Timed Mixed Logical Reasoning ACET Reviewer: Lesson and Practice

TEACHER ABI ACET LOGICAL REASONING

Timed Mixed Logical Reasoning

Apply the complete reasoning pathway under time pressure: read precisely, eliminate invalid moves, and keep moving.

27 original questions12 minutes9 competenciesAutomatic scoring

12:00

0 of 27 answered

FINAL REVIEWER

This set combines the entire Logical Reasoning series

Unlike the earlier competency reviewers, this final set removes most scaffolding. The questions shift rapidly among conclusions, conditions, quantifiers, truth, deductions, definitions, and counterexamples.

ACET pacing target: about 27 seconds per question. Answer the clear items first, skip costly items, and return through the jump buttons.

BEFORE YOU BEGIN

Give yourself one uninterrupted 12-minute attempt

1. The timer starts immediately when you press the button.
2. You may skip any question and return using the numbered navigation.
3. Submitting with unanswered items requires confirmation. At 0:00, the set submits automatically.

JUMP NAVIGATION

YOUR RESULT

Timed Logical Reasoning Report

Items to review

QUICK ANSWERS

Timed Logical Reasoning FAQ

Should I solve every item in order?

No. Under a tight limit, collect the fast points first and return to questions requiring several logical steps.

What if two answers seem defensible?

Choose only what follows from the exact premises. Do not add ordinary-world assumptions unless the item states them.

What score shows readiness?

Use both score and completion. A strong untimed score with many unanswered timed items still shows a pacing gap.

Should I memorize answer patterns?

No. The answer positions are balanced for quality control, but the actual ACET will not follow a dependable letter pattern.

NEED A STUDY PLAN?

Use the competency breakdown, not only the total

Return to the reviewer for the weakest competency, then repeat a fresh timed mixed set after targeted practice.

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Previous: Counterexamples and Flexible Reasoning ACET Student Hub Diagnostic

ACET Student Hub: Diagnostic, Tracker and Free Resources

BY TEACHER ABI

ACETSTUDENT HUB

Your preparation home base for the free diagnostic, coverage, competency reviewers, progress, timed practice, and eventual full simulations.

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YOUR ACET PATH

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What should you study today?

Choose your testing schedule and the time and energy you genuinely have today. If a complete diagnostic is saved on this browser, the planner prioritizes your lowest-scoring section.

My ACET testing scheduleMetro Manila - September 19, 2026Metro Manila - September 20, 2026Provincial Testing Centers - September 26, 2026Provincial Testing Centers - September 27, 2026Time I actually have today30 minutes45 minutes1 hour1.5 hours2 hours3 hoursToday feelsNormalLow-energy dayI can focus deeply

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MY READINESS RESULT

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Seven timed sections measure knowledge gaps, pacing, accuracy, and test endurance. Progress completed on this browser appears below.

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NOT COMPLETEDLanguage Proficiency

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NOT COMPLETEDLogical Reasoning

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NOT COMPLETEDAbstract Reasoning

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NOT COMPLETEDReading Comprehension

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Recommended first step: Take the diagnostic.

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Your next preparation step

This recommendation uses the section results saved by the diagnostic on this browser. It does not reveal the answer key or individual mistakes.

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COMPETENCY REVIEWERS

Logical Reasoning learning path

Recommended route: Diagnostic → individual lessons → timed mixed reviewer → retest. Work in order if Logical Reasoning is unfamiliar, or begin with the competency identified by your diagnostic.

1

Statements and ConclusionsFoundation

OPEN2

Conditionals: if, only if, and unlessCore

OPEN3

Necessary and Sufficient ConditionsCore

OPEN4

Certainty LevelsCore

OPEN5

Syllogisms and QuantifiersCore

OPEN6

Logical Connectives and TruthCore

OPEN7

Valid and Invalid DeductionsStretch

OPEN8

Types of DefinitionsACET-specific

OPEN9

Counterexamples and Flexible ReasoningTransfer

OPEN10

Timed Mixed Logical ReasoningTimed application

OPEN

All ten Logical Reasoning reviewers are now available. Reviewer progress is stored on the browser used to complete each lesson.

ACET RESOURCES

Choose the resource that matches your stage

AVAILABLE

Readiness Diagnostic

Identify broad section weaknesses and pacing problems.

Open diagnostic

COMING NEXT

ACET Coverage Guide

See the complete preparation map, including skills not sampled by one diagnostic.

Link will be added after publication.

IN DEVELOPMENT

Full ACET Simulation

Test readiness under an exam-like sequence after targeted review.

Use after the reviewer pathway.

USE THE HUB WELL

Three rules for useful preparation

Do not review everything equally

Start with the lowest section or a competency you cannot yet explain.

Learn before timing

Build accuracy with worked examples before attempting ACET-speed sets.

Verify with fresh questions

Memorizing one answer set is not mastery. Use a fresh check after review.

