HSC Pro study materials
HSC Pro study resources

HSC Pro cheat sheet

HSC Pro · Keep the key ideas within reach.

Quick reference

Integrated reasoning and problem solving

  • Multi-source reasoning: tabulate each source's claim, date, and scope before synthesis; conflicts are usually scope differences, not contradictions.

  • Two-part analysis requires both parts correct; eliminate any option pair where one part fails, even if the other is strong.

  • Table/graphics interpretation: check axis units and scale breaks first; a 0-to-95 axis versus a truncated axis reverses apparent trends.

  • For multi-step problems, define the target quantity before computing; intermediate values are distractors when they answer a different question.

  • Work-rate and combined-rate: 1/T = 1/a + 1/b for parallel work; subtract rates for opposing flows (fill vs drain).

  • Overlapping sets: |A∪B| = |A| + |B| − |A∩B|; for three sets add singles, subtract pairs, add back the triple intersection.

  • Sufficiency test: a statement is sufficient only if it yields exactly one value; two valid values means insufficient.

  • When sources disagree on a number, prefer the primary/raw dataset over a summary that cites it, and note the as-of date.

  • Sanity-check results against the units and order of magnitude implied by the prompt before selecting an answer.

Quick reference

Quantitative reasoning and data interpretation

  • Percent change = (new − old)/old × 100; successive changes multiply: (1+r1)(1+r2) − 1, not r1 + r2.

  • Percentage points versus percent: a rise from 20% to 25% is 5 percentage points but a 25% relative increase.

  • Weighted average = Σ(wᵢxᵢ)/Σwᵢ; the combined mean lies between the group means, closer to the larger group.

  • Ratios: convert to parts of a whole (a:b → a/(a+b)) before comparing across datasets with different totals.

  • Compound growth: A = P(1 + r/n)^(nt); doubling time ≈ 70/r for small r (rule of 70).

  • Mean is shifted by outliers; median and IQR are robust. Outlier flag: value beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR.

  • Correlation coefficient r ∈ [−1, 1]; r measures linear association only and does not establish causation.

  • Base-rate logic: P(A|B) depends on P(B|A), P(A), and P(not A); a highly accurate test on a rare condition still yields many false positives.

  • Sampling: larger n narrows the margin of error roughly as 1/√n; a biased sample is not fixed by size.

Quick reference

Verbal reasoning and written communication

  • Assumption questions: the correct answer is necessary to the argument - negate it and the conclusion must collapse.

  • Strengthen/weaken: attack or support the link between evidence and conclusion, not the evidence itself.

  • Boldface and role-of-statement items: label each claim as premise, intermediate conclusion, or main conclusion before choosing.

  • Parallel reasoning: match the logical structure (conditional direction, quantifier, scope), not the topic or tone.

  • Modifier placement: a descriptive phrase must sit next to the noun it modifies; dangling modifiers create false attribution.

  • Subject-verb agreement survives intervening phrases; find the true subject by deleting prepositional clauses.

  • Pronoun reference: every 'it', 'they', or 'this' needs one unambiguous antecedent; 'this' alone often lacks a noun.

  • Comparison items must be logically parallel: compare like categories (rates with rates, totals with totals).

  • Concise professional writing: active voice, one idea per sentence, and the recommendation stated before its justification.

Quick reference

Professional judgement and ethical decision making

  • Priority order for a professional dilemma: safety of people, then legal/regulatory compliance, then organizational policy, then efficiency.

  • Conflict of interest: disclose, then recuse from the decision; disclosure alone does not cure a material personal interest.

  • Confidentiality yields only to a specific, documented exception (imminent harm, legal compulsion, or authorized consent).

  • Competence boundary: decline or refer work outside your qualification rather than proceeding with undisclosed risk.

  • Escalation ladder: raise with the direct supervisor, then the designated compliance/ethics channel, then the regulator if unresolved.

  • Document contemporaneously: record facts, dates, advice received, and actions taken; opinion should be labeled as opinion.

  • Whistleblower protections typically require internal reporting first and good-faith belief; retaliation is a separate breach to report.

  • Client/employer duty versus public interest: when they conflict, the public-interest obligation governs where harm is foreseeable.

