CAT फॉर्मूला शीट 2026 पीडीएफ (CAT Formula Sheet 2026 PDF)

Number Systems

• 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
• (1² + 2² + 3² + ….. + n²) = n (n + 1) (2n + 1) / 6
• (1³ + 2³ + 3³ + ….. + n³) = (n(n + 1)/ 2)²
• Sum of first n odd numbers = n ²
• Sum of first n even numbers = n(n+1)
  

Algebra

Percentage

• Percentage Change = New Value−Old Value/Old Value×100
• Percentage Decrease = (Original Value−Decreased Value)/Original Value×100
• What percentage of x is y = (y/x) × 100
• Increase N by S% = N×(1+S/100)
• Decrease N by S% = N×(1-S/100)

Profit, Loss and Discount

• Profit (or) Gain = SP − CP
• Profit % = (Profit/CP) × 100
• SP = (100 + Gain %)/100 × CP
• CP = 100/(100 + Gain %) × SP
• Loss = CP − SP
• Loss % = Loss/(CP) × 100
• SP = (100-Loss%)/100 × CP
• CP = 100/(100-Loss%) × CP

HCF and LCM

• HCF × LCM = Product of the two numbers
• LCM of co-prime numbers = Product of the numbers
• HCF of co-prime numbers = 1
• HCF of two numbers a and b = HCF of (a-b, b)
• LCM of two numbers a and b = (a × b) / HCF(a, b)
• HCF of three numbers a, b, c = HCF of (HCF(a, b), c)

Speed, Time and Distance

• Distance = Speed × Time
• Time = Distance / Speed
• Speed = Distance / Time
• Average Speed = (Total distance travelled) / (Total time taken)

Time and Work

• If A can do a piece of work in n days, then A’s 1 day’s work = 1/n
• If A’s 1 day’s work = 1/n, then A can finish the work in n days.

Averages

Sum of Observations / Number of Observations

Mixture and Alligation

Rule of Alligation: If two ingredients are mixed, then
(Quantity of cheaper / Quantity of dearer) = (C.P. of dearer – Mean Price / Mean price – C.P. of cheaper)

Trigonometry

• cosec θ = 1 / sin θ
• sec θ = 1 / cos θ
• cot θ = 1 / tan θ
• sin θ = 1 / cosec θ
• cos θ = 1 / sec θ
• tan θ = 1 / cot θ

Coordinate Geometry

Distance Between Two Points A(x1, y1) and B(x2, y2): AB² = (x2 – x1)² + (y2 – y1)²

Probability

P(E)=n(E) / n(S)