Welcome to Problem Solving: Processing Information!
Hi there! Welcome to one of the most practical parts of your Thinking Skills course. In the previous chapter, you learned how to organise information. Now, we are going to learn how to process it. Think of this like cooking: organising was gathering your ingredients; processing is the actual cooking that turns those ingredients into a delicious meal (or, in our case, a solution!).
Don't worry if some of these logic problems seem like a puzzle at first. By the end of these notes, you’ll have a toolkit of tricks to handle them with confidence!
2.1 Perform Appropriate Operations
This is all about taking the data you have and doing something with it to find an answer. Sometimes the "operation" is a simple calculation, and sometimes it's following a set of rules (a model).
Calculations: Simple vs. Deduced
In your exam, you might face two types of operations:
1. The Obvious: You are told exactly what to do. For example, if you know the price of three items, you add them up to find the total.
Example: A pack of pens costs \( \$3 \) and a notebook costs \( \$5 \). Total = \( \$3 + \$5 = \$8 \).
2. The Deduced: You have to figure out the steps yourself.
Example: You need to be at school by 08:30. It takes 15 minutes to walk and 10 minutes to eat breakfast. You have to deduce that you must wake up by at least 08:05.
Applying a Model
A model is just a fancy word for a "set of rules" or a "formula." It helps us predict what will happen in a specific situation.
Analogy: A mobile phone data plan is a model. Rule: You pay \( \$10 \) per month, but if you go over 5GB, you pay an extra \( \$2 \) per GB.
Quick Tip: When applying a model, always look for thresholds (the point where the rules change). In the phone example, 5GB is the threshold.
Key Takeaway: Processing information isn't just about math; it's about identifying which rules apply and when to use them.
2.2 Identify Cases That Satisfy Criteria
Sometimes a problem has many possible answers, but only one (or a few) will fit the specific rules (criteria) given to you. Your job is to be a "filter."
Searching for Solutions
When you have a list of options, check them against the criteria one by one.
Real-world Example: You are buying a car. Your criteria are:
• Must be blue.
• Must cost less than \( \$5000 \).
• Must have 4 doors.
If a car is blue and cheap but only has 2 doors, it fails the criteria and you move to the next option.
Common Pitfalls to Avoid:
• The "Almost" Trap: Students often pick an answer that satisfies most criteria but misses one small detail.
• Counting Errors: If the question asks "how many" solutions fit, make sure you have searched through every possibility before stopping.
Did you know? This is exactly how search engines like Google work! They take your "criteria" (search terms) and scan millions of pages to find the ones that satisfy your request.
Key Takeaway: Treat criteria like a checklist. If an option fails even one "check," it's out!
2.3 Make Appropriate Deductions
To deduce means to use the information you have to discover something new that wasn't explicitly stated.
Drawing Conclusions
Deduction is like being a detective. You look at the relationships between pieces of information.
Example:
• Rule 1: All students in the chess club are in Year 12.
• Fact: Sam is in the chess club.
• Deduction: Sam is in Year 12.
Deducing from Numerical Patterns
If you see a set of numbers, look for the "why" behind the pattern.
Example: A bus arrives at 10:05, 10:20, and 10:35. You can deduce that the buses run every 15 minutes, so the next one will be at 10:50.
Necessary vs. Sufficient Conditions
This is a tricky concept, but very important!
• Necessary: Something that must be true for a result to happen. (e.g., You must have a ticket to board the plane).
• Sufficient: Something that is enough on its own to guarantee a result. (e.g., Winning the lottery is sufficient to make you a millionaire, but it's not the only way).
Mnemonic Aid: Use "N-O" for Necessary (Necessary means you can't do it withOut it) and "S-E" for Sufficient (Sufficient is Enough).
Key Takeaway: Deductions are logical "must-be-trues." If you can think of a single situation where your conclusion isn't true, then it's not a valid deduction!
Quick Review Box
1. Operations: Follow the rules/math (the "model") provided.
2. Criteria: Use a checklist to filter out wrong answers.
3. Deductions: Find the "hidden" facts using the information you already have.
Don't worry if this seems tricky at first! Problem solving is a skill that gets better with practice. Keep looking for the rules and the patterns, and you'll be a pro in no time!