Quantitative Aptitude Formula Sheet

• P(A) = favorable outcomes / total outcomes
• P(A or B) = P(A) + P(B) − P(A and B)
• P(at least one) = 1 − P(none)

e.g. "Probability of At Least One Six in Three Die Throws"

• No fixed formula — pattern recognition and case-by-case logic

e.g. "100 Doors Toggled by 100 People — Which Remain Open?"

• No fixed formula — rule-based deduction (see the dedicated guide below)

e.g. "Blood Relation — Chain of Five Relatives"

• Divisibility and remainder arithmetic: (a × b) mod n = [(a mod n) × (b mod n)] mod n
• Fermat's Little Theorem: a^(p−1) ≡ 1 (mod p) for prime p, gcd(a, p) = 1

e.g. "Remainder When 2^50 Is Divided by 31"

• nPr = n! / (n − r)!
• nCr = n! / (r! (n − r)!)
• Circular permutations = (n − 1)!

e.g. "Distinct Arrangements of the Letters in "BANANA""

• a : b = c : d ⇒ a × d = b × c
• Average speed (two equal distances) = 2xy / (x + y)

e.g. "Present Ages From a Changing Ratio (3:5 → 5:7 After 10 Years)"

• Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a
• AP nth term = a + (n − 1)d
• GP nth term = a·r^(n−1)

e.g. "Compound Interest — Two Years, Annual Compounding"

• Circle: Area = πr², Circumference = 2πr
• Triangle: Area = ½ × base × height
• Pythagorean theorem: a² + b² = c²

• AP sum = n/2 × [2a + (n − 1)d]
• GP sum = a(r^n − 1) / (r − 1), r ≠ 1

• Simple Interest = P × R × T / 100
• Compound Interest = P(1 + R/100)^T − P

e.g. "Finding the Principal From the CI–SI Difference"

• Combined rate = 1/A + 1/B (A, B = individual times)
• Time together = 1 / (combined rate)

e.g. "B Is Twice as Efficient as A — Find B's Time"

• |A ∪ B| = |A| + |B| − |A ∩ B|

• Profit % = (SP − CP) / CP × 100
• False-weight profit % = (true weight − false weight) / false weight × 100

e.g. "Dishonest Dealer's Profit From a False Weight"

• No fixed formula — reading and computing from charts/tables directly

• Angle between hands = |30H − 5.5M| degrees

• Odd-days method: 365 days = 1 odd day, leap year = 2 odd days

• No fixed formula — constraint-based reasoning (combines "Optimization" and "Optimization Puzzle" tags)