KMAT key terms

A fraction expressed out of 100, used to compare quantities on a common scale. To find it, divide the part by the whole and multiply by 100; to apply it, multiply the base by the rate divided by 100.

A comparison of two or more quantities of the same kind, written as a:b. It shows how many times one value contains another and can be scaled up or down without changing the underlying relationship.

An equation stating that two ratios are equal, such as a:b = c:d. In a direct proportion both quantities rise together; in an inverse proportion one falls as the other rises. Used to solve work, speed, and mixture problems.

The sum of a set of values divided by how many values there are. If one value changes, the new total shifts by that change, so the mean moves by the change divided by the count.

A mean in which each value counts in proportion to an assigned weight rather than equally. Computed as the sum of value times weight divided by the sum of weights; useful for combined groups of different sizes.

Calculations of gain or loss when an item is sold. Profit equals selling price minus cost price; loss is the reverse. Both are usually expressed as a percentage of the cost price unless the question states otherwise.

Interest computed only on the original principal for the whole period, using the formula principal times rate times time divided by 100. It does not earn interest on previously accrued interest.

Interest calculated on the principal plus any interest already added, so the amount grows geometrically. For a rate r over n years, amount equals principal times (1 + r/100) raised to n.

The relationship distance equals speed multiplied by time. Because the three quantities are linked, fixing any two determines the third; unit conversion between km/h and m/s uses a factor of 5/18.

The speed of one moving object as observed from another. When two bodies move in the same direction, subtract their speeds; when they move towards each other, add them. Used in train and boat problems.

Problems where a boat's speed is affected by a current. Downstream speed is boat plus stream; upstream speed is boat minus stream. The stream speed is half the difference between downstream and upstream speeds.

Problems about how long tasks take when workers combine or separate. A worker's rate is the reciprocal of the time taken alone; combined rates add, and the total time is the reciprocal of the summed rates.

A variant of time-and-work problems in which inlet pipes fill a tank and outlet pipes empty it. Filling rates are added and emptying rates subtracted; the net rate gives the time to fill or drain.

Counting methods for arrangements and selections. Permutations count ordered arrangements where position matters; combinations count unordered selections. The choice depends on whether rearranging the same items creates a new outcome.

A number from 0 to 1 expressing how likely an event is, computed as favourable outcomes divided by total equally likely outcomes. For independent events, the probability of both occurring is the product of their probabilities.

The classification of numbers into natural, whole, integer, rational, irrational, prime, and composite types, along with rules for divisibility, factors, and multiples. A foundation for simplifying arithmetic and solving remainder questions.

The largest number that divides two or more given numbers exactly, also called greatest common divisor. Found by factoring or the Euclidean method; used to split quantities into the largest equal groups.

The smallest number that is a multiple of each of two or more given numbers. Used when events repeat at different intervals, since the LCM gives the first moment they coincide again.

A shortcut for mixing two ingredients of different values or concentrations to obtain a desired mixture. The required ratio is the difference between each ingredient's value and the target, taken crosswise.

The skill of reading tables, bar charts, line graphs, and pie charts to extract values, compute derived figures such as percentages and averages, and compare trends quickly without a calculator.

Rounding numbers to convenient values so an answer can be estimated fast. In timed data-interpretation sets, options are often far apart, so a close estimate identifies the correct choice without exact computation.

A circular graph where each category is a sector whose angle is proportional to its share of the total. A full circle is 360 degrees or 100 percent, so a sector's value equals its share times the total.

A chart using rectangular bars whose heights or lengths represent values of categories. Grouped and stacked versions compare sub-parts across categories; reading the scale and axis labels correctly is essential.

A chart plotting data points joined by lines, typically showing change over time. The slope indicates the rate of change, so steep segments mark periods of rapid growth or decline.

A word with a meaning close to another word in a given context. Synonym questions test vocabulary breadth and sensitivity to nuance, since near-equivalents often differ in tone, formality, or intensity.

A word whose meaning is opposite to another word. Antonym questions require identifying the precise contrast intended, so a word with several senses must be matched against the sense used in the prompt.

Choosing the word or phrase that fits a sentence's meaning, grammar, and tone. Correct answers must satisfy both sense and collocation, so a synonym of the right meaning can still be wrong if it does not combine naturally.

A fixed expression whose meaning cannot be worked out from its individual words, such as 'to bite the bullet'. Idiom questions test recognition of established phrasing rather than literal interpretation.

The central point a passage conveys, broader than any single detail. It is usually stated or implied in the opening or closing sentences, and the correct answer must cover the whole passage, not one paragraph.

A conclusion drawn from evidence in the passage but not stated outright. A valid inference must follow necessarily from the text; answers that merely seem plausible or rely on outside knowledge are incorrect.

The author's attitude towards the subject, conveyed through word choice and emphasis. Described with adjectives such as critical, neutral, optimistic, or ironic; identifying it helps eliminate answer options that misread the author's stance.

A form of deductive reasoning with two premises leading to a conclusion, often using 'all', 'some', and 'no'. Validity depends on structure alone, so a conclusion can be true even if the premises are factually false.

An unstated premise that must be true for an argument's conclusion to follow. Assumption questions ask what the author takes for granted; the correct answer is necessary to the reasoning, not merely helpful.

Question types asking which option makes an argument more or less credible. Strengtheners support the link between evidence and conclusion; weakeners expose an alternative cause, a flaw, or a counterexample.

Reasoning from general rules to a certain conclusion, where true premises guarantee a true result if the form is valid. Contrasts with inductive reasoning, which generalises from specific observations without certainty.

A puzzle requiring people or objects to be placed in rows or around a circle from a set of clues. Drawing a diagram and marking fixed or negative clues first is the standard efficient method.

Puzzles that describe family links through statements or symbols and ask how two people are related. Converting each clue into a small family tree prevents confusion across generations.

Knowledge of current affairs, Indian and world history, geography, polity, economy, science, and static facts. Questions reward regular reading of news and revision of static topics rather than last-minute cramming.

Recent national and international events, appointments, awards, sports results, and economic developments, usually covering roughly the past year. A candidate should track major developments rather than obscure trivia.

Facts that do not change with time: capitals, currencies, national parks, rivers, constitutions, and historical dates. Unlike current affairs, this material can be prepared from fixed reference sources.