LRDI Reference Sheet

Percentage & Growth (DI)6

• % change = (new − old)/old × 100
• Percentage-point change = simple difference of two %s (NOT % change)
• CAGR = (final/initial)^(1/n) − 1
• Value after n yrs at r% = initial × (1 + r/100)ⁿ
• Rule of 70: doubling time ≈ 70 / growth-rate%
• Average of growth ≠ growth of average — compute each separately

Ratios, Averages & Share (DI)5

• Market/category share = part / total × 100
• Weighted average = Σ(value × weight) / Σ(weight)
• Split a total in ratio a:b ⇒ first = total × a/(a+b)
• Index value = (current / base) × 100
• If A:B and B:C known ⇒ A:B:C by making B common

Reading Charts & Tables5

• Pie chart: whole = 360° = 100% · 1% = 3.6°
• Sector angle = (value / total) × 360°
• Stacked bar: each segment = that category's share of the bar's total
• Line graph slope = rate of change between two points
• Always read units, footnotes & axis scales first

Approximation in DI4

• Compare ratios by cross-multiplication or converting to %
• Use benchmark fractions: ¼=25%, ⅓=33%, ⅖=40%, ⅗=60%, ¾=75%
• Round to 2 significant figures for quick comparison
• Options far apart → estimate; options close → compute exactly

Arrangements (Linear & Circular)5

• Linear order of n = n! · circular = (n−1)!
• Facing centre vs outside flips left/right reference
• Start from the most definite (most constrained) clue
• Fix one reference point in circular puzzles, place others around it
• Use a diagram; track positions, not just relations

Order & Ranking4

• Rank from top + rank from bottom = total + 1
• xth from left & yth from right ⇒ total = x + y − 1
• Build one ordered line by chaining pairwise comparisons
• Track max/min possible positions when info is partial

Distribution & Grouping4

• Use a grid/matrix: rows = people, columns = attributes
• Mark ticks ✓ and crosses ✗ as you deduce
• Handle 'exactly / at least / at most' counts carefully
• Venn diagram for overlapping categories

Selection & Conditional (if-then)4

• If A then B ≡ contrapositive: if not-B then not-A
• ‘A or B’ inclusive unless stated exclusive
• Binary grid (yes/no) for membership puzzles
• Eliminate impossible cases early to shrink the tree

Games & Tournaments4

• Round-robin matches among n = ⁿC₂ = n(n−1)/2
• Knockout to find 1 winner among n = n − 1 matches
• Points table: total points = wins·W + draws·D
• Back-calculate results from points & goal/run differences

Networks, Routes & Scheduling4

• Count paths by adding values at each node (grid-path method)
• Critical path = longest-duration path through a schedule
• Use earliest-start / latest-finish for scheduling sets
• Flow/route caps: bottleneck = smallest capacity on the path

Set-selection strategy4

• Scan all sets first; attempt the 2–3 easiest immediately
• Cap time per set (~10–12 min); leave if stuck
• Label each set: calculation-heavy (DI) vs logic-heavy (LR)
• Note doable single questions even in a hard set