HEC HAT cheat sheet

Main-idea answers must cover the whole passage; an option that is true but covers only one paragraph is a detail trap, and an option that generalises beyond the text is a scope trap.

Inference must be necessarily true from the text - if the passage permits the statement to be false, it is not a valid inference.

Vocabulary in context: substitute each option into the original sentence and check both meaning and tone; the correct sense is fixed by surrounding words, not the dictionary's first entry.

Subject-verb agreement: the verb agrees with the true subject, so prepositional phrases such as 'the list of items' never change a singular subject into a plural one.

An introductory participial phrase modifies the subject of the main clause; 'Having finished the report, Ali submitted it' is correct, 'Having finished the report, the deadline passed' is not.

Parallelism: items joined by 'and', 'or', or a series must share grammatical form - all nouns, all infinitives, or all clauses.

Contrast connectors (although, though, despite, however, yet) reverse the expectation built by the first clause; 'despite' takes a noun or gerund, 'although' takes a full clause.

Pronoun reference: a pronoun must agree in number and gender with its nearest logical antecedent; ambiguous 'it' or 'they' with two possible referents makes the sentence incorrect.

Percent change = (new value − original value) ÷ original value × 100; the denominator is always the starting value.

Successive percentage changes multiply: +20% then −20% gives 1.2 × 0.8 = 0.96, a net 4% decrease, not 0%.

Average speed = total distance ÷ total time; arithmetic mean of speeds is valid only when the time intervals are equal.

Combined work rate = 1/a + 1/b jobs per hour for workers finishing alone in a and b hours; time together = ab/(a + b).

Interest: simple = P × r × n ÷ 100; compound amount = P(1 + r/100)^n, so compound interest = amount − P.

Profit and loss percentages are calculated on cost price unless the question explicitly states selling price as the base.

Geometry essentials: triangle area ½ × base × height, circle area πr² and circumference 2πr, angles of a triangle sum to 180°, Pythagoras a² + b² = c² for right triangles.

Statistics: adding a constant to every value shifts mean and median by that constant but leaves standard deviation unchanged; the median resists outliers, the mean does not.

Probability: P(A or B) = P(A) + P(B) − P(A and B); for independent events P(A and B) = P(A) × P(B).

'If P then Q' licenses only the contrapositive 'if not Q then not P'; the converse 'if Q then P' and the inverse 'if not P then not Q' are invalid.

'P only if Q' makes Q a necessary condition and P a sufficient condition, so P → Q holds but Q → P does not.

Sufficient condition guarantees the outcome; necessary condition is required for it - confusing the two is the most common flaw tested.

Sequencing setups: place fixed absolute positions first, then convert 'X immediately before Y' into a single XY block occupying two adjacent slots.

Assumption negation test: negate each candidate; if the argument collapses, the statement was a required assumption, if it survives, it was not.

Weaken/strengthen answers act on the link between evidence and conclusion - an alternative cause, a reversed causal direction, or an unrepresentative sample.

Correlation does not establish causation; a causal claim is weakened by an unobserved third variable or by evidence that the effect preceded the cause.

'Must be true' answers follow with certainty from the stated facts; 'could be true' answers only need consistency, and 'except' questions hide four valid statements behind one invalid choice.

Economics: demand is elastic when the percentage change in quantity exceeds the percentage change in price; with elastic demand a price cut raises total revenue, with inelastic demand it lowers it.

Finance: accept a project when net present value is positive, that is when discounted cash inflows exceed the initial outlay; IRR above the cost of capital gives the same decision.

Accounting: assets = liabilities + equity; debits increase assets and expenses, credits increase liabilities, equity and revenue, and every entry keeps the equation balanced.

Computer science: binary search runs in O(log n), merge sort in O(n log n), and an average hash-table lookup in O(1); nested loops over n items give O(n²).

Biology: mitosis yields two identical diploid cells for growth and repair, meiosis yields four genetically varied haploid gametes; DNA replication is semi-conservative.

Chemistry: one mole contains 6.022 × 10²³ particles and equals the molar mass in grams; pH = −log[H⁺], so a tenfold rise in hydrogen ion concentration lowers pH by one unit.

Physics: F = ma, v = u + at, s = ut + ½at², kinetic energy = ½mv²; acceleration is always in the direction of the net force.

Research methods and statistics: a p-value below 0.05 rejects the null hypothesis at the 5% level; a Type I error is a false positive and its probability equals the significance level alpha.

