IPMAT Indore cheat sheet

Percentage change of a value passed through successive changes a% then b% is a + b + ab/100; a 20% rise then 20% fall gives a net 4% fall, not zero.

If price rises by r%, consumption must fall by 100r/(100 + r)% to keep expenditure constant; if price falls by r%, consumption can rise by 100r/(100 - r)%.

Work: if A alone takes a days and B alone b days, together they take ab/(a + b) days; combined rate is 1/a + 1/b per day.

Pipes: a filling pipe of rate 1/a and a draining pipe of rate 1/b give net rate 1/a - 1/b; time = ab/(b - a) when b > a.

Simple interest = PRT/100; compound interest for 2 years = P[(1 + R/100)^2 - 1] = 2(SI on one year) + interest on that interest.

Rule of 72: money at R% compounded annually doubles in roughly 72/R years; exact doubling time is ln2 / ln(1 + R/100).

Mixtures: alligation gives ratio of quantities = (higher value - mean) : (mean - lower value); use for blending, average speed splits, and profit mixing.

Relative speed: same direction subtract, opposite direction add. Trains crossing each other use sum of lengths divided by relative speed.

Ratio scaling: in a : b : c, set parts to a common unit by LCM of the given numbers before comparing fractional shares.

In linear arrangements, 'A is not adjacent to B' plus a fixed seat often forces the rest; place the most constrained person first.

Circular arrangement: n people have (n - 1)! distinct arrangements; clockwise and anticlockwise mirror images are distinct unless the problem says necklaces or garlands.

Syllogism: 'All A are B' + 'All B are C' implies 'All A are C'; 'Some A are B' never yields 'All A are B'.

Blood relations: draw a tree with generation rows; vertical line = parent-child, horizontal = spouse or sibling, and always re-anchor to the person asked about.

Number series: check first differences, then ratios, then alternating sub-series at odd and even positions before assuming a polynomial rule.

Coding-decoding: test letter-position shifts (A=1 to Z=26) forward and backward, then reverse-alphabet mapping (A=26) if shifts fail.

Direction sense: use a coordinate grid; final displacement = square root of (net east-west)^2 + (net north-south)^2.

Calendar: ordinary year shifts the weekday by 1, a leap year by 2; century years are leap only if divisible by 400.

Data sufficiency: a statement is sufficient only if it gives a unique value; two different possible values means insufficient even if both satisfy the stem.

Subject-verb agreement: 'one of the + plural noun' takes a singular verb; 'each', 'every', 'either', 'neither' are singular.

Collective nouns (team, jury, government) take a singular verb when acting as a unit and a plural verb when members act individually.

Parallelism: items joined by and, or, not only...but also must share the same grammatical form (all nouns, all infinitives, all clauses).

Dangling modifier rule: an introductory participle phrase must describe the subject of the main clause, not a nearby noun.

'Since' marks a point in time, 'for' a duration; 'between' pairs with 'and', 'from' pairs with 'to'.

Articles: 'a' before consonant sounds, 'an' before vowel sounds (an hour, a university); 'the' for unique or already specified nouns.

Conditionals: If + present simple, then will + base (real); If + past simple, then would + base (unreal present); If + had + participle, then would have + participle.

Preposition collocations: 'comprise' takes no 'of', 'consist of', 'differ from', 'similar to', 'superior to', 'prefer to'.

Reading comprehension: the correct option must be supported by the passage text, not by outside knowledge or a plausible general truth.

Quadratic ax^2 + bx + c = 0: roots sum to -b/a and multiply to c/a; discriminant b^2 - 4ac decides real (>0), equal (=0), or complex (<0) roots.

Remainder theorem: the remainder of p(x) divided by (x - k) is p(k); factor theorem holds when p(k) = 0.

Logarithm rules: log(xy) = log x + log y, log(x/y) = log x - log y, log(x^n) = n log x, and log_b a = 1 / log_a b.

Arithmetic progression: nth term a + (n - 1)d, sum n/2 [2a + (n - 1)d]; geometric progression: nth term ar^(n-1), sum a(r^n - 1)/(r - 1) for r not 1.

Permutations and combinations: nPr = n!/(n - r)!, nCr = n!/[r!(n - r)!], and nCr = nC(n - r); use combinations when order is irrelevant.

Probability: P(A or B) = P(A) + P(B) - P(A and B); independent events multiply, and P(not A) = 1 - P(A).

Coordinate geometry: distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2], slope = (y2 - y1)/(x2 - x1), parallel slopes equal, perpendicular slopes multiply to -1.

Mensuration: circle area pi r^2, circumference 2 pi r; sphere volume 4/3 pi r^3, surface 4 pi r^2; cylinder volume pi r^2 h.

Trigonometric identities: sin^2 x + cos^2 x = 1, 1 + tan^2 x = sec^2 x, and sin 2x = 2 sin x cos x.