Civil Service Numerical Test flashcards

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

Order of operations

Brackets first, then orders (powers and roots), then division and multiplication from left to right, then addition and subtraction from left to right. Division does not automatically outrank multiplication.

Divisibility rule for 3

A whole number is divisible by 3 exactly when the sum of its digits is a multiple of 3; for 471 the digits sum to 12, so it divides by 3.

Divisibility rule for 4

A number is divisible by 4 when its last two digits form a multiple of 4; 1,536 ends in 36, which is 4 × 9, so it divides exactly.

Dividing by a fraction

Dividing by a fraction is the same as multiplying by its reciprocal: dividing by 3/4 equals multiplying by 4/3, which turns fraction division into ordinary multiplication.

Difference of two squares

The expression a² − b² factorises as (a + b)(a − b). This makes mental arithmetic fast: 53² − 47² becomes (100)(6), which equals 600.

Pie chart sector share

A sector's share of the whole equals its angle divided by 360 degrees; a 90-degree sector is 25% of the total and a 45-degree sector is 12.5%.

Row versus column percentage

In a two-way table, a row percentage divides each cell by its row total and describes that group; a column percentage divides by the column total instead.

Truncated axis effect

When a bar chart's vertical axis does not start at zero, the visual differences between bars are exaggerated compared with the true proportional differences between the underlying values.

Slope on a line graph

On a line graph the slope equals the change in the plotted value divided by the change in the horizontal variable, so the steeper line shows the faster rate.

Checking table totals

The grand total of a table must equal both the sum of all row totals and the sum of all column totals; any mismatch means a cell has been misread.

Successive percentage changes

Two percentage changes applied in sequence multiply rather than add: a 10% rise followed by a 10% fall gives 1.10 × 0.90 = 0.99, a net fall of 1%.

Percentage points versus percent

Moving from 20% to 25% is a rise of 5 percentage points, but the relative increase is 5 ÷ 20 = 25%. The two measures answer different questions.

Ratio sharing formula

To divide a total T in the ratio a:b, add the parts to get a + b, divide T by that sum, then allocate a parts and b parts respectively.

Original value after increase

If a value has grown by r percent to reach N, the original equals N divided by (1 + r/100); for instance dividing by 1.15 reverses a 15% increase.

Direct and inverse proportion

In direct proportion y = kx, both quantities rise together. In inverse proportion y = k/x, one falls as the other rises and the product xy stays constant.

Weighted mean

Multiply each value by its weight, sum the products, then divide by the total weight. Group sizes serve as the weights when combining subgroup means.

Average speed over two legs

Average speed equals total distance divided by total time. It equals the simple mean of the two speeds only when both legs take exactly the same time.

Converting m/s to km/h

Multiply metres per second by 3.6 to obtain kilometres per hour, because one hour holds 3,600 seconds and one kilometre is 1,000 metres.

Speed distance time relations

Speed equals distance divided by time; distance equals speed times time; time equals distance divided by speed. Convert all units to one system first.

Median versus mean

The median is the middle value of an ordered list and is little affected by extremes; the mean uses every value and shifts with outliers.

Combined work rate

If one worker alone takes a hours and another takes b hours, working together they take ab/(a+b) hours, because their rates 1/a and 1/b add.

Mixture concentration rule

Pure substance equals concentration multiplied by volume. When two solutions are mixed, the pure amounts add and the volumes add, giving the new concentration.

Catch-up time

When a faster mover chases a slower one, the time needed to close the gap equals the starting distance divided by the difference between their speeds.

Working backwards through operations

When a problem gives only the final amount after a chain of operations, undo each step in reverse order, inverting every operation as you go.

Simple interest

Simple interest equals principal × rate × time, with the rate written as a decimal per year. Total amount is principal × (1 + rate × time).

Compound amount formula

Compound amount equals P(1 + r)^n, where r is the decimal rate per period and n counts the periods, because interest itself earns interest each period.

Profit percentage

Profit equals selling price minus cost price, and profit percentage equals profit divided by cost price times 100. It is measured against cost, not selling price.

Successive discounts

Two successive discounts multiply: final price equals marked price × (1 − a/100) × (1 − b/100), which is lower than a single discount of (a + b) percent.

Front-end rounding

Round every number to one or two significant figures, compute with the rounded values, then select whichever answer option lies closest to that rough estimate.

Ten percent anchor

Build percentages from 10%: shift the decimal one place left, halve it for 5%, add the two for 15%, and shift twice for 1%.

Benchmark fraction percentages

Useful benchmarks: 1/6 is about 16.7%, 1/7 about 14.3%, 1/8 is 12.5%, 1/9 about 11.1%, and 1/11 about 9.1%.

Estimating square roots

Place the number between two perfect squares; its root lies between their roots. Interpolating gives a close value, so the square root of 50 sits near 7.07.