Important Formulas: Quantitative Reasoning | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

Arithmetic reasoning often involves using basic formulas to solve problems. Here's a list of some common arithmetic formulas that can be helpful:

1. Addition: a + b = c
2. Subtraction: a - b = c
3. Multiplication: a * b = c
4. Division: a / b = c
5. Average: (a + b + c + ... + n) / n
6. Percentage: (part/whole) * 100
7. Ratio: a: b
8. Proportion: a / b = c / d
9. Distance: Speed * Time
10. Speed: Distance / Time
11. Time: Distance / Speed
12. Simple Interest: I = P * R * T / 100 (where I = interest, P = principal, R = rate, and T = time)
13. Compound Interest: A = P(1 + r/n)^(nt) (where A = amount, P = principal, r = annual interest rate, n = number of times interest is compounded per year, and t = time in years)
14. Profit or Loss: Profit = Selling Price - Cost Price (Loss = Cost Price - Selling Price)
15. Percent Increase or Decrease: (New Value - Old Value) / Old Value * 100
16. Fractions:
    • Addition: a/b + c/d = (ad + bc) / bd
    • Subtraction: a/b - c/d = (ad - bc) / bd
    • Multiplication: (a/b) * (c/d) = (a * c) / (b * d)
    • Division: (a/b) ÷ (c/d) = (a * d) / (b * c)
17. Decimal to Fraction: To convert a decimal to a fraction, write the decimal as the numerator and the denominator as a power of 10 based on the number of decimal places. Then, simplify the fraction.

18. Fraction to Decimal: Divide the numerator by the denominator.

19. Fraction to Percentage: (Fraction) * 100

20. Percentage to Fraction: (Percentage) / 100

21. Percentage to Decimal: (Percentage) / 100

22. Decimal to Percentage: (Decimal) * 100

23. Weighted Average: (w1 * x1 + w2 * x2 + ... + wn * xn) / (w1 + w2 + ... + wn)

24. Least Common Multiple (LCM): The smallest multiple that is exactly divisible by each of the numbers.

25. Greatest Common Divisor (GCD): The largest number that divides two or more numbers without leaving a remainder.

26. Prime Numbers: A number greater than 1 that has only two factors: 1 and itself.

27. Factors: The numbers that can be multiplied together to get the original number.

28. Square of a Number: a² = a * a

29. Cube of a Number: a³ = a * a * a

30. Square Root: √a is the number that, when multiplied by itself, equals a.

31. Cube Root: ∛a is the number that, when multiplied by itself three times, equals a.

32. Permutations: nPr = n! / (n - r)!, where n is the total number of elements and r is the number of elements chosen.

33. Combinations: nCr = n! / [r!(n - r)!], where n is the total number of elements and r is the number of elements chosen.