GNFS Aptitude Test cheat sheet

Percentage change = (new − old) ÷ old × 100; a rise then an equal-percent fall never returns to the original value.

Successive percentage changes multiply: +20% then −15% gives 1.20 × 0.85 = 1.02, a net +2%.

Ratio sharing: total ÷ sum of ratio parts gives one part; multiply each ratio term by that unit value.

Work rates add as reciprocals: if A finishes in 4 h and B in 6 h, together they take 1 ÷ (1/4 + 1/6) = 2.4 h.

Average speed for equal distances = 2ab ÷ (a + b), the harmonic mean, not (a + b) ÷ 2.

Simple interest = P × r × t; compound amount = P × (1 + r)^t, so compounding always exceeds simple interest for t > 1.

Profit percentage is measured against cost price: profit% = (selling price − cost price) ÷ cost price × 100.

Number-series checks in order: differences, then ratios, then alternating or two interleaved sequences, then squares/cubes ± constant.

Validity vs truth: a deductive argument can be valid with false premises; assess structure first, factual accuracy second.

Contrapositive is equivalent: 'if P then Q' equals 'if not Q then not P'; the converse ('if Q then P') is not equivalent.

'Some A are B' does not imply 'some A are not B' when A could be empty or wholly inside B - check quantifier scope.

Necessary vs sufficient: 'X is required for Y' means Y implies X; 'X guarantees Y' means X implies Y.

In passage questions, an answer choice is wrong if it is true but unsupported by the text, or supported but overstated.

Strong distractors swap scope words: all/some, always/sometimes, must/may, only/at least - compare these words before judging.

Analogy relations to test: function, part-to-whole, cause-to-effect, degree, category, and worker-to-tool.

'Unless P, Q' translates to 'if not P then Q'; 'only if P, Q' translates to 'if Q then P'.

Rotation sequence rule: track one element's position across frames first; if it advances a fixed number of steps, that rule governs the series.

Count invariants separately: number of sides, closed regions, intersections, and line segments often change at different rates.

Alternating series: odd-numbered frames and even-numbered frames may each follow their own rule; split before concluding.

Negation test for assumptions: remove the statement and see whether the conclusion still follows; if it collapses, the statement was an assumption.

Syllogism elimination: draw the two premises as sets; a conclusion is forced only if it holds in every possible diagram.

Seating/ordering puzzles: fix the most constrained entity first, then place items with two constraints, then fill the rest.

'If and only if' chains are bidirectional; a one-way arrow chain cannot be reversed, so direction errors are the main trap.

Odd-one-out: name the shared property of four options explicitly; the fifth must fail that exact property, not merely look different.

Compare digit strings in fixed-width blocks (e.g. groups of three) rather than left to right, to catch transpositions.

Common transcription traps: 0 vs O, 1 vs l vs I, 5 vs S, 2 vs Z, rn vs m, and doubled letters in names.

Date formats differ (DD/MM/YY vs MM/DD/YY); confirm which convention the item uses before flagging a mismatch.

Rounding rule for half values: round half up, half to even, or truncate - the item's stated rule overrides habit.

Unit mismatches (kg vs g, km vs m, £ vs $) are deliberate errors; verify units before verifying numbers.

Check totals twice by a different route: sum columns, then sum rows, and compare both to the stated grand total.

Sign errors: a negative in brackets changes every downstream figure; re-read the sign of each term as written.

Alphabetical or numerical sort checks: verify only the boundary pairs and any item adjacent to an equal value.

Expected value = sum of (probability × payoff); choose the option with the highest expected value only when risk-neutral.

Break-even volume = fixed costs ÷ (price per unit − variable cost per unit); below this volume the option loses money.

Sunk costs are irrelevant to a forward decision; include only future costs and benefits that differ between options.

Opportunity cost is the value of the best alternative forgone, not the sum of all alternatives.

Prioritise by urgency × impact; a task that is urgent but low-impact ranks below one that is important but not yet urgent.

Sensitivity check: vary the least certain input by ±20% and see whether the ranking of options reverses.

Capacity constraint rule: maximise contribution per unit of the scarce resource, not contribution per unit sold.

When information is insufficient, the defensible answer names the missing datum rather than assuming a convenient value.

Read the axis origin first: a truncated y-axis exaggerates differences; a zero-based axis shows true proportion.

Percentage of total vs percentage change are different measures; a bigger share does not mean a bigger increase.

Pie charts show composition at one point in time and cannot show trends; use the bar or line chart for change over time.

Weighted averages: combine group means by group size, never by simple mean of the means.

Index numbers are relative to a stated base year (base = 100); an index of 130 means a 30% rise from that base.

Per-capita or per-unit figures = total ÷ population or units; compare rates, not raw totals, across unequal groups.

Stacked bars give segment values only by subtraction from the running total, not by segment height alone.

Check that percentages sum to 100 (±1 for rounding) and that segment values sum to the stated total before analysis.