SPJAT key terms

A fraction expressed as a number out of 100, used to compare quantities of different sizes. Converting between percentages, decimals, and fractions is a core arithmetic skill on this test.

A comparison of two or more quantities of the same kind, written in lowest terms. Ratios let you split a total into proportional parts and solve mixture and partnership problems.

An equation stating that two ratios are equal. In direct proportion both quantities grow together; in inverse proportion one rises as the other falls.

The sum of a set of values divided by how many values there are. Problems often ask for a missing value or a changed average after one item is added or removed.

A mean in which each value counts in proportion to an assigned weight rather than equally. Used for combined-group averages, mixture prices, and speed over unequal distances.

Calculations of selling price against cost price, giving profit or loss as an amount and as a percentage. Marked price, discount, and successive changes are common extensions.

The net effect of applying two or more percentage changes one after another. The changes do not simply add because each is applied to the already-changed quantity.

Interest computed only on the original principal for the whole period, with no interest on interest. The formula is principal times rate times time, divided by 100.

Interest calculated on the principal plus all interest already earned, so the amount grows geometrically. Compounding frequency changes the effective annual growth rate.

The relationship that distance equals speed multiplied by time. Problems involve relative speed, trains crossing objects, boats in current, and average speed over a journey.

The speed of one moving object as seen from another. Add speeds when moving in opposite directions and subtract them when moving the same way.

The amount of a job completed per unit time, often written as a fraction of the whole task. Rates of people or machines working together are added.

A work-rate setting where inlet pipes fill a tank and outlet pipes empty it. Filling rates are positive and draining rates negative, then combined.

Methods for combining ingredients of different prices or strengths and finding the resulting value. Alligation uses the gap between each component and the mean to fix the mixing ratio.

An arrangement of items in which order matters. The count of arrangements of r items chosen from n distinct items uses factorials.

A selection of items in which order does not matter. Choosing r items from n distinct items gives fewer possibilities than the corresponding permutation.

A number from 0 to 1 measuring how likely an event is, found by dividing favourable outcomes by total equally likely outcomes. Independent and conditional events are frequent topics.

A logical argument built from two or more premises that share a term, from which a conclusion is drawn. Test questions ask which conclusion necessarily follows and which is only possible.

A statement given as true within an argument and used as evidence for the conclusion. In reasoning questions, premises are accepted without challenge.

The claim an argument is trying to establish from its premises. A valid conclusion must follow necessarily, not merely be plausible or consistent with the evidence.

A property of an argument's structure: if the premises were true, the conclusion could not be false. Validity concerns form, while truth concerns the actual content of statements.

An unstated belief the author must hold for the argument to work. Spotting assumptions is central to strengthening, weakening, and evaluating arguments.

A conclusion drawn from given information rather than stated outright. A correct inference must be supported by the passage and not go beyond what it allows.

Question types that ask which option makes an argument more or less likely to be true. The right answer adds evidence bearing directly on the link between premises and conclusion.

A list of numbers, letters, or figures following a hidden rule that you must identify to find the next item or the odd one out. Patterns may involve differences, products, or alternating rules.

A pair of items linked by a specific relationship, where you must apply the same relationship to a new item. The relationship may be functional, causal, or categorical.

A set of items in which all but one share a common property; you identify the exception. The shared property can be numerical, verbal, or visual.

Grouping items by a defining shared feature, or recognising which category an item belongs to. Often paired with odd-one-out tasks that test category boundaries.

A puzzle placing people around a table or in a row using positional clues such as left, right, opposite, and adjacent. Solving requires building a consistent layout from constraints.

Puzzles that give family relationships in coded or indirect form and ask how two people are related. Drawing a family tree with clear generation levels prevents errors.

Problems tracking movement on a compass grid, usually ending with a question about final direction or shortest distance. Sketching each turn reduces mistakes.

Questions where words or letters are converted by a rule and you must decode a new word or encode one. Rules may shift letters, reverse order, or map by position.

A word with a meaning close to another word's meaning. Synonym questions test precision, so pick the option closest in sense and tone, not merely related.

A word opposite in meaning to another. The best answer contrasts directly in the same sense the given word is used, so watch for words with several meanings.

The sense a word carries in a specific sentence, which may differ from its most common dictionary sense. Reading surrounding clues is essential before choosing an option.

A fixed expression whose meaning cannot be worked out from its individual words. Idiom questions ask you to choose the correct meaning or the right phrase for a situation.

A question type where a marked part of a sentence must be swapped for the grammatically and idiomatically correct option. Errors may involve tense, agreement, or prepositions.

Rules governing sentence structure, including subject-verb agreement, tense consistency, articles, and prepositions. Error-spotting questions test these rules directly.

Answering questions about a passage by locating stated facts, inferring implied points, and identifying the author's tone or main idea. Answers must be grounded in the text provided.

The central point a passage is developed to support, broader than any single detail. It usually appears in the opening or closing lines and unifies the whole text.

The attitude an author conveys toward the subject, such as critical, neutral, or approving. Tone questions require evidence from word choice rather than personal reaction.

A grid of rows and columns presenting values for categories and periods. Reading it well means tracking units, totals, and which row or column a question refers to.

A graph using rectangular bars whose lengths represent values across categories. Questions often compare bars, compute differences, or read grouped and stacked variants.

A circle divided into sectors whose angles are proportional to each part's share of a total. Each sector's share can be read as a percentage of 360 degrees.

A chart plotting values as points joined by lines, usually over time. Slope indicates rate of change, so steepness matters as much as the plotted heights.

The difference between a new and an old value, divided by the old value and expressed as a percentage. Always divide by the starting value, not the final one.

A format asking whether the information supplied is enough to answer a question, without requiring the actual answer. Judge each statement alone, then together.