  • Data handling: collect the minimum necessary, use it only for the stated purpose, and apply the stricter rule when jurisdictions differ.

Quick reference

Integrated reasoning and problem solving

  • Multi-source reasoning: tabulate each source's claim, date, and scope before synthesis; conflicts are usually scope differences, not contradictions.

  • Two-part analysis requires both parts correct; eliminate any option pair where one part fails, even if the other is strong.

  • Table/graphics interpretation: check axis units and scale breaks first; a 0-to-95 axis versus a truncated axis reverses apparent trends.

  • For multi-step problems, define the target quantity before computing; intermediate values are distractors when they answer a different question.

  • Work-rate and combined-rate: 1/T = 1/a + 1/b for parallel work; subtract rates for opposing flows (fill vs drain).

  • Overlapping sets: |A∪B| = |A| + |B| − |A∩B|; for three sets add singles, subtract pairs, add back the triple intersection.

  • Sufficiency test: a statement is sufficient only if it yields exactly one value; two valid values means insufficient.

  • When sources disagree on a number, prefer the primary/raw dataset over a summary that cites it, and note the as-of date.

  • Sanity-check results against the units and order of magnitude implied by the prompt before selecting an answer.

Quick reference

Quantitative reasoning and data interpretation

  • Percent change = (new − old)/old × 100; successive changes multiply: (1+r1)(1+r2) − 1, not r1 + r2.

  • Percentage points versus percent: a rise from 20% to 25% is 5 percentage points but a 25% relative increase.

  • Weighted average = Σ(wᵢxᵢ)/Σwᵢ; the combined mean lies between the group means, closer to the larger group.

  • Ratios: convert to parts of a whole (a:b → a/(a+b)) before comparing across datasets with different totals.

  • Compound growth: A = P(1 + r/n)^(nt); doubling time ≈ 70/r for small r (rule of 70).

  • Mean is shifted by outliers; median and IQR are robust. Outlier flag: value beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR.

  • Correlation coefficient r ∈ [−1, 1]; r measures linear association only and does not establish causation.

  • Base-rate logic: P(A|B) depends on P(B|A), P(A), and P(not A); a highly accurate test on a rare condition still yields many false positives.

  • Sampling: larger n narrows the margin of error roughly as 1/√n; a biased sample is not fixed by size.

Quick reference

Verbal reasoning and written communication

  • Assumption questions: the correct answer is necessary to the argument - negate it and the conclusion must collapse.

  • Strengthen/weaken: attack or support the link between evidence and conclusion, not the evidence itself.

  • Boldface and role-of-statement items: label each claim as premise, intermediate conclusion, or main conclusion before choosing.

  • Parallel reasoning: match the logical structure (conditional direction, quantifier, scope), not the topic or tone.

  • Modifier placement: a descriptive phrase must sit next to the noun it modifies; dangling modifiers create false attribution.

  • Subject-verb agreement survives intervening phrases; find the true subject by deleting prepositional clauses.

  • Pronoun reference: every 'it', 'they', or 'this' needs one unambiguous antecedent; 'this' alone often lacks a noun.

  • Comparison items must be logically parallel: compare like categories (rates with rates, totals with totals).

  • Concise professional writing: active voice, one idea per sentence, and the recommendation stated before its justification.

Quick reference

Professional judgement and ethical decision making

  • Priority order for a professional dilemma: safety of people, then legal/regulatory compliance, then organizational policy, then efficiency.

  • Conflict of interest: disclose, then recuse from the decision; disclosure alone does not cure a material personal interest.

  • Confidentiality yields only to a specific, documented exception (imminent harm, legal compulsion, or authorized consent).

  • Competence boundary: decline or refer work outside your qualification rather than proceeding with undisclosed risk.

  • Escalation ladder: raise with the direct supervisor, then the designated compliance/ethics channel, then the regulator if unresolved.

  • Document contemporaneously: record facts, dates, advice received, and actions taken; opinion should be labeled as opinion.

  • Whistleblower protections typically require internal reporting first and good-faith belief; retaliation is a separate breach to report.

  • Client/employer duty versus public interest: when they conflict, the public-interest obligation governs where harm is foreseeable.

