ABHYAS · PLACEMENT TESTS, SSC AND BANK EXAMS

Abhyas Prep: Advanced Quant अभ्यास प्रेप: उन्नत मात्रात्मक योग्यता

Exam-style questions with explained wrong options and shortcuts: arrangements and selections, probability with dice, coins, cards and bags, laws of logarithms, surds and indices, square and cube roots, and problems on numbers.

Permutation & combination

Arranging letters of a word and people in a circleLetters with repeats: n! ÷ (p! q! …). Letters that must stay together: tie them into one block, then arrange the block inside. Around a circle: (n − 1)!.
Selections and committees with conditionsChoosing (order does not matter) is nCr. Split conditions into cases and multiply within a case; for “at least one”, subtract the “none” case from the total.

Probability

Probability with dice, coins, cards and bagsProbability = favourable outcomes ÷ total equally likely outcomes. List ordered outcomes for dice, subtract overlaps for “or”, and reduce the total after each draw when there is no replacement.

Logarithm

Laws of logarithmslog (xy) = log x + log y, log (x/y) = log x − log y, log xⁿ = n log x, and log_b x = log x / log b. A log is just the power: log_b x = k means bᵏ = x.

Surds & indices

Laws of indices and surdsSame base: multiply → add powers, divide → subtract, power of a power → multiply. a⁻ⁿ = 1/aⁿ and a^(p/q) = (q-th root of a)ᵖ. Surds combine only when the number under the root is the same.

Square & cube roots

Square and cube roots by the unit-digit methodThe last digit of a perfect square or cube narrows down the last digit of its root; bracketing the leading digits between two known squares or cubes fixes the rest.

Problems on numbers

Problems on numbers: digits, sums, differences and percentagesWrite a two-digit number as 10a + b; reversing it changes the value by 9 × (difference of digits). For percentages, the base is the number before the change.