JIPMAT cheat sheet

Percentage change is (new − old)/old × 100; successive changes of a% and b% compound to a + b + ab/100, so a 20% rise then 20% fall gives a net 4% fall.

Profit% and loss% are always computed on cost price unless stated otherwise; selling price = CP × (100 ± p)/100, and discount is computed on marked price.

Simple interest = PRT/100; compound interest = P[(1 + R/100)^T − 1]. For 2 years the CI − SI gap equals P(R/100)^2.

For two articles sold at the same price with equal profit% and loss%, the seller always makes a net loss of (x/10)^2 percent, never zero.

Speed conversion: 1 km/h = 5/18 m/s. For a train of length L crossing a platform of length P, time = (L + P)/speed; for a pole, time = L/speed.

Boats: downstream speed = b + s, upstream = b − s, so b = (D + U)/2 and s = (D − U)/2; time ratio downstream:upstream equals (b − s):(b + s).

Mixing rule (alligation): the ratio of two components equals the difference of each from the mean taken crosswise, i.e. quantity ratio = (mean − cheaper):(dearer − mean).

Work: if A finishes in a days and B in b days, together they take ab/(a + b) days; if A is twice as fast as B, work ratio 2:1 and time ratio 1:2.

Number facts worth memorising: sum of first n natural numbers = n(n+1)/2, sum of squares = n(n+1)(2n+1)/6; a number is divisible by 8 when its last three digits are.

In tables with mixed units (thousands vs lakhs, or percentages vs absolute values), normalise every entry to one unit before comparing or computing ratios.

Percentage of total is not the same as percentage change: a share falling from 40% to 30% is a 25% relative drop, not 10%.

For pie charts, each sector angle = (value/total) × 360°, so a 15% share corresponds to 54°; use angles directly when values are missing.

Average growth rate over n intervals uses the geometric mean: (final/initial)^(1/n) − 1; arithmetic averaging of yearly percentages overstates the true rate.

In bar or line comparisons, read the axis origin first - a truncated y-axis exaggerates differences and is a common trap.

Number series: check differences, then ratios, then squares/cubes, then alternating or two interleaved sequences before assuming a single rule.

Linear arrangements with n distinct people have (n − 1)! circular permutations (clockwise and anticlockwise distinct), and n!/2 if the circle can be flipped.

In seating puzzles, fix the most constrained clue first (fixed position or immediate neighbour), then eliminate; 'A is second to the left of B' means one person sits between them.

Syllogism: a conclusion follows only if true in every possible Venn arrangement of the premises; 'some A are B' does not imply 'some B are not A'.

Subject-verb agreement: the verb agrees with the head noun, not the nearest noun, so 'The list of items is long'; phrases like 'along with', 'as well as' do not make a subject plural.

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

'Neither … nor' and 'either … or' take a verb agreeing with the nearer subject; 'each', 'every', 'everyone', 'none of' are singular in formal usage.

Use 'fewer' with countable nouns and 'less' with uncountable; 'amount' for mass nouns, 'number' for countable ones.

Dangling modifiers: an introductory participle must describe the subject of the main clause, so 'Walking down the road, the tower was seen' is wrong.

In reading comprehension, the answer must be supported by the passage, not by outside knowledge; extreme words such as 'always', 'never', 'only' usually signal a wrong option.

Main-idea questions require the option covering the whole passage; an option true only of one paragraph is a detail trap.

Para-jumbles: openers introduce a new noun in full, later sentences use pronouns or 'this/these'; chronological or cause-effect links decide the rest.

Vocabulary in context: choose the meaning that fits the sentence's logic, since a familiar dictionary sense may be the distractor.