest amount
Formula: (A = P(1+\frac{r}{100})^n) Trap: For half yearly compounding, r/2 and 2n. People forget both changes.
10) Difference between CI and SI (2 years)
Formula: CI − SI = (P(\frac{r}{100})^2) Trap: Only for 2 years. Don’t force it for 3 years.
11) Ratio basics
Formula: If A:B = m:n then A = km, B = kn Trap: k changes with context. If total is fixed, solve for k. Don’t assume k = 1.
12) Proportion
Formula: a:b = c:d ⇒ ad = bc Trap: Works only when they are in proportion. Often question says “in the ratio”, not “in proportion to”.
13) Average
Formula: Average = Sum / n Trap: Weighted situations. If group sizes differ, simple average of averages is wrong.
14) Weighted average
Formula: (\bar{x} = \frac{w_1x_1 + w_2x_2 + ...}{w_1+w_2+...}) Trap: Weights are quantities, not percentages unless specified.
15) Alligation (mixtures)
Formula: Ratio of quantities = (difference with mean) crosswise Trap: This gives ratio, not actual quantities. Also mean must lie between the two values.
16) Mixture replacement (remove x, add x)
Formula: Final quantity of original = (Initial \times (1-\frac{x}{V})^n) Trap: Only when you remove and replace equal volume, repeatedly.
17) Work and wages proportionality
Formula: Wages ∝ Work done Trap: Work done depends on time and efficiency. Don’t split wages just by time if efficiencies differ.
18) Partnership
Formula: Profit share ∝ (Capital × Time) Trap: If someone invests later or withdraws early, adjust time in months.
B) Time, work, pipes, speed, boats (19 to 30)
19) Work = Rate × Time
Formula: W = R×T Trap: Define work as 1 unit. Do not randomly use “days” as work.
20) If A takes x days, rate of A
Formula: Rate = 1/x Trap: If “x days working 8 hours/day” and another works 6 hours/day, rates change.
21) Combined work
Formula: If A does in x, B in y then together: (\frac{1}{T}=\frac{1}{x}+\frac{1}{y}) Trap: If one is a leak or destroys work, subtract.
22) Pipes and cisterns
Formula: Fill rate − leak rate = net rate Trap: Many forget leak starts after some time. Then do in phases.
23) Relative speed
Formula: Same direction: (v_1 - v_2), opposite: (v_1 + v_2) Trap: Decide direction carefully. “Chasing” is same direction, “towards” is opposite.
24) Time = Distance / Speed
Formula: T = D/S Trap: Units mismatch is a silent killer. km/h with meters, minutes etc.
25) Average speed (equal distances)
Formula: Avg speed = (\frac{2v_1v_2}{v_1+v_2}) Trap: This is only for equal distances, not equal times.
26) Average speed (unequal distances)
Formula: Avg speed = Total distance / Total time Trap: Don’t try to shortcut. Just compute total time.
27) Trains crossing a pole
Formula: Time = Train length / Speed Trap: Speed must be in m/s. Convert: km/h × (5/18)
28) Trains crossing a platform
Formula: Time = (Train length + Platform length) / Speed Trap: People forget to add lengths. Every year.
29) Boats and streams
Formula: Downstream = b+s, Upstream = b−s Trap: If upstream speed is given, b is not that speed. Solve b and s.
30) Races
Formula: If A beats B by d in race of L: speed ratio (= \frac{L}{L-d}) Trap: “By time” vs “by distance” changes approach. Read carefully.
C) Algebra: identities, equations, inequalities, logs (31 to 40)
31) (a+b)²
Formula: (a^2 + b^2 + 2ab) Trap: This shows up in “minimum value” questions. Don’t expand blindly, sometimes factor helps more.
32) (a−b)²
Formula: (a^2 + b^2 - 2ab) Trap: Used for turning expressions into squares. Also for non negativity.
