HEC HAT key terms

A word that carries the same or a very close meaning to another word in a particular sentence. Items test whether you can pick the option that fits the context, not just a dictionary equivalent.

A word with the opposite meaning to another word. Antonym items often hinge on degree and context, so a word that is merely different is not automatically the correct opposite.

A pair of words whose relationship is compared with another pair, such as part to whole or cause to effect. You must name the link in the first pair and find the option with the same link.

The emotional or cultural association a word carries beyond its literal meaning, such as 'thrifty' versus 'stingy'. Questions ask which option matches the shade of feeling the passage intends.

The central point a passage is built to support, usually broader than any single detail. Distractors are often true statements that are too narrow or only partly relevant.

The writer's attitude towards the subject, shown through word choice, such as critical, neutral or amused. Tone questions ask you to justify your choice with evidence from the text.

A conclusion drawn from stated evidence rather than stated outright. A valid inference must follow from the text and not depend on outside knowledge or personal opinion.

The noun or noun phrase that a pronoun such as 'it' or 'they' stands for. Ambiguous reference, where two nouns could fit, is a common error tested in sentence correction.

An introductory phrase that does not logically describe the subject of the main clause, as in 'Walking home, the rain began'. The sentence must be rewritten so the doer is clear.

The rule that items in a list, comparison or pair must share the same grammatical form, such as all infinitives or all nouns. Breaking the pattern creates an uneven, often ambiguous sentence.

A connector such as 'however', 'therefore' or 'moreover' that signals contrast, cause, result or addition. Choosing the right one depends on the logical link between the two sentences.

A comparison of two or more quantities by division, written as 3:5 or as a fraction. Ratios scale together, so multiplying every part by the same number keeps the relationship unchanged.

An equation stating that two ratios are equal, used to scale a known relationship up or down. In direct proportion both quantities grow together; in inverse proportion one falls as the other rises.

A fraction expressed out of one hundred. To convert a fraction, divide then multiply by 100; to increase a value by a percentage, multiply by one plus the rate as a decimal.

The arithmetic average, found by adding all values and dividing by how many there are. It is pulled strongly by extreme values, unlike the median.

The middle value when data are arranged in order; with an even count it is the average of the two middle values. It resists distortion from outliers.

A measure of how far values typically spread from the mean. A small value means the data cluster tightly; a large one means they are widely scattered.

The chance of an event, calculated as favourable outcomes divided by all equally likely outcomes. Values run from 0 for impossible to 1 for certain.

An arrangement of items in which order matters, such as finishing positions in a race. The number of arrangements of n distinct items taken r at a time uses factorials.

A selection of items in which order does not matter, such as choosing a committee. Every group counts once even if its members could be listed in several orders.

Interest calculated only on the original principal for each period, never on interest already earned. The formula is principal times rate times time, with the rate written as a decimal.

Interest calculated on the principal plus interest already added, so the balance grows faster than with simple interest. Compounding more often per year raises the final amount.

The steepness of a straight line, found as the change in the vertical value divided by the change in the horizontal value between two points. Parallel lines share a slope; perpendicular slopes multiply to minus one.

A statement comparing expressions that are not equal, using symbols such as less than, greater than, or their or-equal forms. Multiplying or dividing by a negative number reverses the direction of the sign.

A statement given as evidence in an argument, offered in support of the conclusion. Premises may be false or unwarranted, so identifying them is separate from judging whether they are true.

The claim an argument is trying to establish, supported by the other statements. In long passages the conclusion is often signalled by words like 'therefore' or 'so'.

An unstated belief the argument needs in order for its evidence to support its conclusion. Finding the assumption means asking what must be true for the reasoning to work.

A deductive argument with two premises sharing a term that lead to a conclusion, as in 'All A are B; all B are C; so all A are C'. Validity depends on form, not content.

A statement of the form 'if P then Q', where P is the sufficient condition and Q the necessary condition. It says nothing about what follows when P is false.

'If not Q then not P', formed by reversing and negating a conditional. It is logically equivalent to the original statement, while the converse and the inverse are not.

A single case that satisfies an argument's premises but contradicts its conclusion, proving the reasoning invalid. One clear counterexample is enough to defeat a general claim.

Something that must be present for an outcome to occur, though it may not be enough on its own. Without it the outcome cannot happen; with it, the outcome may still fail.

Something whose presence guarantees the outcome, even if other routes to that outcome also exist. Confusing 'sufficient' with 'necessary' is a standard trap in reasoning items.

A pattern of reasoning that looks persuasive but fails to support its conclusion, such as attacking a person instead of the argument. Naming the flaw helps you reject the wrong answer choices.

The property of an argument whose conclusion must follow if its premises are true. Validity is about structure; an argument can be valid yet still have false premises.

A testable proposed explanation for an observation, stated so that evidence could support or contradict it. In subject-specific study it links theory to the data you plan to collect.

The factor a researcher deliberately changes or groups by, to see whether it affects the outcome. In graphs it is usually placed on the horizontal axis.

The comparison group that does not receive the treatment or condition being tested. Differences between it and the experimental group are attributed to the variable under study.

A statistical association in which two variables tend to move together or in opposite directions. Correlation alone does not establish that one variable causes the other.