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ICAC Investigator Written Test study materials
ICAC Investigator Written Test study resources

ICAC Investigator Written Test: Numerical and Analytical Reasoning: Percentages, Ratios and Data

ICAC Investigator Written Test · Work through your exam, one topic at a time.

All guide sections

Numerical and Analytical Reasoning: Percentages, Ratios and Data

What the paper tests

Numerical and Analytical Reasoning checks whether you can extract figures from tables, prose and charts, choose the right operation, and present a sensible answer under time pressure. Expect percentages, ratios, rates, averages, unit conversion, currency and data interpretation. Write the formula before substituting numbers; this reduces careless errors.

Core rules and concepts

  • Percentage change: divide the change by the original (base) value, not the new value. An increase from 240 to 300 is 60 ÷ 240 = 25%, not 60 ÷ 300 = 20%.
  • Percentage points: a rise from 12% to 15% is 3 percentage points, but 25% relative to the old figure.
  • Weighted averages: an average of averages is not the overall average unless the groups are equal in size. Weight each group by its size.
  • Ratios: keep the order; convert to a common unit before comparing.
  • Rates: distance = speed × time; work rates add only when people or machines work simultaneously on the same task.
  • Data interpretation: read the axis labels and any note under the table; a footnote can change the definition of a figure.
  • Estimation: round late, not early; keep enough precision to distinguish the answer options.

Worked example

A unit has a budget of HK$80,000. It spends 15% on training and then 20% of the remaining budget on equipment. How much remains? Training = 0.15 × 80,000 = 12,000. Remaining = 68,000. Equipment = 0.20 × 68,000 = 13,600. Total spent = 25,600. Remaining = 80,000 − 25,600 = 54,400. A common wrong answer takes 20% of the original 80,000 and gets 52,000 remaining; that misreads the base.

Traps

  • Applying a percentage to the wrong base after a change.
  • Adding percentages that are percentages of different totals.
  • Mixing percentage points with percent.
  • Rounding a unit price before multiplying by a large quantity.
  • Ignoring units such as thousands, millions, HK$ and RMB, or mixing monthly and annual figures.
  • Confusing a stock figure (number of cases) with a flow figure (cases per year).