Unit 6
Identifying Sufficient Information
About this unit
Determine exactly which pieces of information are needed to answer a question — no more, no less. This unit trains precision thinking: you must understand what constitutes a complete proof and what information is truly necessary versus merely relevant.
What types of questions will you face?
- 1Given a claim about a hidden data table with some cells missing, identify which specific cells must be checked to test the claim
- 2Choose the two statements from a list that together prove a given conclusion
- 3Given a customer's requirements, identify which pieces of information are sufficient to determine if a product qualifies
- 4Find which single additional fact would be enough to determine a missing quantity
- 5Verify logical completeness — can the conclusion be reached from the given premises alone?
Skills you will build
- Understanding what "sufficient" means in a logical context vs. "related" or "helpful"
- Testing whether a combination of statements together prove a conclusion
- Reading data tables with partial information to identify the critical gaps
- Working backwards from a conclusion to determine what premises are required
- Evaluating whether given information overcounts, undercounts, or exactly meets what's needed
By the end of this unit, you will be able to
- Determine what information is logically necessary and sufficient to verify any statement
- Avoid the trap of collecting too much or too little evidence for a conclusion
- Work efficiently in logic and reasoning problems by identifying the minimum required information
- Build a strong foundation for higher-level logical and mathematical proofs
Difficulty profile
Easy difficulty (avg 2.20). Questions require careful logical thinking but are rarely tricky once you understand what "sufficient" means. Practice with the data-table style questions first.
Exam tip: Identifying Sufficient Information
For data-table questions: look at exactly what the claim says, then ask which cells you MUST know to test it. Often you need to check the "yes/yes" cell and the "yes/no" cell — and nothing else.
Sample Questions
Sufficient-information questions ask what you must know to test a claim — not what is merely helpful or related.
Claim-testing tables appear on Selective TS when an ad or statement needs evidence; they reward students who separate “nice to know” from “proves or disproves the claim.”
The examiner checks whether you can design a fair test: for each case you need to know if the treatment was used and whether the outcome happened — so you can compare like with like.
A bold claim is made (e.g. a product works in under four wipes). A table lists trials with missing answers (a), (b), (c). You pick which missing facts are essential to test the claim.
Best approach: State the claim precisely. For a fair test you usually need both “was the method used?” and “did the result occur?” on each row. Eliminate facts that do not pin down success vs failure or used vs not used.
Question
An advertisement for a window cleaning spray claimed: Spray cleans window in less than 4 wipes. Four windows were cleaned and 2 questions were asked in each case:
| Room | Was the window spray used? | Did it clean in less than 4 wipes? |
|---|---|---|
| 1 | Yes | (a) |
| 2 | (b) | Yes |
| 3 | No | (c) |
| 4 | (d) | No |
Which two of the missing answers must be known in order to test the truth of the claim in the advertisement?
- Aa and b
- Ba and d
- Cb and d
- Dc and d
Decided on your answer? Check how you went below.
Harder sufficient-information items pack the same logic into a denser trial grid — you must see which pair of facts completes the test design.
Scientific test-design questions at the end of Selective mocks are a common stretch item; the skill is identical to earlier claim tables but with more rows and traps.
You must identify the minimum set of answers that lets you check every case where the product was used and every case where it was not — without redundant or irrelevant questions.
An absolute claim (“removes every odour”) is tested on several items. Some cells show yes/no; others are blank. You choose which blanks must be filled in to evaluate the claim fairly.
Best approach: Map each item: used vs not used, outcome yes vs no. The claim needs evidence from both treated and untreated cases. Pick the two missing cells that complete that comparison — not extra detail that changes nothing.
Question
An ad claimed: "FRESH-START removes every odour." Four items were treated. To test the claim, which two answers must we know? Item 1: used? yes, removed? (a). Item 2: used? no, removed? (b). Item 3: used? (c), removed? yes. Item 4: used? (d), removed? no.
- Aa and b
- Ba and d
- Cc and d
- Db and c
Decided on your answer? Check how you went below.
Three clues about a 4-picture code sequence leave exactly two possible arrangements — and they differ only in whether Bell or Book is at position 3 or 4. You get to ask one yes/no question. Which question gives a different answer in each arrangement, letting you uniquely deduce the code?
'Which question is sufficient to determine the arrangement?' is a top-difficulty NSW Selective TS variant. It combines two skills: (1) enumerating all valid arrangements from the clues, and (2) testing each candidate question against every arrangement to see if the answers differ.
The examiner tests whether students can (a) correctly derive that only two arrangements satisfy all three clues, (b) understand that a useful question must give DIFFERENT answers in each arrangement, and (c) reject B, C, D which give identical answers across both arrangements.
Multiple clues constrain an ordering but leave two (or more) arrangements valid. Four yes/no questions are offered. Only one question has different answers across the remaining valid arrangements, making it the one that uniquely resolves the ambiguity.
Best approach: Step 1: Enumerate all valid arrangements from the clues — be systematic. Step 2: For each question option, check what answer it gives in each valid arrangement. If the same answer is given in all arrangements → not useful. If different answers → this question uniquely determines the code.
Question
The code to open a door in a computer game is a sequence of four pictures in a row. You have found the following clues about the code:
The bell is next to the book. The apple is somewhere between the bell and the cat. The book is somewhere to the right of the cat.
You have to choose one of four possible questions to ask. When the question has been answered you must deduce the code.
Which one of the following questions would allow you to deduce the code?
- AIs the apple next to the book?
- BIs the cat next to the apple?
- CIs the bell next to the cat?
- DIs the book next to the cat?
Decided on your answer? Check how you went below.
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