KMAT cheat sheet

Percentage change = (new − old)/old × 100; successive changes of a% and b% give a net change of a + b + ab/100 percent.

Simple interest = PRT/100; compound interest = P[(1 + R/100)^T − 1], and CI exceeds SI by P(R/100)^2 for two years.

Work: if A alone takes x days and B alone takes y days, together they take xy/(x + y) days; combined rate is the sum of individual rates.

Speed conversion: 1 km/h = 5/18 m/s and 1 m/s = 18/5 km/h; relative speed adds for opposite directions and subtracts for same direction.

Boats: downstream speed = boat + stream, upstream = boat − stream; boat speed = (down + up)/2, stream speed = (down − up)/2.

Mixtures: replacement formula gives final pure quantity = initial × (1 − replaced/total)^n after n identical replacements.

Permutations nPr = n!/(n − r)!; combinations nCr = n!/[r!(n − r)!]; nCr = nC(n − r).

Profit and loss: profit% is always computed on cost price unless stated; selling price = CP × (1 + profit/100).

Averages: new average after adding value v to n items = (n·old average + v)/(n + 1); weighted average = Σwx/Σw.

Read the axis scale and units first; a chart starting at a non-zero baseline exaggerates visual differences between bars.

Percentage of total = (part/total) × 100; percentage increase = (new − old)/old × 100, never divide by the new value.

In pie charts, each sector angle = (component/total) × 360°, so a 1% share equals 3.6°.

For tables with mixed units, convert everything to one unit before comparing or summing rows.

Approximation is a valid speed tool when options are far apart: round to two significant figures and check the closest option.

Compound growth over years: final = initial × (1 + r)^n; average annual growth rate = (final/initial)^(1/n) − 1.

Ratio questions: if A:B = m:n and the total is T, then A = Tm/(m + n) and B = Tn/(m + n).

Cross-check a derived percentage by recomputing the absolute value; DI errors usually come from a misread base, not arithmetic.

Subject-verb agreement: a singular subject takes a singular verb regardless of intervening phrases; 'one of the + plural noun' takes a singular verb.

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' make the verb agree with the nearer subject.

Correct pairs: 'not only...but also', 'between...and', 'neither...nor', 'scarcely...when', 'no sooner...than'.

Dangling modifier test: the opening participial phrase must describe the subject of the main clause.

Redundancy flags: 'return back', 'discuss about', 'more better', 'very unique' are always wrong.

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

In para-jumbles, find the opening sentence (introduces the topic, no pronoun references) and link sentences by pronouns and connectors.

Main idea is usually stated in the first or last paragraph; supporting detail questions point to specific lines.

Tone words: critical, analytical, neutral, laudatory, cautious - match the author's attitude, not the subject's.

Inference must follow necessarily from the passage; an option that adds outside knowledge is wrong even if true.

Extreme qualifiers ('always', 'never', 'all') are usually incorrect for inference and tone questions unless the passage states them.

'According to the passage' questions require textual support; 'the author would agree' allows a controlled logical extension.

Watch contrast markers (however, although, yet, despite) - they often carry the author's real position.

Vocabulary-in-context: substitute each option into the sentence and check that the passage's logic still holds.

Eliminate options that are too broad, too narrow, or reversed in cause and effect relative to the passage.

Syllogism: 'All A are B' plus 'All B are C' gives 'All A are C'; a valid conclusion must hold in every possible diagram.

'Some A are B' does not convert to 'Some B are A' being false - 'some' is symmetric and means at least one.

Contrapositive is valid: 'If P then Q' implies 'If not Q then not P'; the converse 'if Q then P' is invalid.

Necessary vs sufficient: P is sufficient for Q when P→Q; P is necessary for Q when Q→P.

Blood relations: draw a family tree with gender and generation markers; never assume gender from a name or role.

Seating arrangement: fix the definite clue first, then place relative clues; circular arrangements have (n − 1)! distinct orders.

Number and letter series: check differences, then ratios, then alternating subsequences, then squares/cubes and primes.

Assumption questions: the correct answer is unstated but required for the argument; a restatement of the premise is not an assumption.

Strengthen/weaken: attack or support the link between evidence and conclusion, not the evidence itself.

Indian polity: the Constitution was adopted on 26 November 1949 and came into force on 26 January 1950.

Fundamental Rights are Part III (Articles 12–35); Directive Principles are Part IV (Articles 36–51).

The RBI was established in 1935 and nationalised in 1949; it sets the repo rate under the monetary policy framework.

GDP measures output within a country's borders; GNP = GDP + net factor income from abroad.

Inflation is measured in India by CPI (base 2012) and WPI (base 2011-12); the MPC targets CPI inflation at 4% ± 2%.