QUICK ANSWERS

ACET Student Hub FAQ

Is this an official Ateneo resource?

No. It is an independent Teacher Abi preparation system based on available coverage evidence, supplied reviewers, and original practice materials.

Should I begin with the diagnostic?

Yes, unless you already know the exact competency you need. The diagnostic helps prevent unfocused review.

Why are some resources marked coming soon?

The hub is being published first to establish one permanent navigation page. Reviewer and coverage links will be activated as those pages are completed.

Where is my progress stored?

Diagnostic and reviewer progress are stored in the browser used to complete them. Clearing browser data or changing devices may remove that local progress.

Does completing a reviewer mean I am ready for the ACET?

It verifies one competency only. Readiness also requires coverage, speed, endurance, and performance on mixed timed practice.

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Counterexamples and Flexible Reasoning ACET Reviewer: Lesson and Practice

TEACHER ABI ACET LOGICAL REASONING

Counterexamples and Flexible Reasoning

Test sweeping claims, revise assumptions, and choose the conclusion that still works when the situation changes.

One focused competency27 original questionsProgressive difficultyACET-style transfer

LessonMethodExamplesGuided TrySkill CheckPracticeMastery

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Counterexamples and Flexible Reasoning

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One possible exception can defeat a universal claim

Claim: Every student who studies with music remembers more.Possible case: Mara studies with music but remembers less because the lyrics distract her.

The case does not prove what usually happens. It does prove that the word every is too strong.

A counterexample must obey the conditions of the claim and make its conclusion false.

DO IT FAST

Use CLAIM → BUILD → CHECK → REVISE

1. CLAIM: Find the strong word: all, every, none, must, always, never.
2. BUILD: Imagine one case that satisfies the claim’s condition.
3. CHECK: Can the stated result fail in that case?
4. REVISE: If a rule changes, keep only conclusions supported by the new rule.

To challenge “All A are B,” find one A that is not B.
To challenge “No A are B,” find one thing that is both A and B.

WORKED EXAMPLES

Three ways ACET-style items test flexibility

1. Break an absolute claim

“Every rectangle has four equal sides.” A 3-by-5 rectangle is a rectangle without four equal sides.

That single valid case defeats the universal statement.

2. Protect the exact conditions

To test “Every metal conducts electricity,” a plastic ruler is useless because it is not metal.

A supposed counterexample fails if it does not meet the original condition.

3. Update after a rule changes

Old rule: Only members may enter. New rule: Members and invited guests may enter.

“Nonmembers cannot enter” is no longer safe; an invited guest may enter.

GUIDED TRY

Test the claim without arguing from habit

If a number is divisible by 4, it is even. Therefore, if a number is even, it is divisible by 4.

1. The conclusion reverses the original condition.
2. Find an even number.
3. Check whether it must also be divisible by 4.

Use 6. It is even but not divisible by 4, so it is a counterexample to the reversed claim.

COMMON TRAPS

What does not count as a counterexample?

Irrelevant case: It fails the condition before testing the result.

Another supporting example: It agrees with the claim instead of breaking it.

Unverified possibility: It merely says “maybe not” without constructing a coherent case.

Changed wording: It attacks a stronger or weaker claim than the one given.

FIVE-FORM SKILL CHECK

Do you need Foundations or Core Practice?

CHOOSE YOUR PRACTICE

Build the skill in stages

Foundations

Recognize valid counterexamples.

Core

Test rules and conditional claims.

ACET Transfer

Update conclusions under changing constraints.

FRESH MASTERY CHECK

Can you decide without the scaffolding?

Score 5/5 to verify this competency. If not, a fresh set loads.

QUICK ANSWERS

Counterexamples and Flexible Reasoning FAQ

Does one counterexample really disprove a claim?

It disproves a universal claim such as “all,” “none,” or “always.” It does not establish what happens most of the time.

Must a counterexample be real?

It must at least be logically possible under the stated rules. In mathematical items, an actual value is usually strongest.

Can an example support a claim without proving it?

Yes. Many confirming cases still cannot prove a universal statement, but one valid exception can refute it.

What is flexible reasoning?

It is the ability to update a conclusion when a premise, rule, category, or constraint changes.

What should I do when two options seem possible?

Check every word of the original condition. The correct option must satisfy the condition and produce the required logical effect.

NEED A STUDY PLAN?

Use your diagnostic result to decide what to review next

If Logical Reasoning was one of your lowest sections, master the competencies individually before attempting the timed mixed reviewer.

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Choose your next step

Next competency: Timed Mixed Logical Reasoning

Previous: Types of Definitions ACET Student Hub Diagnostic

Types of Definitions ACET Reviewer: Lesson and Practice

TEACHER ABI ACET LOGICAL REASONING

Types of Definitions

Identify what a definition is trying to do and whether it defines the term clearly and fairly.

