Probability

• Complementary Probability: P(A’)=1−P(A)
• Shortcut for "At least one" problems: P(At least one)= 1− P(None)

• "At Most":
  P(X≤N)= P(X=1)+P(X=2)+P(X=3) + … + P(X=N)

Divisibility

Primes of number n: [where n=p1^e1 * p2^e2 * … * pn^en]
then Number of divisors = (e1+1) * (e2+1) * … * (en+1)

Example: 60=2^2 × 3^1 × 5^1 -> then 60 has (3 x 2 x 2) = 12 divisors

Interest

• Simple Interest (SI): (P x R x T) / 100 [if % is taken as x/100 ex: 10% = 10/100] or else: (P x R x T) [if % is taken as decimal ex: 10% = 0.10]

  • P = Principal amount
  • R = Rate of interest per annum
  • T= Time in years

Amount at End: P + Simple Interest = P * (1 + (RT)/100 )

Compound Interest: [ P x (1 + R)^T ] - P

Percentage