Nobel Prizes are announced in October; the Economics prize is formally the Sveriges Riksbank Prize, not a original Nobel.

Key dates: UN founded 24 October 1945; WTO 1 January 1995; Bretton Woods conference 1944 created IMF and World Bank.

Books and authors, capitals and currencies, and current heads of state are common one-liner areas; verify recent changes.

Area of triangle = ½ × base × height; Heron's formula uses s = (a + b + c)/2 and area = √[s(s − a)(s − b)(s − c)].

Pythagorean triples to memorise: 3-4-5, 5-12-13, 7-24-25, 8-15-17 and their multiples.

Circle: area = πr², circumference = 2πr; sector area = (θ/360)πr², arc length = (θ/360)2πr.

Cylinder volume = πr²h, curved surface = 2πrh; cone volume = (1/3)πr²h, slant height l = √(r² + h²).

Sphere volume = (4/3)πr³, surface = 4πr²; hemisphere total surface = 3πr².

Sum of interior angles of an n-sided polygon = (n − 2) × 180°; each exterior angle of a regular polygon = 360°/n.

Similar figures: areas scale as the square of the linear ratio, volumes as the cube.

Bar chart comparison: compare heights only within the same axis scale; dual-axis charts need separate scale reading for each series.

Line graph slope indicates rate of change, not absolute value; a steep line can still be at a low level.

Table totals: verify row and column sums agree before answering any percentage-of-total question.

Stacked bar segments show composition; the segment height, not its top edge, gives the component value.

Caselet DI: extract numbers into a small table before computing; keep units consistent.

Percentage-point difference ≠ percentage difference: a move from 20% to 25% is 5 percentage points but a 25% relative rise.

If a question asks 'by what percent is A more than B', divide the difference by B.

Idioms: 'to bite the bullet' = to endure a difficult situation; 'to let the cat out of the bag' = to reveal a secret.

One-word substitutions: 'philanthropist' = lover of mankind; 'misanthrope' = hater of mankind; 'ephemeral' = short-lived.

Confusables: 'affect' (verb) vs 'effect' (noun); 'principal' (main/head) vs 'principle' (rule); 'complement' vs 'compliment'.

Antonym pairs often hinge on prefixes: 'benevolent/malevolent', 'credible/incredible', 'transparent/opaque'.

Spelling traps: 'accommodate', 'occurrence', 'embarrass', 'harass', 'maintenance', 'recommend'.

Prepositions: 'comply with', 'averse to', 'capable of', 'deprived of', 'insist on', 'proficient in'.

Active to passive: object becomes subject, verb becomes 'be + past participle', and the agent is introduced by 'by'.

Linear arrangement facing north: left is west and right is east; facing south reverses left and right.

Circular arrangement facing centre: clockwise movement goes left; facing outward reverses it.

For 'n people in a row', the number of people between positions a and b is |a − b| − 1.

Floor puzzles: list floors top to bottom and mark each clue as a fixed slot or a relative gap.

Scheduling puzzles: draw a grid of days/slots and eliminate; a clue like 'A is two days after B' fixes the gap, not the start.

Selection puzzles: use 'if A is selected, B is not' as a pair rule and test options against every rule.

If a puzzle yields two valid arrangements, the question's extra condition must resolve it; otherwise check for a missed clue.

Direction sense: track net displacement with a rough sketch; final direction uses the last segment, not the net vector.

GDP deflator = (nominal GDP/real GDP) × 100.

Fiscal deficit = total expenditure − total receipts excluding borrowings; revenue deficit = revenue expenditure − revenue receipts.

Repo rate is the rate at which RBI lends to banks; reverse repo absorbs liquidity.

CRR is the share of deposits held with RBI; SLR is held in approved securities - both are percentages of net demand and time liabilities.

Balance of payments = current account + capital account + errors and omissions; a current account deficit means imports exceed exports broadly.

FDI is long-term and involves control; FPI is portfolio flow without control.

Types of business entities: sole proprietorship, partnership (Indian Partnership Act 1932), LLP (2008), company (Companies Act 2013).

Factual question: answer is explicitly stated; locate the keyword and read the surrounding two lines.

Inference question: answer is implied but not stated; reject options requiring assumptions beyond the passage.

Tone/attitude question: match adjectives to the author's stance; neutral or objective is common in expository passages.

Purpose question: ask why the author wrote the passage - to describe, argue, compare, or refute.

Paragraph-completion: the added sentence must connect logically to both the preceding and following lines.

Except/not questions: three options are supported; find the one that contradicts or is absent from the passage.

Title question: the best title covers the whole passage, not just one paragraph's detail.