33) a² − b²
Formula: (a−b)(a+b) Trap: Very common in simplification. But don’t factor if it complicates equation solving.
34) (a+b)³ and (a−b)³
Formula: ((a+b)^3 = a^3 + b^3 + 3ab(a+b)) ((a-b)^3 = a^3 - b^3 - 3ab(a-b)) Trap: People misplace signs. Slow down.
35) a³ + b³ and a³ − b³
Formula: (a^3+b^3=(a+b)(a^2-ab+b^2)) (a^3-b^3=(a-b)(a^2+ab+b^2)) Trap: The middle sign flips. Memorize it, don’t “derive” in exam.
36) Quadratic formula
Formula: For (ax^2+bx+c=0), (x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}) Trap: CAT often expects factorization, not quadratic formula. Formula is fine, but time isn’t.
37) Sum and product of roots
Formula: If roots α, β then α+β = −b/a and αβ = c/a Trap: Only for quadratic written in standard form. Don’t forget dividing by a.
38) Remainder theorem
Formula: Remainder when f(x) divided by (x−a) is f(a) Trap: Division by (x+a) means a = −a. People plug +a.
39) Factor theorem
Formula: (x−a) is a factor of f(x) if f(a)=0 Trap: Again, (x+a) factor means f(−a)=0.
40) Log basics
Formulas: (\log(ab)=\log a + \log b) (\log(\frac{a}{b})=\log a - \log b) (\log(a^k)=k\log a) Trap: Log rules work for positive a, b (in real numbers). CAT loves sneaky domain restrictions.
D) Geometry and Mensuration (41 to 50)
41) Angle sum of triangle
Formula: A + B + C = 180° Trap: Applies to Euclidean triangles only. For quadrilateral, sum is 360°. Don’t mix.
42) Pythagoras
Formula: In right triangle, (a^2+b^2=c^2) Trap: Only for right triangles. Not “almost right”.
43) Area of triangle
Formula: Area = 1/2 × base × height Trap: Height is perpendicular. Not a random side.
44) Heron’s formula
Formula: Area = (\sqrt{s(s-a)(s-b)(s-c)}), where (s=\frac{a+b+c}{2}) Trap: Works when all 3 sides known. But check triangle validity (a+b>c etc).
45) Equilateral triangle area
Formula: (\frac{\sqrt{3}}{4}a^2) Trap: People use 1/2 a². No. That’s not a thing.
46) Circle basics
Formulas: Circumference = (2\pi r) Area = (\pi r^2) Trap: Diameter given, r = d/2. Too basic, yet it gets people.
47) Sector area and arc length
Formulas: Sector area = (\frac{\theta}{360}\pi r^2) Arc length = (\frac{\theta}{360}2\pi r) Trap: θ in degrees here. If radians, use (\frac{1}{2}r^2\theta) and (r\theta).
48) Rectangle, square
Formulas: Rectangle area = l×b, perimeter = 2(l+b) Square area = a², perimeter = 4a Trap: Diagonal of square = (a\sqrt{2}). CAT uses that more than area sometimes.
49) Cylinder
Formulas: Curved surface area = (2\pi rh) Total surface area = (2\pi r(h+r)) Volume = (\pi r^2 h) Trap: Open cylinder vs closed cylinder changes TSA. Read wording.
50) Cone
Formulas: Slant height (l=\sqrt{r^2+h^2}) CSA = (\pi rl) TSA = (\pi r(l+r)) Volume =(\frac{1}{3}\pi r^2 h) Trap: They’ll give slant height and ask height. Or give height and ask l. Don’t assume.
The real traps that don’t look like traps
Let me add a few “meta traps” CAT Quant repeats, regardless of topic.
Trap 1: “integer” is not “positive integer”
If they say integer, negative is allowed. Zero is allowed. This changes everything in inequalities, divisibility, and number of solutions.
Trap 2: “distinct” and “different”
If they say distinct, duplicates are not allowed. If they don’t say distinct, duplicates are usually allowed. Usually. CAT is cruel like that.
