EPSO Numerical Reasoning flashcards

34 cards. Read the term and the definition here. The deck at the top of this page is optional.

Percentage change formula

Divide the absolute change by the original value and multiply by 100: (new − old) ÷ old × 100. The original value is always the denominator, never the new value.

Percentage points versus percent

A move from 20% to 25% is 5 percentage points but a 25% relative increase, because 5 ÷ 20 = 0.25. Mixing the two units is a common distractor.

Successive percentage multipliers

Apply each change as a multiplier: +20% then −20% gives 1.2 × 0.8 = 0.96, a net fall of 4%. Multipliers multiply; percentages themselves do not add.

Recovering from a percentage fall

After a fall of p%, the rise needed to return to the original is p ÷ (100 − p) × 100. A 20% fall therefore needs a 25% rise, not 20%.

Splitting an amount in a ratio

For ratio a : b : c, the total number of parts is a + b + c. Each share equals the amount multiplied by that term divided by the total parts.

Direct versus inverse proportion

Direct proportion keeps y ÷ x constant, so doubling x doubles y. Inverse proportion keeps x × y constant, so doubling x halves y.

Combining two ratios

Given a : b and b : c, scale both so the shared term b matches, then read off a : b : c. Example: 2 : 3 and 4 : 5 become 8 : 12 : 15.

Area and volume scaling

When a shape is scaled by linear factor k, lengths multiply by k, areas by k squared and volumes by k cubed. Map-scale problems depend on this rule.

Weighted average formula

The weighted mean equals the sum of each value times its weight, divided by the total of the weights. Weights can be counts, hours, populations or amounts.

Combined mean of two groups

Pool the totals: (n1m1 + n2m2) ÷ (n1 + n2). The result always lies between the two group means, nearer the mean of the larger group.

Finding group sizes from means

If two groups with means m1 and m2 combine to mean M, the size ratio is n1 ÷ n2 = (m2 − M) ÷ (M − m1), assuming M lies between the means.

Mean versus median

The mean is the sum divided by the count and is pulled by outliers. The median is the middle ordered value and resists extreme values.

Average speed for a journey

Average speed equals total distance divided by total time. It is not the arithmetic mean of the segment speeds unless the times spent are equal.

Equal-distance speed average

Travelling equal distances at speeds a and b gives average speed 2ab ÷ (a + b), the harmonic mean, which is below the simple midpoint of a and b.

Speed unit conversion

Multiply metres per second by 3.6 to get kilometres per hour; divide kilometres per hour by 3.6 to get metres per second. Always match units before computing time.

Relative speed for meeting

Objects moving towards each other close the gap at the sum of their speeds; moving the same way, at the difference. Time to meet equals gap divided by closing speed.

Cross-multiplication to compare fractions

For positive denominators, a/b exceeds c/d exactly when ad exceeds bc. This avoids converting both fractions to decimals before comparing.

Common fraction-decimal anchors

Memorise 1/8 = 0.125, 1/6 ≈ 0.1667, 1/3 ≈ 0.3333, 3/8 = 0.375, 5/8 = 0.625 and 1/7 ≈ 0.1429 to speed up estimation and comparison.

Scientific notation arithmetic

Write numbers as a × 10^n with a between 1 and 10. To multiply, multiply the leading parts and add exponents; to divide, divide the leading parts and subtract exponents.

Estimation by rounding first

Round each number to one significant figure, compute the rough result, then compare with the options. If the gap exceeds the rounding error, the estimate decides the answer.

Absolute versus relative change

Absolute change is new minus old in the data's own units. Relative change divides that by the base and multiplies by 100, giving a unit-free percentage.

Index numbers rebased to 100

An index expresses each period relative to a base period set at 100: index = actual ÷ base actual × 100. Ratios of two index values give the relative change.

Truncated axis distortion

A line chart whose vertical axis starts above zero exaggerates slopes visually. Check the axis start and step before concluding that one series grew faster.

Reading stacked chart shares

In a stacked or segmented chart each segment's share is its value divided by that period's total. Shares from two periods are only comparable if the totals are stated.

Combined work rate

Rates add: if A finishes in a hours and B in b hours, together they take ab ÷ (a + b) hours, since their rates are 1/a and 1/b per hour.

Worker-days as total work

At constant daily output, total work equals workers multiplied by days. Halving the workers doubles the days needed to complete the same task.

Filling and draining pipes

Add all filling rates and subtract all draining rates to get the net rate. Time to fill equals the tank capacity divided by that net rate.

Profit margin versus markup

Margin divides profit by revenue; markup divides profit by cost. The same profit therefore gives a larger percentage when expressed as markup on a lower cost base.

Compound growth formula

Final value equals initial value multiplied by (1 + r) raised to the power n, where r is the periodic rate as a decimal and n the number of periods.

Removing tax from a price

A tax-inclusive price equals net × (1 + rate). To recover the net figure, divide by (1 + rate); subtracting the rate from the gross price is wrong.

Combinations versus permutations

Permutations count ordered selections, n! ÷ (n − r)!. Combinations count unordered selections, n! ÷ [r!(n − r)!]. Choose combinations when order is irrelevant.

Probability of at least one

For n independent trials each with success probability p, the chance of at least one success is 1 − (1 − p)^n. Subtract the all-failure case from one.

Sufficiency requires a unique answer

Data is sufficient only if it forces exactly one numerical value. If two different valid scenarios satisfy the information, the data is insufficient.

Counterexample to reject a claim

A statement claiming something must always hold is disproved by a single valid numerical case where it fails. One counterexample settles the question.