Irish Numerical Reasoning flashcards

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

Arithmetic sequence nth term

For a sequence with first term a and common difference d, the nth term equals a + (n − 1)d. Find d by subtracting any term from the next.

Geometric sequence nth term

For a sequence with first term a and common ratio r, the nth term equals a × r^(n−1). Find r by dividing a term by the previous one.

Sum of arithmetic series

The sum of n terms of an arithmetic sequence is n/2 × (first term + last term), or n/2 × (2a + (n−1)d).

Second difference test

If first differences of a sequence are not constant but second differences are, the sequence follows a quadratic rule of the form an² + bn + c.

Interleaved series rule

When a series alternates unpredictably, split terms by odd and even positions. Each sub-series often follows its own simple arithmetic or geometric rule.

Sum of first n integers

The sum 1 + 2 + … + n equals n(n + 1)/2. For example, the sum of the first 10 integers is 55.

Fibonacci-type sequence

Each term equals the sum of the two preceding terms. Check three consecutive terms before assuming this rule applies to a series.

Average formula

Average (mean) equals total sum divided by count. Rearranged, total sum equals mean × count, which recovers a missing value.

Combined work rate

If worker A takes a days and worker B takes b days, together they take ab/(a + b) days, derived from 1/T = 1/a + 1/b.

Simple interest formula

Simple interest equals Principal × Rate × Time ÷ 100, where rate is the annual percentage and time is in years.

Profit percentage base

Profit or loss percentage is calculated on cost price: (selling price − cost price) ÷ cost price × 100.

Consecutive integer setup

For three consecutive integers, let the middle be n, so the terms are n−1, n, n+1. Their sum is 3n.

Percentage change formula

Percentage change equals (new value − old value) ÷ old value × 100. A positive result is an increase; negative is a decrease.

Successive percentage changes

Apply successive changes by multiplying factors: (1 + a)(1 + b). A 20% rise then 20% fall gives 1.2 × 0.8 = 0.96, a 4% net fall.

Reverse percentage

If a value after a p% increase is X, the original is X ÷ (1 + p/100). For a decrease, divide by (1 − p/100).

Ratio share formula

To split total T in ratio a : b : c, each share is aT/(a+b+c), bT/(a+b+c), cT/(a+b+c) respectively.

Direct proportion

Two quantities are directly proportional when y = kx for a constant k. Then y₁/x₁ = y₂/x₂ for any two pairs.

Inverse proportion

Two quantities are inversely proportional when their product is constant: x₁y₁ = x₂y₂. Doubling one halves the other.

Percentage points versus percent

A change from 10% to 15% is 5 percentage points but a 50% relative increase, since 5 ÷ 10 = 0.5.

Pie chart sector angle

Each pie sector angle equals (value ÷ total) × 360°. Each percentage equals (value ÷ total) × 100.

Non-zero axis baseline

A bar or line chart whose vertical axis does not start at zero exaggerates differences between values. Check the baseline before comparing.

Line graph slope meaning

On a line graph, slope represents the rate of change between points, not the absolute value at any single point.

Table total cross-check

When a table has a total row or column, verify your sums against it before answering. Mismatches reveal a misread cell.

Speed distance time relation

Distance equals speed × time. Rearranged, speed equals distance ÷ time and time equals distance ÷ speed.

km/h to m/s conversion

Multiply kilometres per hour by 5/18 to get metres per second. Multiply metres per second by 18/5 to get kilometres per hour.

Average speed equal distances

For two equal distances covered at speeds a and b, average speed is 2ab/(a + b), the harmonic mean, not (a + b)/2.

Relative speed rule

When moving in the same direction, relative speed is the difference; when moving in opposite directions, it is the sum.

Train crossing a platform

A train crossing a pole covers its own length; crossing a platform covers train length plus platform length, at the train's speed.

Front-end estimation

Round each number to one or two significant figures, then compute. 497 × 21 ≈ 500 × 20 = 10,000, enough to pick the closest choice.

Square root bracketing

If a² < n < b², then a < √n < b. Use nearby perfect squares to bracket the square root before estimating further.

Rule of 70

Doubling time in periods approximately equals 70 divided by the percentage growth rate per period. At 7% growth, doubling takes about 10 periods.

Benchmark fractions

Useful approximations: 1/3 ≈ 0.333, 1/6 ≈ 0.167, 1/7 ≈ 0.143, 1/9 ≈ 0.111, 1/11 ≈ 0.091. Convert fractions to decimals quickly.