  • Data handling: collect the minimum necessary, use it only for the stated purpose, and apply the stricter rule when jurisdictions differ.

Quick reference

Integrated reasoning and problem solving

  • Multi-source reasoning: tabulate each source's claim, date, and scope before synthesis; conflicts are usually scope differences, not contradictions.

  • Two-part analysis requires both parts correct; eliminate any option pair where one part fails, even if the other is strong.

  • Table/graphics interpretation: check axis units and scale breaks first; a 0-to-95 axis versus a truncated axis reverses apparent trends.

  • For multi-step problems, define the target quantity before computing; intermediate values are distractors when they answer a different question.

  • Work-rate and combined-rate: 1/T = 1/a + 1/b for parallel work; subtract rates for opposing flows (fill vs drain).

  • Overlapping sets: |A∪B| = |A| + |B| − |A∩B|; for three sets add singles, subtract pairs, add back the triple intersection.

  • Sufficiency test: a statement is sufficient only if it yields exactly one value; two valid values means insufficient.

  • When sources disagree on a number, prefer the primary/raw dataset over a summary that cites it, and note the as-of date.

  • Sanity-check results against the units and order of magnitude implied by the prompt before selecting an answer.

Quick reference

Quantitative reasoning and data interpretation

  • Percent change = (new − old)/old × 100; successive changes multiply: (1+r1)(1+r2) − 1, not r1 + r2.

  • Percentage points versus percent: a rise from 20% to 25% is 5 percentage points but a 25% relative increase.

  • Weighted average = Σ(wᵢxᵢ)/Σwᵢ; the combined mean lies between the group means, closer to the larger group.

  • Ratios: convert to parts of a whole (a:b → a/(a+b)) before comparing across datasets with different totals.

  • Compound growth: A = P(1 + r/n)^(nt); doubling time ≈ 70/r for small r (rule of 70).

  • Mean is shifted by outliers; median and IQR are robust. Outlier flag: value beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR.

  • Correlation coefficient r ∈ [−1, 1]; r measures linear association only and does not establish causation.

  • Base-rate logic: P(A|B) depends on P(B|A), P(A), and P(not A); a highly accurate test on a rare condition still yields many false positives.

  • Sampling: larger n narrows the margin of error roughly as 1/√n; a biased sample is not fixed by size.

Quick reference

Verbal reasoning and written communication

  • Assumption questions: the correct answer is necessary to the argument - negate it and the conclusion must collapse.

  • Strengthen/weaken: attack or support the link between evidence and conclusion, not the evidence itself.

  • Boldface and role-of-statement items: label each claim as premise, intermediate conclusion, or main conclusion before choosing.

  • Parallel reasoning: match the logical structure (conditional direction, quantifier, scope), not the topic or tone.

  • Modifier placement: a descriptive phrase must sit next to the noun it modifies; dangling modifiers create false attribution.

  • Subject-verb agreement survives intervening phrases; find the true subject by deleting prepositional clauses.

  • Pronoun reference: every 'it', 'they', or 'this' needs one unambiguous antecedent; 'this' alone often lacks a noun.

  • Comparison items must be logically parallel: compare like categories (rates with rates, totals with totals).

  • Concise professional writing: active voice, one idea per sentence, and the recommendation stated before its justification.

Quick reference

Professional judgement and ethical decision making

  • Priority order for a professional dilemma: safety of people, then legal/regulatory compliance, then organizational policy, then efficiency.

  • Conflict of interest: disclose, then recuse from the decision; disclosure alone does not cure a material personal interest.

  • Confidentiality yields only to a specific, documented exception (imminent harm, legal compulsion, or authorized consent).

  • Competence boundary: decline or refer work outside your qualification rather than proceeding with undisclosed risk.

  • Escalation ladder: raise with the direct supervisor, then the designated compliance/ethics channel, then the regulator if unresolved.

  • Document contemporaneously: record facts, dates, advice received, and actions taken; opinion should be labeled as opinion.

  • Whistleblower protections typically require internal reporting first and good-faith belief; retaliation is a separate breach to report.

  • Client/employer duty versus public interest: when they conflict, the public-interest obligation governs where harm is foreseeable.

