EPSO Numerical Reasoning common mistakes
EPSO Numerical Reasoning · Understand the traps and how to avoid them.
When asked for the percentage change between two values, the candidate divides the difference by the new (later) value instead of by the original (earlier) value, or divides the difference by the sum of the two values.
The word 'change' pulls attention to the two numbers themselves, and candidates grab whichever number is at hand as the denominator; many also half-remember 'average of the two' formulas from index-number work and apply them indiscriminately.
What to do instead
Before computing, write the formula down explicitly as (new − old) ÷ old × 100, and label which figure is the base. Do a sanity check: if a price rises from 80 to 100 the answer must be 25%, not 20%, because the base is 80. Practise pairs where the direction reverses (100→80 gives −20%) so the asymmetry becomes automatic.
The candidate adds percentage changes instead of compounding them, e.g. treating a 20% rise followed by a 10% fall as a net 10% rise rather than a net 8% rise.
Percentages feel like plain numbers that can be added, and successive changes in a table are often presented in adjacent columns, inviting simple addition. The multiplicative nature of percentage change is easy to forget under time pressure.
What to do instead
Convert every successive change into a multiplier (1.20, 0.90) and multiply them: 1.20 × 0.90 = 1.08, so +8%. Adopt the habit of never adding percentages that apply to different bases. Drill chains of three or four changes until multiplying multipliers is reflex.
When scaling a recipe, map or model, the candidate multiplies or divides every dimension by the scale factor instead of applying it once to a single dimension, or applies an area/volume factor to lengths.
Candidates conflate linear scale with area and volume scale, and under exam pressure they apply the given ratio to whichever quantity appears first without asking whether the ratio refers to length, area or volume.
What to do instead
State the ratio as a sentence first: '1 cm on the map = 25,000 cm on the ground, so lengths scale by 25,000; areas scale by 25,000².' For recipes, scale all ingredients by the same factor but remember cooking time and pan size do not scale linearly. Check the units of the answer against the units of the question.
The candidate computes a simple average of two group averages instead of weighting by group size, e.g. averaging a 70% pass rate for 200 candidates with a 90% pass rate for 50 candidates and reporting 80%.
The word 'average' triggers the arithmetic-mean routine, and the group sizes are often in a separate column or sentence that is easy to skim past. The unweighted mean is also a rounder, more tempting number.
What to do instead
Rewrite the question as total-over-total: (0.70×200 + 0.90×50) ÷ 250 = 185 ÷ 250 = 74%. Before answering, ask 'are the groups the same size?' If not, weight. If the question gives only the two averages and no sizes, the correct response is that the combined average cannot be determined.
On a speed/distance/time question the candidate mixes units - minutes with hours, metres with kilometres - and reports a numerically plausible but wrong answer, such as 90 minutes for a 120 km trip at 80 km/h.
The arithmetic is easy once units are consistent, so candidates rush the conversion step; decimal time (1.5 h) and mixed time (1 h 30 min) are also confused, and 1.5 h is sometimes read as 1 h 50 min.
What to do instead
Convert everything to one unit system before calculating, and write the units into the equation: 120 km ÷ 80 km/h = 1.5 h = 1 h 30 min. Memorise that 0.25 h = 15 min, 0.5 h = 30 min, 0.75 h = 45 min. Finish by checking the answer's magnitude: a 120 km trip cannot take 90 minutes at 80 km/h, since that implies 1.33 h.
When comparing absolute and relative values in a table, the candidate picks the row with the largest absolute increase as the one with the largest percentage increase (or vice versa), without checking which measure the question asks for.
Large absolute numbers dominate attention, and the question stem's wording ('biggest rise' vs 'fastest growth') is easily blurred. Tables often place absolute and percentage columns side by side, encouraging a glance at the wrong column.
What to do instead
Underline the key phrase in the stem before reading the table: 'largest increase' means absolute; 'largest percentage increase' or 'fastest growth' means relative. Compute both for the top two candidates and compare. Remember a small base can produce a huge percentage change from a tiny absolute movement.
On a work-rate question the candidate adds the times two workers take individually (e.g. 6 h + 4 h = 10 h) instead of adding their rates (1/6 + 1/4 = 5/12, so 12/5 = 2.4 h).
Times look like quantities that combine additively, and the intuition that two people together take less than either alone is easily overridden by the habit of adding the numbers given.
What to do instead
Always convert times to rates first: work per hour = 1/time. Add rates, then invert the total rate to get the combined time. Sanity check: the combined time must be less than the faster individual time. Practise three-worker and 'one leaves partway' variants with the same rate-first structure.
The candidate computes a percentage mark-up on cost and reports it as the margin on selling price, or applies VAT/indexation to the wrong base, producing answers that are close but wrong.
Mark-up and margin are both expressed as percentages and are routinely confused; indexation questions often give a base-year figure and a chain of annual indices, and candidates apply the latest index directly to the wrong year's value.
What to do instead
Write the base under the percentage: mark-up = profit ÷ cost; margin = profit ÷ selling price. For indexation, express each year as a multiplier on the previous year and chain them, or divide the two index values to move between any two years. Check that a 20% mark-up on 100 gives a selling price of 120 and a margin of 16.7%, not 20%.
On a combinatorics or probability question the candidate adds where they should multiply (or vice versa), or counts ordered arrangements when the question asks for unordered selections, giving an answer that is out by a factor of 2, 6 or more.
The 'and/or' distinction maps onto multiply/add but is not stated explicitly, and the difference between permutations and combinations is invisible unless the candidate consciously asks whether order matters.
What to do instead
Before calculating, ask two questions: does order matter, and can items repeat? Write 'AND → multiply, OR → add' at the top of the working. For selections from a group, divide by the factorial of the chosen count to remove ordering: choosing 3 from 8 is (8×7×6) ÷ (3×2×1) = 56. Verify small cases by listing them.
On data-sufficiency questions the candidate solves the problem fully and marks the answer as sufficient only if a unique numerical answer emerges, rather than judging whether the data would determine a unique answer - and often overlooks that one statement alone is enough.
Years of ordinary numerical reasoning train candidates to compute; data-sufficiency format rewards a different judgement, and the five standard answer options are easily misremembered under time pressure.
What to do instead
Test each statement in isolation first, without the other, and ask only 'does this force a single value?'. Do not actually compute the value if the structure shows it is determined. Memorise the five options and practise classifying ten short items into them, timing yourself so the judgement becomes faster than the calculation.