Quantitative Aptitude

Pure recurring decimal 0.abcabc... = abc / (999... with same number of digits as abc)

Div by 2: last digit is 0, 2, 4, 6, or 8

HCF × LCM = Product of two numbers (only for two numbers)

log_a(mn) = log_a(m) + log_a(n)

Check first differences

LCM × HCF = Product of two numbers

Look for: AP, GP, squares, cubes, primes, alternating series

Sum of first n natural numbers = n(n+1)/2

BODMAS = Brackets, Orders, Division, Multiplication, Addition, Subtraction

√(a × b) = √a × √b

aᵐ × aⁿ = aᵐ⁺ⁿ (same base, add powers)

Unit digit of aⁿ depends only on the unit digit of a and the cycle of n

Average = Sum of all items / Number of items

Direct proportion: x₁/y₁ = x₂/y₂

Discount = Marked Price (MP) − Selling Price (SP)

Mean value = total value ÷ total quantity

Profit share ratio = capital x time

x% = x/100

If present age = x, then age n years ago = x − n

Profit = SP - CP

If A:B = a:b, then A = ak and B = bk

Downstream speed = boat speed + stream speed

Odd days in ordinary year = 1; leap year = 2

Angle = |30H - 5.5M|

Filling pipe rate = +1/t (positive contribution)

Train crossing pole/person: time = train length / speed

If A beats B by d metres in a race of L metres, B runs (L - d) metres when A runs L metres

Work done by one person in one day = 1/n (if the person completes the job in n days)

Distance = Speed × Time

BD = SI on face value (Amount)

A = P(1 + R/100)^n

Equal installment under SI: P = n×I × [1 + r(n+1)/(2×100)] where I = installment, n = number, r = rate

SI = (P × N × R) / 100

Income = (Dividend% × Face Value) / 100

PW = (Amount × 100) / (100 + R×T)

Angles of a triangle = 180 degrees

tan θ = Height / Horizontal Distance

Rectangle area = l x b

sin θ = Opposite / Hypotenuse

Write facts as a mini table before solving

Percentage change = change / original x 100

Test Statement 1 alone → sufficient?

Part = Total × percentage ÷ 100

Position from left: A=1, B=2, ... Z=26

Find the exact relation in the first pair, then apply the SAME relation to the second

Mother's brother = Uncle (maternal uncle)

Alphabet positions: A=1, B=2, C=3 ... Z=26

Left turn from N = W, from W = S, from S = E, from E = N

Identify: what changes each step — position, value, or both?

Total people = rank from left + rank from right − 1

Linear: left of X = lower seat number (seats numbered left to right)

All A are B → A circle fully inside B

Subset → smaller circle fully inside the larger circle

(a + b)² = a² + 2ab + b²

n! = n × (n−1) × … × 2 × 1, and 0! = 1

P(E) = n(E) / n(S) — favourable outcomes / total outcomes