Civil Service Numerical Reasoning Test Word Problems and Applied Reasoning Syllabus

Word Problems and Applied Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Word Problems and Applied Reasoning in Civil Service Numerical Reasoning Test, not a summary of it.

1. 1

   Translating Words into Calculations

   3 topics

   • Identifying the operation required
     • Keyword cues (per, total, difference, share)
     • Stripping out irrelevant information
   • Multi-step problem structuring
     • Breaking a problem into ordered steps
     • Tracking units through each step
   • Setting up and solving equations
     • Forming a simple linear equation from text
2. 2

   Civil Service and Financial Contexts

   4 topics

   • Budgets and expenditure
     • Allocating and reconciling departmental spend
     • Under- and over-spend against budget
   • Cost-benefit and value-for-money sums
     • Cost per outcome comparisons
   • Targets, KPIs and performance figures
     • Percentage of target met
   • Tax, VAT and deductions
     • Calculating and removing VAT
     • Gross-to-net adjustments
3. 3

   Time, Scheduling and Logistics

   3 topics

   • Time and date calculations
     • Elapsed time across hours and days
     • 24-hour clock and time zones
   • Rotas, capacity and resource planning
     • Staff-hours to complete a workload
   • Distance, cost and journey planning
     • Comparing route or option costs

Word Problems and Applied Reasoning flashcards for Civil Service Numerical Reasoning Test

25 of 50 cards from the Word Problems and Applied Reasoning deck — real questions with worked answers.

1. In word problems, which keywords typically signal that you should ADD?

   Words like 'total', 'sum', 'combined', 'altogether', 'increased by', 'more than' and 'plus' signal addition.

2. In word problems, which keywords typically signal that you should SUBTRACT?

   Words like 'difference', 'less than', 'fewer', 'decreased by', 'reduced', 'remaining' and 'how many more' signal subtraction.

3. In word problems, which keywords typically signal MULTIPLICATION?

   Words like 'product', 'of', 'times', 'each', 'per', 'rate of' and 'twice/double/triple' signal multiplication.

4. In word problems, which keywords typically signal DIVISION?

   Words like 'per', 'share equally', 'split', 'distribute', 'quotient', 'ratio', 'average' and 'how many fit into' signal division.

5. What is the recommended four-step process for tackling any numerical word problem?

   1) Read and identify what is asked; 2) Extract the relevant numbers and units; 3) Choose the operation(s) and set up the calculation; 4) Compute, then sanity-check the answer and units.

6. When a word problem requires several operations, what does the order of operations (BIDMAS/BODMAS) state?

   Brackets, Indices (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

7. What is the key technique for 'multi-step problem structuring' in numerical reasoning?

   Break the problem into a sequence of single-step sub-calculations, solve each in order, and carry intermediate results forward (do not round until the final step).

8. In a problem where 'the answer to one part feeds into the next', what should you avoid doing with intermediate values?

   Avoid rounding intermediate values; keep full precision and only round the final answer, otherwise rounding errors compound.

9. How do you translate the phrase 'a number increased by 7 equals 22' into an equation, and solve it?

   Let the number be $x$: $x + 7 = 22$, so $x = 22 - 7 = 15$.

10. What is the general method for solving a one-step linear equation such as $5x = 40$?

    Apply the inverse operation to both sides. Divide both sides by 5: $x = \frac{40}{5} = 8$.

11. Solve the two-step equation $3x + 4 = 19$.

    Subtract 4: $3x = 15$. Divide by 3: $x = 5$.

12. How do you set up an equation for: 'A taxi charges a £3 base fare plus £2 per mile; the total was £17. How many miles?'

    Let $m$ be miles: $3 + 2m = 17$, so $2m = 14$ and $m = 7$ miles.

13. To find an unknown that appears on both sides, e.g. $4x + 2 = 2x + 10$, what is the first step?

    Collect like terms: subtract $2x$ from both sides to get $2x + 2 = 10$, then $2x = 8$, $x = 4$.

14. What is the formula for a percentage of an amount, e.g. finding 15% of £240?

    $\text{Amount} \times \frac{\%}{100}$. So $240 \times \frac{15}{100} = \pounds 36$.

15. In budgeting, how do you calculate the remaining (unspent) budget?

    $\text{Remaining} = \text{Total budget} - \text{Total expenditure}$ (sum all spending first, then subtract).

16. A department has a £50,000 budget and has spent £38,500. What percentage of the budget remains?

    Remaining $= 50000 - 38500 = \pounds 11500$. As a percentage: $\frac{11500}{50000} \times 100 = 23\%$.

17. What does it mean for a budget to be 'overspent' and how is the overspend calculated?

    Overspend means expenditure exceeds the budget. Overspend $= \text{Expenditure} - \text{Budget}$ (a positive value indicates the amount over).

18. How do you calculate the percentage of a budget allocated to one category?

    $\frac{\text{Category amount}}{\text{Total budget}} \times 100$.

19. In a cost-benefit calculation, what is the formula for Net Benefit?

    $\text{Net Benefit} = \text{Total Benefits} - \text{Total Costs}$.

20. What is the Benefit-Cost Ratio (BCR) and how is it interpreted?

    $\text{BCR} = \frac{\text{Total Benefits}}{\text{Total Costs}}$. A BCR $> 1$ means benefits outweigh costs (good value); BCR $< 1$ means costs exceed benefits.

21. For 'value for money' comparisons between two products, what is the standard approach?

    Reduce each to a unit cost (cost per item, per gram, per litre, etc.) using $\frac{\text{Price}}{\text{Quantity}}$, then the lower unit cost is better value.

22. Product A costs £6 for 500 g; Product B costs £10 for 1 kg. Which is better value per 100 g?

    A: $\frac{600\text{p}}{500\text{g}} = 1.2$p/g $= \pounds 1.20$ per 100 g. B: $\frac{1000\text{p}}{1000\text{g}} = 1.0$p/g $= \pounds 1.00$ per 100 g. B is better value.

23. What is the formula for percentage savings when a price is reduced?

    $\frac{\text{Original} - \text{New}}{\text{Original}} \times 100$.

24. How do you calculate the payback period for an investment with even annual savings?

    $\text{Payback period} = \frac{\text{Initial cost}}{\text{Annual saving}}$, giving the number of years to recover the cost.

25. What is a KPI (Key Performance Indicator)?

    A measurable value that shows how effectively an organisation is achieving a key objective or target.

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