  • Data handling: collect the minimum necessary, use it only for the stated purpose, and apply the stricter rule when jurisdictions differ.

Quick reference

Integrated reasoning and problem solving

  • Multi-source reasoning: tabulate each source's claim, date, and scope before synthesis; conflicts are usually scope differences, not contradictions.

  • Two-part analysis requires both parts correct; eliminate any option pair where one part fails, even if the other is strong.

  • Table/graphics interpretation: check axis units and scale breaks first; a 0-to-95 axis versus a truncated axis reverses apparent trends.

  • For multi-step problems, define the target quantity before computing; intermediate values are distractors when they answer a different question.

  • Work-rate and combined-rate: 1/T = 1/a + 1/b for parallel work; subtract rates for opposing flows (fill vs drain).

  • Overlapping sets: |A∪B| = |A| + |B| − |A∩B|; for three sets add singles, subtract pairs, add back the triple intersection.

  • Sufficiency test: a statement is sufficient only if it yields exactly one value; two valid values means insufficient.

  • When sources disagree on a number, prefer the primary/raw dataset over a summary that cites it, and note the as-of date.

  • Sanity-check results against the units and order of magnitude implied by the prompt before selecting an answer.

Quick reference

Quantitative reasoning and data interpretation

  • Percent change = (new − old)/old × 100; successive changes multiply: (1+r1)(1+r2) − 1, not r1 + r2.

  • Percentage points versus percent: a rise from 20% to 25% is 5 percentage points but a 25% relative increase.

  • Weighted average = Σ(wᵢxᵢ)/Σwᵢ; the combined mean lies between the group means, closer to the larger group.

  • Ratios: convert to parts of a whole (a:b → a/(a+b)) before comparing across datasets with different totals.

  • Compound growth: A = P(1 + r/n)^(nt); doubling time ≈ 70/r for small r (rule of 70).

  • Mean is shifted by outliers; median and IQR are robust. Outlier flag: value beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR.

  • Correlation coefficient r ∈ [−1, 1]; r measures linear association only and does not establish causation.

  • Base-rate logic: P(A|B) depends on P(B|A), P(A), and P(not A); a highly accurate test on a rare condition still yields many false positives.

  • Sampling: larger n narrows the margin of error roughly as 1/√n; a biased sample is not fixed by size.

Quick reference

Verbal reasoning and written communication

  • Assumption questions: the correct answer is necessary to the argument - negate it and the conclusion must collapse.

  • Strengthen/weaken: attack or support the link between evidence and conclusion, not the evidence itself.

  • Boldface and role-of-statement items: label each claim as premise, intermediate conclusion, or main conclusion before choosing.

  • Parallel reasoning: match the logical structure (conditional direction, quantifier, scope), not the topic or tone.

  • Modifier placement: a descriptive phrase must sit next to the noun it modifies; dangling modifiers create false attribution.

  • Subject-verb agreement survives intervening phrases; find the true subject by deleting prepositional clauses.

  • Pronoun reference: every 'it', 'they', or 'this' needs one unambiguous antecedent; 'this' alone often lacks a noun.

  • Comparison items must be logically parallel: compare like categories (rates with rates, totals with totals).

  • Concise professional writing: active voice, one idea per sentence, and the recommendation stated before its justification.

Quick reference

Professional judgement and ethical decision making

  • Priority order for a professional dilemma: safety of people, then legal/regulatory compliance, then organizational policy, then efficiency.

  • Conflict of interest: disclose, then recuse from the decision; disclosure alone does not cure a material personal interest.

  • Confidentiality yields only to a specific, documented exception (imminent harm, legal compulsion, or authorized consent).

  • Competence boundary: decline or refer work outside your qualification rather than proceeding with undisclosed risk.

  • Escalation ladder: raise with the direct supervisor, then the designated compliance/ethics channel, then the regulator if unresolved.

  • Document contemporaneously: record facts, dates, advice received, and actions taken; opinion should be labeled as opinion.

  • Whistleblower protections typically require internal reporting first and good-faith belief; retaliation is a separate breach to report.

  • Client/employer duty versus public interest: when they conflict, the public-interest obligation governs where harm is foreseeable.

  • Data handling: collect the minimum necessary, use it only for the stated purpose, and apply the stricter rule when jurisdictions differ.

