ADF YOU Session cheat sheet

Common analogy links: part-to-whole (wheel : car), cause-to-effect (fire : smoke), function (pen : write), category-to-member (fruit : apple), degree (warm : hot), and opposite (up : down).

Transitive ordering rule: if A is greater than B and B is greater than C, then A is greater than C; order the items on a single line before answering.

"All A are B" never converts to "All B are A"; the reverse inference is invalid unless a second premise supplies it.

"No A are B" converts validly to "No B are A", and "Some A are B" converts validly to "Some B are A".

"Some A are B" plus "All B are C" yields "Some A are C"; a particular premise combined with a universal premise gives a particular conclusion.

Odd-one-out rule: three options must share a single stated category or attribute; the answer is the option that fails that attribute, not the one that is merely unfamiliar.

Common prefixes: bene- (good), mal- (bad), circum- (around), anti- (against), pre- (before), post- (after), sub- (under), super- (above).

Passage questions are answered only from information printed in the passage; outside knowledge and plausible real-world facts are not admissible.

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

To increase an amount by p%, multiply by (1 + p/100); to decrease by p%, multiply by (1 − p/100).

Average = total ÷ count, so total = average × count, which gives a missing total or a missing member without summing every value.

Speed = distance ÷ time; distance = speed × time; time = distance ÷ speed. Convert km/h to m/s by dividing by 3.6.

A ratio a : b splits a total into (a + b) equal parts, so one part = total ÷ (a + b) and the shares are a × part and b × part.

Combined work rates add as reciprocals: 1/T = 1/t₁ + 1/t₂, so two workers alone in 6 h and 3 h finish together in 2 h.

Simple interest I = P × R × T ÷ 100, where R is the annual percentage rate and T is the time in years.

Series strategy in order: constant first difference, constant second difference, constant ratio, then two interleaved sequences at odd and even positions.

Reverse percentage: if a price after a 20% rise is $96, the original is 96 ÷ 1.20 = $80, not 96 − 20%.

Count first: sides, vertices, enclosed regions, straight versus curved lines, dots, and arrows often follow a simple arithmetic sequence.

Rotation preserves handedness; reflection reverses it, so a shape that gains a mirror image has been reflected, not rotated.

Four successive 90° rotations return a figure to its start; three successive 90° rotations equal one 270° rotation in the opposite direction.

When alternate frames change independently, split the series into odd-positioned and even-positioned sequences and solve each separately.

Overlay rules: lines common to both figures either cancel (exclusive-OR) or combine (OR); test the rule against two or three consecutive pairs before choosing.

Symmetry axis counts: equilateral triangle 3, square 4, regular pentagon 5, regular hexagon 6, circle infinitely many, scalene triangle 0.

Track a single feature at a time (shading, position, size, orientation, count) and eliminate options that break any confirmed rule.

In 3×3 matrices the transformation holds along every row and down every column, so a candidate rule must be checked in both directions.

Order of operations: brackets, orders (powers and roots), then multiplication and division left to right, then addition and subtraction left to right.

To divide by a fraction, multiply by its reciprocal: a/b ÷ c/d = a/b × d/c.

Fractions, decimals and percentages are interchangeable: 3/8 = 0.375 = 37.5%; divide numerator by denominator to convert.

Triangle area = ½ × base × perpendicular height; trapezium area = ½ × (a + b) × h.

Circle: circumference = 2πr, area = πr², diameter = 2r; using π ≈ 3.14 is normally sufficient for multiple-choice options.

Pythagoras: a² + b² = c² in a right-angled triangle, where c is the hypotenuse opposite the right angle.

Volume: prism or cylinder = cross-sectional area × length (cylinder πr²h); rectangular box = length × width × height.

Metric conversions: 1 km = 1000 m, 1 m = 100 cm, 1 kg = 1000 g, 1 L = 1000 mL, 1 hour = 3600 s.

Algebraic expansion: (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b²; a² − b² = (a + b)(a − b).