Thinking Skills Assessment (TSA) Problem Solving (Section 1) Syllabus

Problem Solving (Section 1) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Problem Solving (Section 1) in Thinking Skills Assessment (TSA), not a summary of it.

1. 1

   Relevant Selection

   5 topics

   • Identifying necessary information
     • Distinguishing relevant from irrelevant data in a scenario
     • Stripping away distractor figures and superfluous detail
     • Recognising which quantities the question actually requires
   • Working with tables and price lists
     • Reading multi-column tables to extract target values
     • Comparing options across rows to find a best fit
     • Handling conditional pricing, discounts and surcharges
   • Selecting from textual scenarios
     • Parsing word problems for the operative constraint
     • Ignoring narrative padding that does not affect the answer
   • Timetable and schedule problems
     • Reading bus, train and flight timetables
     • Calculating durations across changeovers and time zones
     • Choosing the earliest, cheapest or shortest route
   • Multi-source selection
     • Combining information split across two or more displays
     • Cross-referencing a key with a chart
2. 2

   Finding Procedures

   6 topics

   • Devising a method to reach a goal
     • Sequencing operations to satisfy all constraints
     • Identifying the minimum number of steps
   • Optimisation problems
     • Maximising output within a budget or resource limit
     • Minimising cost, time or waste
     • Greedy versus exhaustive trial strategies
   • Combination and packing problems
     • Bin-packing and fitting items into containers
     • Making exact totals from a set of denominations
   • Route and network procedures
     • Shortest-path reasoning on simple maps
     • Covering all nodes or edges efficiently
   • Scheduling and rota construction
     • Allocating tasks to time slots without clashes
     • Respecting precedence and dependency rules
   • Working backwards from a target
     • Reverse calculation to find a starting value
     • Reconstructing earlier states from a final outcome
3. 3

   Identifying Similarity

   4 topics

   • Recognising shared structure
     • Matching the logical form of two problems
     • Spotting that two scenarios use the same underlying rule
   • Reasoning by analogy
     • Transferring a method from a worked case to a new case
     • Detecting where an analogy breaks down
   • Equivalent representations of data
     • Translating between tables, graphs and prose
     • Recognising the same information shown two ways
   • Pattern equivalence in figures
     • Matching diagrams that encode identical relationships
     • Identifying which option mirrors a given example
4. 4

   Numerical and Spatial Reasoning Toolkit

   4 topics

   • Core arithmetic under time pressure
     • Mental estimation and rounding to eliminate options
     • Percentages, ratios and proportion
     • Rates, speed-distance-time and unit conversion
   • Interpreting charts and graphs
     • Bar charts, pie charts and line graphs
     • Reading scatter plots and trends
     • Misleading axes and scale traps
   • Spatial visualisation
     • Nets, cubes and 3D folding
     • Rotation, reflection and views from different angles
     • Tiling, overlap and area reasoning
   • Logical deduction puzzles
     • Grid logic and elimination tables
     • Ordering and ranking from clues

Problem Solving (Section 1) flashcards for Thinking Skills Assessment (TSA)

19 of 51 cards from the Problem Solving (Section 1) deck — real questions with worked answers.

1. In TSA Problem Solving, what is meant by "identifying necessary information"?

   The skill of determining exactly which pieces of given data are required to answer a question, while disregarding irrelevant or redundant information. A datum is necessary if removing it makes the question unanswerable.

2. How do you test whether a given piece of information in a problem is actually necessary?

   Cover or ignore that piece and check whether the question can still be solved. If the answer becomes impossible to determine, the information was necessary; if it can still be found, it was redundant.

3. What is the difference between "sufficient" and "necessary" information in problem solving?

   Necessary information is required to reach the answer; sufficient information is enough on its own to guarantee the answer. A set can be sufficient without every item being individually necessary, and a necessary item may not be sufficient alone.

4. When working with a price list, how do you compute the total cost of a multi-item order?

   Multiply each item's unit price by its quantity, then sum the results: $\text{Total}=\sum_{i} p_{i}\,q_{i}$, where $p_{i}$ is unit price and $q_{i}$ is quantity of item $i$. Apply any discounts or surcharges afterward.

5. In table/price-list problems, how is a percentage discount applied to a price $P$?

   Multiply by one minus the discount fraction: discounted price $=P\left(1-\dfrac{d}{100}\right)$, where $d$ is the discount percentage.

6. How do you find the cheapest option when a price list offers both individual items and bundles?

   Compute the total cost under each purchasing combination (all singles, all bundles, and mixes), including any leftover items, then compare totals and select the minimum.

7. What is the effective unit price of a "buy $n$ get 1 free" offer on an item costing $p$ each?

   You pay $np$ for $n+1$ items, so the effective unit price is $\dfrac{np}{n+1}$.

8. In a "selecting from textual scenarios" question, what is the recommended first step?

   Extract the explicit constraints stated in the passage (rules, conditions, exclusions), then test each candidate option against every constraint, eliminating any that violate one.

9. How do you handle conditional statements ("if X then Y") when selecting from a textual scenario?

   Treat them as filters: whenever the antecedent X holds, the consequent Y must hold. Eliminate options where X is true but Y is false. Note that "if X then Y" says nothing when X is false.

10. For timetable problems, how do you compute a journey's duration that crosses times like 14:50 to 15:25?

    Convert to minutes from the hour boundary or to a 24-hour minute count. From 14:50 to 15:25: 10 minutes to 15:00 plus 25 minutes = $35$ minutes total.

11. In a timetable, how do you determine whether a connection between two services is possible?

    Check that the arrival time of the first service is at or before the departure time of the second, allowing any required minimum transfer/interchange time: $t_{\text{arrive}}+t_{\text{transfer}}\le t_{\text{depart}}$.

12. How do you find the latest train someone can catch to arrive by a deadline $D$, given journey time $J$?

    They must depart no later than $D-J$. Scan the timetable for the latest departure time that is $\le D-J$ and whose arrival is $\le D$.

13. In schedule problems, what is "layover" or "dwell time" and why does it matter?

    It is the waiting time between arrival and the next departure (e.g., at an interchange or stop). It must be added to travel time when computing total journey duration and feasibility of connections.

14. What is "multi-source selection" in TSA problem solving?

    Questions requiring you to combine information drawn from two or more sources (e.g., a table plus a paragraph plus a chart) to identify the option that satisfies all sources simultaneously.

15. What is the key strategy for multi-source selection problems?

    Apply each source as an independent filter on the candidates, eliminating any option that fails any one source. The correct answer is the option (often unique) surviving all filters.

16. What does "devising a method to reach a goal" require you to identify?

    A valid sequence of allowed operations or steps that transforms the given starting state into the target/goal state, respecting all stated rules and constraints at each step.

17. In a "devise a method" puzzle with operations of given sizes, how do you reach a target amount?

    Find integers (counts of each operation) solving the equation, e.g. for jugs of $a$ and $b$ litres reaching $t$: solve $ax+by=t$ where $x,y$ are step counts (positive for adding, negative for pouring out). Solvable when $t$ is a multiple of $\gcd(a,b)$.

18. What is the general form of an optimisation problem in TSA Problem Solving?

    Find the choice that maximises or minimises an objective (e.g., cost, time, profit, quantity) subject to one or more constraints (budget, capacity, time limits).

19. What is a practical method for solving a small optimisation problem under a budget constraint?

    Enumerate feasible combinations within the constraint, compute the objective value for each, and select the best. For maximising value per cost, prioritise items with the highest value-to-cost ratio $\dfrac{v_{i}}{c_{i}}$.

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