Quick reference

Integrated reasoning and problem solving

  • Multi-source reasoning: tabulate each source's claim, date, and scope before synthesis; conflicts are usually scope differences, not contradictions.

  • Two-part analysis requires both parts correct; eliminate any option pair where one part fails, even if the other is strong.

  • Table/graphics interpretation: check axis units and scale breaks first; a 0-to-95 axis versus a truncated axis reverses apparent trends.

  • For multi-step problems, define the target quantity before computing; intermediate values are distractors when they answer a different question.

  • Work-rate and combined-rate: 1/T = 1/a + 1/b for parallel work; subtract rates for opposing flows (fill vs drain).

  • Overlapping sets: |A∪B| = |A| + |B| − |A∩B|; for three sets add singles, subtract pairs, add back the triple intersection.

  • Sufficiency test: a statement is sufficient only if it yields exactly one value; two valid values means insufficient.

  • When sources disagree on a number, prefer the primary/raw dataset over a summary that cites it, and note the as-of date.

  • Sanity-check results against the units and order of magnitude implied by the prompt before selecting an answer.

Quick reference

Quantitative reasoning and data interpretation

  • Percent change = (new − old)/old × 100; successive changes multiply: (1+r1)(1+r2) − 1, not r1 + r2.

  • Percentage points versus percent: a rise from 20% to 25% is 5 percentage points but a 25% relative increase.

  • Weighted average = Σ(wᵢxᵢ)/Σwᵢ; the combined mean lies between the group means, closer to the larger group.

  • Ratios: convert to parts of a whole (a:b → a/(a+b)) before comparing across datasets with different totals.

  • Compound growth: A = P(1 + r/n)^(nt); doubling time ≈ 70/r for small r (rule of 70).

  • Mean is shifted by outliers; median and IQR are robust. Outlier flag: value beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR.

  • Correlation coefficient r ∈ [−1, 1]; r measures linear association only and does not establish causation.

  • Base-rate logic: P(A|B) depends on P(B|A), P(A), and P(not A); a highly accurate test on a rare condition still yields many false positives.

  • Sampling: larger n narrows the margin of error roughly as 1/√n; a biased sample is not fixed by size.

Quick reference

Verbal reasoning and written communication

  • Assumption questions: the correct answer is necessary to the argument - negate it and the conclusion must collapse.

  • Strengthen/weaken: attack or support the link between evidence and conclusion, not the evidence itself.

  • Boldface and role-of-statement items: label each claim as premise, intermediate conclusion, or main conclusion before choosing.

  • Parallel reasoning: match the logical structure (conditional direction, quantifier, scope), not the topic or tone.

  • Modifier placement: a descriptive phrase must sit next to the noun it modifies; dangling modifiers create false attribution.

  • Subject-verb agreement survives intervening phrases; find the true subject by deleting prepositional clauses.

  • Pronoun reference: every 'it', 'they', or 'this' needs one unambiguous antecedent; 'this' alone often lacks a noun.

  • Comparison items must be logically parallel: compare like categories (rates with rates, totals with totals).

  • Concise professional writing: active voice, one idea per sentence, and the recommendation stated before its justification.

Quick reference

Professional judgement and ethical decision making

  • Priority order for a professional dilemma: safety of people, then legal/regulatory compliance, then organizational policy, then efficiency.

  • Conflict of interest: disclose, then recuse from the decision; disclosure alone does not cure a material personal interest.

  • Confidentiality yields only to a specific, documented exception (imminent harm, legal compulsion, or authorized consent).

  • Competence boundary: decline or refer work outside your qualification rather than proceeding with undisclosed risk.

  • Escalation ladder: raise with the direct supervisor, then the designated compliance/ethics channel, then the regulator if unresolved.

  • Document contemporaneously: record facts, dates, advice received, and actions taken; opinion should be labeled as opinion.

  • Whistleblower protections typically require internal reporting first and good-faith belief; retaliation is a separate breach to report.

  • Client/employer duty versus public interest: when they conflict, the public-interest obligation governs where harm is foreseeable.

  • Data handling: collect the minimum necessary, use it only for the stated purpose, and apply the stricter rule when jurisdictions differ.

