IPMAT Indore key terms

The increase or decrease of a value expressed as a fraction of its original amount, calculated by dividing the difference by the starting value and multiplying by 100.

A ratio compares two quantities of the same kind by division; a proportion states that two ratios are equal, allowing one unknown quantity to be found by cross-multiplication.

The sum of a set of values divided by the number of values. Useful shortcuts: total equals mean times count, and deviations from an assumed mean sum to zero.

A mean in which each value is multiplied by a weight reflecting its importance or frequency before summing, then divided by the total of all weights.

A shortcut method for finding the ratio in which two mixtures of different concentrations must be combined to obtain a desired concentration, using differences arranged in a cross.

The relationship distance equals speed multiplied by time, with the corollary that for a fixed distance, speed and time are inversely proportional to each other.

The rate at which the gap between two moving objects changes: add speeds when moving in opposite directions, subtract when moving in the same direction.

Total distance divided by total time for a journey. It is not the simple mean of the individual speeds unless equal times, not equal distances, were spent at each speed.

The reciprocal of the arithmetic mean of the reciprocals of the values. It correctly gives average speed over equal distances and average of rates such as work per day.

Problems where the rate of completing a task is expressed as a fraction of the job per unit time; combined rates add, and total work is often set to the LCM of the given days.

A variant of time-and-work problems in which inlet pipes add to the filling rate and outlet pipes subtract from it, with net rate determining the filling time.

The amount of work a person or machine completes per unit time. Efficiency is inversely proportional to the time taken to finish the same task.

Interest computed only on the original principal for the whole period, equal to principal times rate times time divided by 100, with no compounding.

Interest calculated on principal plus previously accrued interest, so the amount grows geometrically; the difference from simple interest widens with each period.

Two or more discounts applied one after another, each on the already reduced price. The net discount is less than the sum of the individual percentage discounts.

Cost price is what a seller pays to acquire goods; marked price is the listed tag before discount. Profit or loss is measured against cost price, discount against marked price.

Counting tools: permutations count ordered arrangements where position matters, while combinations count selections where order is irrelevant, using factorials and the nCr formula.

If one choice can be made in m ways and a second in n ways, the two together can be made in m times n ways, extended to any number of independent stages.

The ratio of favourable outcomes to total equally likely outcomes in a sample space; values range from zero to one, and complementary events sum to one.

Two events that cannot occur in the same trial. For such events the probability of either occurring is the sum of their individual probabilities.

Events whose outcomes do not influence each other, so the probability of both happening equals the product of their separate probabilities.

Problems tracking the quantity of a component when two solutions of different concentration are mixed, or when a solution is diluted or partly replaced.

The original sum of money borrowed or invested, on which interest is calculated, as distinct from the accumulated interest added over time.

The fall in the value of an asset over time, often modelled as a fixed percentage reduction each year applied to the reducing balance.

A deductive argument with two premises and a conclusion, tested for validity by checking whether the conclusion must follow from the premises however the terms are interpreted.

Representing sets and their overlaps as circles to test whether a stated relation between categories is possible, necessary, or impossible.

For a statement 'if P then Q', the converse is 'if Q then P' and the contrapositive is 'if not Q then not P'; only the contrapositive is logically equivalent to the original.

A necessary condition must hold for the outcome; a sufficient condition guarantees it. Confusing the two is a common flaw in reasoning questions.

An unstated premise that must be true for an argument's conclusion to follow. Negating a genuine assumption tends to destroy the argument.

A conclusion that follows necessarily from the given information alone, without adding outside knowledge or personal opinion.

Question types asking which option makes an argument more or less credible, usually by supplying evidence that supports or undermines the link between premise and conclusion.

Puzzles using kinship statements or family-tree diagrams to determine how two people are related, requiring careful tracking of gender and generation.

Puzzles placing people around a line or circle under positional clues such as immediate left, opposite, or between, solved by fixing one anchor and testing cases.

Problems tracking displacement after a sequence of turns, using the fact that a left turn from north faces west and right turns reverse that logic.

A sequence with a hidden rule such as constant difference, ratio, alternating operations, or squares; the task is to identify the pattern and supply the missing term.

Questions where words or letters are transformed by a rule such as shifting positions in the alphabet, reversing, or substituting symbols, and the rule must be applied to a new word.

Selecting the item that does not share the defining property of the rest, which may involve letter patterns, categories, or arithmetic relationships.

Concepts of union, intersection, complement and subset, and the inclusion-exclusion rule that the size of a union equals the sum of sizes minus the overlap.

Analysing short arguments to identify premises, conclusions and flaws, then choosing the option that best explains, evaluates or completes the reasoning.

Answering questions on a passage by locating stated detail, inferring the author's tone, and identifying main idea, all grounded strictly in the text provided.

Determining the meaning of a word from the surrounding sentence rather than from a memorised list, since the same word can carry different senses.

Words with closely similar meaning and words with opposite meaning respectively; exam items test precision, so near-misses in connotation must be distinguished.

A pair of words linked by a specific relationship, such as part to whole or cause to effect, which must be matched by a second pair with the same link.

Reordering a set of shuffled sentences into a coherent paragraph by spotting opening sentences, pronoun references, connectors, and the logical flow of ideas.

Spotting the part of a sentence that violates rules of subject-verb agreement, tense consistency, preposition use, parallelism, or article choice.

Filling one or more blanks with the option that fits both the meaning of the sentence and its grammatical structure, often signalled by contrast or cause words.

An expression whose meaning is not deducible from its individual words, such as 'to bite the bullet', tested for correct usage in a sentence.