Thinking Skills (9694) | Organise information

Welcome to the Problem-Solving Toolkit!

Hello! You've just started one of the most crucial parts of Thinking Skills: Problem Solving. Before you can solve a complex problem, you must first understand and manage the pile of information you are given. Think of this chapter, Organise Information, as learning how to unpack a giant box of LEGOs before you build the spaceship.

If you find problem-solving tricky, don't worry! This section is all about creating structure and clarity, which makes everything else much easier. We will focus on two key areas:

1. Handling information in different formats (text, tables, diagrams).
2. Understanding the logical connections and rules within that information.

1.1 Understanding and Extracting Information

A typical Thinking Skills problem scenario throws a lot of different facts at you. Your first job is to handle this diverse data efficiently.

A. Information in Various Forms

You need to be comfortable interpreting data presented in three main ways:

• Text: Paragraphs describing the scenario, conditions, or rules. This often hides the most crucial constraints.
• Tables: Structured data, often numerical (e.g., prices, schedules, distances). Tables are excellent for quick comparison.
• Diagrams: Visual representations (e.g., maps, flowcharts, graphs, floor plans). Diagrams show relationships spatially or sequentially.

Quick Tip: The Three-Step Read

When you encounter stimulus material, read it three times:

1. First Read: Get the general context (What is the scenario about?).
2. Second Read: Highlight or underline numerical data and specific constraints (What are the costs? What are the limits?).
3. Third Read: Link the different forms (How does the rule in the text affect the values in the table?).

B. Extracting Relevant Information (The Filter)

The syllabus requires you to extract the information that is relevant to the problem to be solved. This is the difference between an efficient problem solver and one who gets stuck.

Analogy: Imagine you are making a sandwich. You don't need the frying pan, the oven, or the dog food. You only need the bread, filling, and knife.

How to Filter Information:

1. Identify the Question Goal: What exactly are you being asked to find? (e.g., Find the minimum cost, or Find the longest travel time).
2. Look at the information and ask: "Does this fact help me calculate or find the goal?"
3. Ignore information that is merely descriptive or relates to irrelevant parameters.

Common Mistake to Avoid: Assuming every number or fact given in the stimulus material must be used. Sometimes, there is distracting "noise" designed to test your filtering skills.

C. Extracting Data from Related Data Sets

Often, the answer doesn't come from one source alone. You need to combine data from related data sets.

Example: You are booking a trip.

• Data Set 1 (Table): Train Timetable (Departure/Arrival times).
• Data Set 2 (Text): Local Transport Rules (Buses only run between 10:00 and 18:00).
• Data Set 3 (Diagram): Map (Distance between the station and the hotel).

To find the total journey time, you must pull information from all three sources: Train time + wait for bus (checking the rules) + walking time (checking the map distance).

Key Takeaway for 1.1: Problem solving begins with efficient data management. Treat the stimulus like a treasure hunt: ignore the dirt and only keep the relevant, combinable gold.

1.2 Understanding Logical Relationships

Once you have the information, you need to understand the 'logic' or the rules governing how those pieces interact. This moves beyond simple extraction into genuine analysis.

A. Understanding Descriptions of Simple Models

A simple model is a set of rules or calculations that govern a situation. They simplify reality so a problem can be solved. The syllabus highlights two main types of models:

1. Calculation Instructions based on Threshold Values

These models involve a calculation where the rule changes when a parameter (like distance, time, or quantity) passes a specific point—the threshold.

Example (The Taxi Fare Model):

• Rule 1 (Below Threshold): First 5 km cost $10. (This is the threshold: 5 km)
• Rule 2 (Above Threshold): Every kilometer after the first 5 km costs $1.50.

If you travel 8 km, you must break the calculation into two parts: $10 (for the first 5 km) + $4.50 (for the remaining 3 km at $1.50/km). You must respect the exact point where the rule changes.

2. Rules that Should Be Followed (e.g., Traffic Movement)

These models involve sequential or directional rules. They define how components interact or move.

Example (Traffic Rules):

• Vehicles approaching Junction X must turn right or proceed straight.
• Vehicles turning right must yield to vehicles proceeding straight.

These rules create constraints. If asked to model the fastest route, you must follow these rules exactly, ensuring no step violates the defined flow.

B. Identifying Necessary and Sufficient Conditions

This is a fundamental logical concept. It helps you understand exactly what is required for a conclusion to be true.

Key Terms Explained:

Necessary Condition (Must have, but not enough)

A condition that must be present for the outcome to occur, but its presence alone does not guarantee the outcome.

Analogy: To pass the exam, it is necessary that you attend the exam.

(If you don't attend, you can't pass. But attending doesn't guarantee you pass—you also need to answer the questions correctly!)

Sufficient Condition (Enough on its own, but not required)

A condition whose presence guarantees the outcome, but the outcome might be achieved another way.

Analogy: To pass the exam, scoring 100% is sufficient.

(If you score 100%, you definitely pass. But you don't need 100%—you only need 50%.)

Did you know? In problem-solving, identifying necessary conditions helps you eliminate impossible options quickly. Identifying sufficient conditions helps you confirm a successful solution.

C. Deduce Information from Summaries (Working Backwards)

This skill requires you to use processed data (like statistics or calculations) to infer details about the original, raw data.

Candidates should be able to deduce some information about the original data given a summary of some processed data.

Example:

Processed Data: "The mean (average) salary of 5 employees is $40,000."

Deduction about Original Data: This summary means the total salary paid to those 5 employees is \(5 \times \$40,000 = \$200,000\). If you know four salaries, you can deduce the missing fifth salary.

This skill is often used when dealing with simple statistical measures (mean, median, mode, percentages) which are covered in the Problem Solving section's prerequisites.