Quick reference

Integrated reasoning and problem solving

  • Multi-source reasoning: tabulate each source's claim, date, and scope before synthesis; conflicts are usually scope differences, not contradictions.

  • Two-part analysis requires both parts correct; eliminate any option pair where one part fails, even if the other is strong.

  • Table/graphics interpretation: check axis units and scale breaks first; a 0-to-95 axis versus a truncated axis reverses apparent trends.

  • For multi-step problems, define the target quantity before computing; intermediate values are distractors when they answer a different question.

  • Work-rate and combined-rate: 1/T = 1/a + 1/b for parallel work; subtract rates for opposing flows (fill vs drain).

  • Overlapping sets: |A∪B| = |A| + |B| − |A∩B|; for three sets add singles, subtract pairs, add back the triple intersection.

  • Sufficiency test: a statement is sufficient only if it yields exactly one value; two valid values means insufficient.

  • When sources disagree on a number, prefer the primary/raw dataset over a summary that cites it, and note the as-of date.

  • Sanity-check results against the units and order of magnitude implied by the prompt before selecting an answer.

Quick reference

Quantitative reasoning and data interpretation

  • Percent change = (new − old)/old × 100; successive changes multiply: (1+r1)(1+r2) − 1, not r1 + r2.

  • Percentage points versus percent: a rise from 20% to 25% is 5 percentage points but a 25% relative increase.

  • Weighted average = Σ(wᵢxᵢ)/Σwᵢ; the combined mean lies between the group means, closer to the larger group.

  • Ratios: convert to parts of a whole (a:b → a/(a+b)) before comparing across datasets with different totals.

  • Compound growth: A = P(1 + r/n)^(nt); doubling time ≈ 70/r for small r (rule of 70).

  • Mean is shifted by outliers; median and IQR are robust. Outlier flag: value beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR.

  • Correlation coefficient r ∈ [−1, 1]; r measures linear association only and does not establish causation.

  • Base-rate logic: P(A|B) depends on P(B|A), P(A), and P(not A); a highly accurate test on a rare condition still yields many false positives.

  • Sampling: larger n narrows the margin of error roughly as 1/√n; a biased sample is not fixed by size.

Quick reference

Verbal reasoning and written communication

  • Assumption questions: the correct answer is necessary to the argument - negate it and the conclusion must collapse.

  • Strengthen/weaken: attack or support the link between evidence and conclusion, not the evidence itself.

  • Boldface and role-of-statement items: label each claim as premise, intermediate conclusion, or main conclusion before choosing.

  • Parallel reasoning: match the logical structure (conditional direction, quantifier, scope), not the topic or tone.

  • Modifier placement: a descriptive phrase must sit next to the noun it modifies; dangling modifiers create false attribution.

  • Subject-verb agreement survives intervening phrases; find the true subject by deleting prepositional clauses.

  • Pronoun reference: every 'it', 'they', or 'this' needs one unambiguous antecedent; 'this' alone often lacks a noun.

  • Comparison items must be logically parallel: compare like categories (rates with rates, totals with totals).

  • Concise professional writing: active voice, one idea per sentence, and the recommendation stated before its justification.

Quick reference

Professional judgement and ethical decision making

  • Priority order for a professional dilemma: safety of people, then legal/regulatory compliance, then organizational policy, then efficiency.

  • Conflict of interest: disclose, then recuse from the decision; disclosure alone does not cure a material personal interest.

  • Confidentiality yields only to a specific, documented exception (imminent harm, legal compulsion, or authorized consent).

  • Competence boundary: decline or refer work outside your qualification rather than proceeding with undisclosed risk.

  • Escalation ladder: raise with the direct supervisor, then the designated compliance/ethics channel, then the regulator if unresolved.

  • Document contemporaneously: record facts, dates, advice received, and actions taken; opinion should be labeled as opinion.

  • Whistleblower protections typically require internal reporting first and good-faith belief; retaliation is a separate breach to report.

  • Client/employer duty versus public interest: when they conflict, the public-interest obligation governs where harm is foreseeable.

  • Data handling: collect the minimum necessary, use it only for the stated purpose, and apply the stricter rule when jurisdictions differ.

