Government Operational Research Service (GORS) Assessment Quantitative Reasoning and Aptitude Tests Syllabus

Quantitative Reasoning and Aptitude Tests syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Reasoning and Aptitude Tests in Government Operational Research Service (GORS) Assessment, not a summary of it.

1. 1

   Numerical reasoning

   4 topics

   • Working with tables, charts and graphs
     • Reading and combining multiple data sources
     • Estimation and sense-checking
   • Percentages, ratios, proportions and rates of change
   • Currency, units and rate conversions
   • Speed, accuracy and time management strategies
2. 2

   Verbal and critical reasoning

   4 topics

   • Critical reasoning: evaluating arguments and assumptions
     • Distinguishing inference, assumption and conclusion
     • Strengthening and weakening arguments
   • True / False / Cannot Say verbal reasoning
   • Reading comprehension under time pressure
   • Avoiding outside-knowledge errors
3. 3

   Logical and abstract reasoning

   4 topics

   • Pattern, sequence and series recognition
   • Deductive and inductive reasoning
   • Diagrammatic and inductive reasoning items
   • Situational judgement and prioritisation tasks
4. 4

   Quantitative problem solving for OR

   4 topics

   • Order-of-magnitude and Fermi estimation
     • Decomposing estimation problems
     • Stating and testing assumptions
   • Interpreting and manipulating formulae
   • Basic algebra, functions and equations
   • Spreadsheet-style calculation reasoning

Quantitative Reasoning and Aptitude Tests flashcards for Government Operational Research Service (GORS) Assessment

18 of 50 cards from the Quantitative Reasoning and Aptitude Tests deck — real questions with worked answers.

1. When reading a value from a line graph or bar chart, what three things must you always check first?

   The axis labels (what each axis measures), the units, and the scale/interval of the gridlines (including whether the axis starts at zero or is truncated).

2. On a stacked bar chart, how do you read the value of a single (non-bottom) segment?

   Subtract the cumulative top of the segment below it from the cumulative top of that segment: $\text{value} = \text{upper boundary} - \text{lower boundary}$. You cannot read it directly off the axis.

3. What is the formula to convert a quantity into a percentage of a total?

   $\text{percentage} = \frac{\text{part}}{\text{whole}} \times 100\%$

4. What is the percentage change formula, and what sign convention applies?

   $\text{percentage change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%$. A positive result is an increase; a negative result is a decrease.

5. How do you increase a value by a percentage in one step (a multiplier), e.g. a 15% increase?

   Multiply by $(1 + \frac{p}{100})$. For 15%: $\times 1.15$. For a 15% decrease use $\times 0.85$.

6. If a quantity rises 20% then falls 20%, what is the net change?

   A net decrease of 4%: $1.20 \times 0.80 = 0.96$, so $-4\%$. Successive percentage changes multiply, they do not add.

7. How do you reverse a percentage increase to find the original value (e.g. price is £120 after a 20% rise)?

   Divide by the multiplier: $\text{original} = \frac{120}{1.20} = 100$. Do not subtract 20% of the new value.

8. What is the difference between a percentage and a percentage point?

   A percentage point is the arithmetic difference between two percentages (e.g. 40% to 45% is +5 percentage points), whereas the percentage change is $\frac{45-40}{40}\times100 = +12.5\%$.

9. How do you divide a quantity $T$ in the ratio $a:b$?

   Total parts $= a+b$. First share $= \frac{a}{a+b}\times T$; second share $= \frac{b}{a+b}\times T$.

10. What does it mean for two quantities to be in direct proportion versus inverse proportion?

    Direct: $y = kx$ (one doubles, the other doubles; ratio constant). Inverse: $y = \frac{k}{x}$ (one doubles, the other halves; product constant).

11. What is a rate, and give the general form for combining a rate over time?

    A rate is a quantity per unit of another quantity (e.g. £/hour, km/L). General relation: $\text{quantity} = \text{rate} \times \text{base}$, e.g. $\text{output} = \text{rate} \times \text{time}$.

12. To convert an amount from currency A to currency B given the exchange rate '1 A = r B', what do you do?

    Multiply by the rate: $\text{amount in B} = \text{amount in A} \times r$. To go back from B to A, divide by $r$ (or multiply by $\frac{1}{r}$).

13. You have a chained conversion rate $1\,\text{GBP} = 1.25\,\text{USD}$ and $1\,\text{USD} = 110\,\text{JPY}$. How many JPY is 1 GBP?

    Multiply the rates: $1\times 1.25 \times 110 = 137.5\,\text{JPY}$.

14. What is the key technique for any unit conversion to avoid errors (dimensional analysis)?

    Multiply by conversion factors written as fractions equal to 1, arranged so unwanted units cancel, e.g. $90\,\frac{\text{km}}{\text{h}} \times \frac{1000\,\text{m}}{1\,\text{km}} \times \frac{1\,\text{h}}{3600\,\text{s}} = 25\,\frac{\text{m}}{\text{s}}$.

15. What is the factor to convert km/h to m/s, and vice versa?

    km/h $\to$ m/s: multiply by $\frac{1000}{3600} = \frac{5}{18}$. m/s $\to$ km/h: multiply by $\frac{18}{5} = 3.6$.

16. State the speed-distance-time relationship and its two rearrangements.

    $\text{speed} = \frac{\text{distance}}{\text{time}}$, hence $\text{distance} = \text{speed} \times \text{time}$ and $\text{time} = \frac{\text{distance}}{\text{speed}}$.

17. How do you find the average speed for a journey of several legs?

    $\text{average speed} = \frac{\text{total distance}}{\text{total time}}$. It is NOT the simple mean of the individual speeds.

18. In a timed numerical test, how should you set your per-question time budget?

    Divide total time by number of questions to get an average pace (e.g. 35 questions in 25 min $\approx$ 43 s each), then flag/skip any question exceeding it and return later if time allows.

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