Main-idea answers must cover the whole passage; an option that is true but covers only one paragraph is a detail trap, and an option that generalises beyond the text is a scope trap.

Inference must be necessarily true from the text - if the passage permits the statement to be false, it is not a valid inference.

Vocabulary in context: substitute each option into the original sentence and check both meaning and tone; the correct sense is fixed by surrounding words, not the dictionary's first entry.

Subject-verb agreement: the verb agrees with the true subject, so prepositional phrases such as 'the list of items' never change a singular subject into a plural one.

An introductory participial phrase modifies the subject of the main clause; 'Having finished the report, Ali submitted it' is correct, 'Having finished the report, the deadline passed' is not.

Parallelism: items joined by 'and', 'or', or a series must share grammatical form - all nouns, all infinitives, or all clauses.

Contrast connectors (although, though, despite, however, yet) reverse the expectation built by the first clause; 'despite' takes a noun or gerund, 'although' takes a full clause.

Pronoun reference: a pronoun must agree in number and gender with its nearest logical antecedent; ambiguous 'it' or 'they' with two possible referents makes the sentence incorrect.

Percent change = (new value − original value) ÷ original value × 100; the denominator is always the starting value.

Successive percentage changes multiply: +20% then −20% gives 1.2 × 0.8 = 0.96, a net 4% decrease, not 0%.

Average speed = total distance ÷ total time; arithmetic mean of speeds is valid only when the time intervals are equal.

Combined work rate = 1/a + 1/b jobs per hour for workers finishing alone in a and b hours; time together = ab/(a + b).

Interest: simple = P × r × n ÷ 100; compound amount = P(1 + r/100)^n, so compound interest = amount − P.

Profit and loss percentages are calculated on cost price unless the question explicitly states selling price as the base.

Geometry essentials: triangle area ½ × base × height, circle area πr² and circumference 2πr, angles of a triangle sum to 180°, Pythagoras a² + b² = c² for right triangles.

Statistics: adding a constant to every value shifts mean and median by that constant but leaves standard deviation unchanged; the median resists outliers, the mean does not.

Probability: P(A or B) = P(A) + P(B) − P(A and B); for independent events P(A and B) = P(A) × P(B).

'If P then Q' licenses only the contrapositive 'if not Q then not P'; the converse 'if Q then P' and the inverse 'if not P then not Q' are invalid.

'P only if Q' makes Q a necessary condition and P a sufficient condition, so P → Q holds but Q → P does not.

Sufficient condition guarantees the outcome; necessary condition is required for it - confusing the two is the most common flaw tested.

Sequencing setups: place fixed absolute positions first, then convert 'X immediately before Y' into a single XY block occupying two adjacent slots.

Assumption negation test: negate each candidate; if the argument collapses, the statement was a required assumption, if it survives, it was not.

Weaken/strengthen answers act on the link between evidence and conclusion - an alternative cause, a reversed causal direction, or an unrepresentative sample.

Correlation does not establish causation; a causal claim is weakened by an unobserved third variable or by evidence that the effect preceded the cause.

'Must be true' answers follow with certainty from the stated facts; 'could be true' answers only need consistency, and 'except' questions hide four valid statements behind one invalid choice.

Economics: demand is elastic when the percentage change in quantity exceeds the percentage change in price; with elastic demand a price cut raises total revenue, with inelastic demand it lowers it.

Finance: accept a project when net present value is positive, that is when discounted cash inflows exceed the initial outlay; IRR above the cost of capital gives the same decision.

Accounting: assets = liabilities + equity; debits increase assets and expenses, credits increase liabilities, equity and revenue, and every entry keeps the equation balanced.

Computer science: binary search runs in O(log n), merge sort in O(n log n), and an average hash-table lookup in O(1); nested loops over n items give O(n²).

Biology: mitosis yields two identical diploid cells for growth and repair, meiosis yields four genetically varied haploid gametes; DNA replication is semi-conservative.

Chemistry: one mole contains 6.022 × 10²³ particles and equals the molar mass in grams; pH = −log[H⁺], so a tenfold rise in hydrogen ion concentration lowers pH by one unit.

Physics: F = ma, v = u + at, s = ut + ½at², kinetic energy = ½mv²; acceleration is always in the direction of the net force.

Research methods and statistics: a p-value below 0.05 rejects the null hypothesis at the 5% level; a Type I error is a false positive and its probability equals the significance level alpha.