Number Puzzles
Money, time, ratio, percentages and multi-step word problems — the numerical half of an 11+ paper. Rated as its own subject, so a reasoning score means reasoning and a numerical score means numbers.
What's covered
- Money and time: totals, change, meal deals, timetables, the cheapest way to buy something.
- Proportional reasoning: ratio, percentages, fractions and rates applied across several stated facts.
- Multi-stage problems: set overlap (both / neither), rounding up to whole units, and thresholds.
More Number Puzzles
The cinema charges £6 for a child ticket and £9 for an adult ticket. A family of 2 adults and 2 children want to watch a film. How much will the family pay in total?
- £24
- £28
- £30 ✓
- £36
Two adults cost 2 × £9 = £18 and two children cost 2 × £6 = £12, so the total is £18 + £12 = £30.
A recipe uses flour, sugar and butter in the ratio 3:2:1 by weight. Ben makes a batch using 90g of sugar. How much flour does Ben use?
- 45g
- 135g ✓
- 180g
- 270g
Sugar is 2 parts of the ratio and equals 90g, so 1 part is 45g; flour is 3 parts: 3 × 45g = 135g.
In a survey of 40 children, 25 like football, 18 like swimming, and 10 like both sports. How many children like neither sport?
- 3
- 7 ✓
- 15
- 17
The number liking at least one sport is 25 + 18 − 10 = 33, so those liking neither are 40 − 33 = 7.
Money · multi-step
A café sells a sandwich for £3.50 and a drink for £1.20. A meal deal combines one sandwich and one drink for £4.00.
How much cheaper is the meal deal than buying a sandwich and a drink separately?
- £0.50
- £0.70
- £4.70
- £1.20
- £4.00
Nicely worked out!
Buying separately costs £3.50 + £1.20 = £4.70, so the meal deal saves £4.70 - £4.00 = £0.70.
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A real question from the Numerical Reasoning bank, with the correct option highlighted in leaf-tint green — never red.
How the difficulty adapts
Number Puzzles, tuned question by question
Numerical Reasoning has its own live rating, separate from Maths and from Verbal Reasoning, so what it reports is what it measured.
Its own rating, on purpose
These questions used to sit inside Verbal Reasoning. They are arithmetic word problems, so a Verbal Reasoning score was partly measuring number work. They now rate their own subject — which is the whole reason it exists.
Difficulty is arithmetic depth
What makes one question harder than the next is the number of steps between the facts you are given and the answer — not how hard the passage is to read. One operation at the easiest level; ratio, percentages and set overlap at the hardest.
The same score you see as a parent
That rating becomes a 55–145 standardised-style score on the parent dashboard, centred on 100 like an 11+ standardised score — a useful guide, not an official result.
Every wrong option is a real mistake
The distractors are the answers a child actually reaches — adding when they should subtract, using one part of a ratio instead of three, forgetting the overlap in a survey. Getting one wrong tells you which step slipped.
One operation, then two facts combined, then money and time under a stated rule, then ratio and percentages, then several stages chained together.
The rating a typical child is expected to be secure at, by the end of each school year — about 250 points per year.