Trap 3: Units and conversion
Especially in Time Speed Distance, SI, CI, mensuration. If you’re off by a factor of 60 or 1000, you will still find an option that matches. That’s why it’s dangerous.
Trap 4: Approximating π or √ values
If the options are close, approximation can backfire. If options are far apart, approximation is smart. Choose based on options, not habit.
Trap 5: Overusing formulas
CAT rewards structure more than formula flexing. Many questions are faster with:
picking values
eliminating options
using ratios
back solving from answers
Formulas are just the base layer.
A quick way to revise these in 7 days
If your exam is close, do this.
Day 1: Percentages, profit loss, SI CI
Day 2: Ratios, averages, mixtures
Day 3: Work, pipes
Day 4: Speed, trains, boats
Day 5: Algebra identities, quadratics
Day 6: Logs, remainders, basic functions
Day 7: Geometry, mensuration, mixed mock review
And every day, solve 20 questions mixed. Not chapter wise. Because CAT isn’t chapter wise.
For those considering alternative paths to IIMs without taking the CAT exam1, it's important to understand the different routes available such as GMAT which has its own set of guidelines and requirements2.
As you prepare for your upcoming exams whether it be CAT or GMAT34, remember to stay focused and utilize effective strategies for success.
One last thing (that actually helps)
If you’re preparing seriously, formulas are not your bottleneck. Strategy and practice quality are.
If you’re still deciding where to prep from, or you want to compare coaching options by city, fees, and reviews, you can check MBA Entrance Exam Guide by GOALisB at: https://mbaentrance.goalisb.com/
It’s built exactly for that. Discovery first, then decision. Saves time, and honestly reduces confusion.
Alright. Keep this list tight, keep your errors tighter, and don’t let “I knew the formula” become the story of your CAT attempt.
Footnotes
FAQs (Frequently Asked Questions)
Why is CAT Quant considered tricky, and how can I avoid common pitfalls?
CAT Quant is tricky because it often tests not just formula knowledge but the application of formulas in appropriate contexts. Common pitfalls include misapplying formulas, rushing through problems, making unwarranted assumptions, and overlooking statements like "unless stated otherwise". To avoid these, understand each formula deeply, note typical traps, and practice applying formulas carefully in diverse problems.
How should I prepare and use the list of CAT Quant formulas effectively?
Start by jotting down formulas that don't come to mind easily on a single sheet. For each trap associated with a formula, write a brief explanation in your own words to internalize it. Then challenge yourself by solving mixed questions—before solving each, explicitly mention the relevant formula. This approach helps reinforce understanding and prepares you for CAT-style curveballs.
What is a common mistake when calculating percentage change in CAT Quant questions?
A common mistake is dividing by the new value instead of the old value when calculating percentage change. The correct formula is % change = ((New - Old) / Old) × 100. Always ensure you divide by the original (old) value to avoid errors.
How do successive percentage changes work, and what should I watch out for?
For two successive percentage changes 'a' and 'b', the net percentage change is given by (a + b + (ab/100)). However, this formula works only for two changes. For three or more changes, apply the changes step-by-step rather than trying to extend this formula directly.
What are some important traps related to profit and discount calculations in CAT Quant?
In profit calculations, if marked price, discount, or tax are involved, cost price (CP) and selling price (SP) can become complex; always define CP and SP clearly before solving. For discounts, when there are two successive discounts, do not add them; instead multiply: SP = MP × (1 - d1) × (1 - d2). Also remember that loss% divides by CP, not SP.
How can understanding CAT percentiles impact my preparation strategy?
Understanding CAT percentiles helps you gauge your relative performance and set realistic targets for IIM interview calls. High percentiles improve chances of selection. Incorporating this insight into your preparation strategy allows focused study plans and stress management during exams. For detailed insights, exploring resources on CAT percentiles and their impact on interviews is beneficial.
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