Quick reference

Integrated reasoning and problem solving

  • Multi-source reasoning: tabulate each source's claim, date, and scope before synthesis; conflicts are usually scope differences, not contradictions.

  • Two-part analysis requires both parts correct; eliminate any option pair where one part fails, even if the other is strong.

  • Table/graphics interpretation: check axis units and scale breaks first; a 0-to-95 axis versus a truncated axis reverses apparent trends.

  • For multi-step problems, define the target quantity before computing; intermediate values are distractors when they answer a different question.

  • Work-rate and combined-rate: 1/T = 1/a + 1/b for parallel work; subtract rates for opposing flows (fill vs drain).

  • Overlapping sets: |A∪B| = |A| + |B| − |A∩B|; for three sets add singles, subtract pairs, add back the triple intersection.

  • Sufficiency test: a statement is sufficient only if it yields exactly one value; two valid values means insufficient.

  • When sources disagree on a number, prefer the primary/raw dataset over a summary that cites it, and note the as-of date.

  • Sanity-check results against the units and order of magnitude implied by the prompt before selecting an answer.

Quick reference

Quantitative reasoning and data interpretation

  • Percent change = (new − old)/old × 100; successive changes multiply: (1+r1)(1+r2) − 1, not r1 + r2.

  • Percentage points versus percent: a rise from 20% to 25% is 5 percentage points but a 25% relative increase.

  • Weighted average = Σ(wᵢxᵢ)/Σwᵢ; the combined mean lies between the group means, closer to the larger group.

  • Ratios: convert to parts of a whole (a:b → a/(a+b)) before comparing across datasets with different totals.

  • Compound growth: A = P(1 + r/n)^(nt); doubling time ≈ 70/r for small r (rule of 70).

  • Mean is shifted by outliers; median and IQR are robust. Outlier flag: value beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR.

  • Correlation coefficient r ∈ [−1, 1]; r measures linear association only and does not establish causation.

  • Base-rate logic: P(A|B) depends on P(B|A), P(A), and P(not A); a highly accurate test on a rare condition still yields many false positives.

  • Sampling: larger n narrows the margin of error roughly as 1/√n; a biased sample is not fixed by size.

Quick reference

Verbal reasoning and written communication

  • Assumption questions: the correct answer is necessary to the argument - negate it and the conclusion must collapse.

  • Strengthen/weaken: attack or support the link between evidence and conclusion, not the evidence itself.

  • Boldface and role-of-statement items: label each claim as premise, intermediate conclusion, or main conclusion before choosing.

  • Parallel reasoning: match the logical structure (conditional direction, quantifier, scope), not the topic or tone.

  • Modifier placement: a descriptive phrase must sit next to the noun it modifies; dangling modifiers create false attribution.

  • Subject-verb agreement survives intervening phrases; find the true subject by deleting prepositional clauses.

  • Pronoun reference: every 'it', 'they', or 'this' needs one unambiguous antecedent; 'this' alone often lacks a noun.

  • Comparison items must be logically parallel: compare like categories (rates with rates, totals with totals).

  • Concise professional writing: active voice, one idea per sentence, and the recommendation stated before its justification.

Quick reference

Professional judgement and ethical decision making

  • Priority order for a professional dilemma: safety of people, then legal/regulatory compliance, then organizational policy, then efficiency.

  • Conflict of interest: disclose, then recuse from the decision; disclosure alone does not cure a material personal interest.

  • Confidentiality yields only to a specific, documented exception (imminent harm, legal compulsion, or authorized consent).

  • Competence boundary: decline or refer work outside your qualification rather than proceeding with undisclosed risk.

  • Escalation ladder: raise with the direct supervisor, then the designated compliance/ethics channel, then the regulator if unresolved.

  • Document contemporaneously: record facts, dates, advice received, and actions taken; opinion should be labeled as opinion.

  • Whistleblower protections typically require internal reporting first and good-faith belief; retaliation is a separate breach to report.

  • Client/employer duty versus public interest: when they conflict, the public-interest obligation governs where harm is foreseeable.

  • Data handling: collect the minimum necessary, use it only for the stated purpose, and apply the stricter rule when jurisdictions differ.