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Numerical Reasoning and English Usage Rules

Flashcards with the formulas for the numerical reasoning section and the grammar and word-choice rules for English language use in the Hong Kong civil service recruitment exam. Original study material.

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Percentage change

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Percentage change

\frac{new - old}{old} \times 100%

(divide by the original figure).

Percentage point change

The plain difference between two percentages, not a relative change.

Reverse percentage (after an increase of p%)

Original

=

new

\div (1 + \frac{p}{100})

Successive percentage changes

Multiply the factors: increase 20% then decrease 25% gives

1.2 \times 0.75 = 0.9

Simple interest

I = P \times r \times t

Compound interest

A = P (1 + r)^{n}

Speed, distance and time

speed = \frac{distance}{time}

Average speed for equal distances at speeds a and b

\frac{2 ab}{a + b}

, not

\frac{a + b}{2}

Work rate for two workers (times a and b)

Together they need

\frac{ab}{a + b}

days.

Average

Sum of the values divided by the number of values.

Missing value from an average

Total

=

average

\times

number of values; subtract the known values.

Ratio sharing

Add the parts, divide the total by that sum, multiply by each part.

Pie chart angle

Angle

= \frac{value}{total} \times 36 0^{\circ}

Arithmetic sequence

A constant difference is added each time:

T_{n} = a + (n - 1) d

Geometric sequence

Each term is multiplied by a constant ratio:

T_{n} = a r^{n - 1}

Sequence with increasing differences

Check the differences of the differences: if they rise by 1 each time, add 1 more each step.

Comply

Take the preposition 'with': comply with the rules.

Depend

Take the preposition 'on': depend on the support.

Since / for

'Since' gives a starting point (since 2015); 'for' gives a length of time (for ten years).

Fewer / less

'Fewer' with countable nouns (fewer people); 'less' with uncountable nouns (less money).

Affect / effect

'Affect' is usually the verb (to influence); 'effect' is usually the noun (a result).

Advice / advise

'Advice' is the uncountable noun; 'advise' is the verb.

Principal / principle

'Principal': main, or the head of a school; 'principle': a basic rule or belief.

Its / it's

'Its' is possessive; 'it's' means 'it is' or 'it has'.

Letter ending after 'Dear Sir or Madam'

Yours faithfully

Letter ending after 'Dear Ms Chan'

Yours sincerely

Past perfect

Used for an action completed before another past action: had + past participle.

Second conditional

If + past simple, would + verb.

Neither ... nor

The verb agrees with the subject nearest to it.

The number of / a number of

'The number of' takes a singular verb; 'a number of' takes a plural verb.

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