One focused competency6 definition types27 original questionsACET-specific

LessonMethodExamplesGuided TrySkill CheckPracticeMastery

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Types of Definitions

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Definitions can report, assign, sharpen, or persuade

Compare these statements about the word screen time:

Lexical: Screen time commonly means time spent using a device with a screen.Stipulative: In this study, “screen time” means recreational device use only.Precising: Under this clinic’s rule, “excessive screen time” means more than four hours per day.Persuasive: Screen time is the mindless surrender of childhood to glowing machines.

The wording reveals the definition’s purpose. ACET-style questions ask you to identify that purpose quickly.

Ask what job the definition performs: report usage, assign usage, sharpen a vague boundary, or influence attitude.

DO IT FAST

Use DICTIONARY → DECISION → EMOTION

1. DICTIONARY: If it reports an established meaning, choose lexical.
2. DECISION: If the writer creates a meaning for the present discussion, choose stipulative. If a rule sharpens an already vague word, choose precising.
3. EMOTION: If loaded wording tries to influence approval or disapproval, choose persuasive.

reports existing use = lexical
assigns a special use = stipulative
fixes a vague boundary = precising
loads the wording = persuasive

WORKED EXAMPLES

Four ACET-relevant types to recognize

1. Lexical

“Harbor” means a sheltered place where ships may anchor.

It reports established usage, like a dictionary.

2. Stipulative

For this debate, “local resident” means anyone who has lived in the town for at least one year.

It assigns a meaning for a particular discussion.

3. Precising

For the discount, “senior citizen” means a customer aged 60 or older.

It sharpens a vague boundary for a practical rule.

4. Persuasive

A tax is the government’s greedy seizure of a worker’s earnings.

The emotional wording tries to shape attitude, not merely clarify meaning.

Closest-pair warning: Stipulative and precising definitions both set a meaning. Choose precising when the main purpose is to settle a vague cutoff for a rule, policy, or decision.

GUIDED TRY

Separate stipulative from precising

For the library’s penalty rule, “long overdue” means unreturned for more than 14 days.

1. Is this merely reporting ordinary dictionary usage? No.
2. Does the rule settle the vague boundary of long overdue? Yes.
3. Which type sharpens a vague expression for a practical decision?

Precising definition. It converts a vague expression into a definite cutoff for applying the rule.

COMMON DEFECTS

A definition can have the right purpose but poor boundaries

Too broad: “A bird is an animal that flies” includes bats and insects.

Too narrow: It excludes genuine members of the term.

Circular: “Justice is whatever is just.”

Obscure: The definition is harder than the term.

Figurative: A metaphor may inspire but fail to specify meaning.

Loaded: Emotional language disguises persuasion as description.

FIVE-FORM SKILL CHECK

Do you need Foundations or Core Practice?

CHOOSE YOUR PRACTICE

Build the skill in stages

Foundations

Recognize definition purposes.

Core

Judge breadth, clarity, and circularity.

ACET Transfer

Distinguish close types in context.

FRESH MASTERY CHECK

Can you decide without the scaffolding?

Score 5/5 to verify this competency. If not, a fresh set loads.

QUICK ANSWERS

Types of Definitions FAQ

Is a stipulative definition true or false?

It is a proposed usage for a context. Judge whether it is clear and useful, not whether it matches every dictionary.

How is precising different from stipulative?

Both set a usage, but precising narrows an already vague term for a practical purpose.

How is operational different from precising?

Operational definitions specify a test or measurement procedure; precising definitions chiefly sharpen boundaries.

Can a persuasive definition contain facts?

Yes, but its distinctive feature is emotionally slanted wording meant to influence attitude.

What is genus and difference?

A good definition often names the broader class, then the feature that distinguishes the term from other members of that class.

Can a definition be both too broad and too narrow?

Yes. It may include some outsiders while excluding some genuine members.

RELATED LOGICAL REASONING COMPETENCIES

Continue the reasoning pathway

Statements and conclusionsCertainty levelsValid deductionsCounterexamplesFlexible reasoningTimed mixed reasoning

NEED A STUDY PLAN?

Use your diagnostic result to decide what to review next

If Logical Reasoning was one of your lowest sections, complete the reviewer pathway in order and retake a timed mixed set only after the individual competencies are secure.

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REVIEW DASHBOARD

Choose your next step

Next competency: Counterexamples and Flexible Reasoning

Previous: Valid and Invalid Deductions ACET Student Hub Diagnostic

Statements and Conclusions ACET Reviewer: Lesson and Practice

TEACHER ABI ACET LOGICAL REASONING

Statements and Conclusions

Learn how to tell the difference between what the facts prove and what merely sounds believable.

One focused competency5 worked examples27 original questionsEasy to ACET-level

LessonMethodExamplesGuided TrySkill CheckPracticeMastery

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Statements and Conclusions

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A conclusion is something the facts force us to accept

Imagine that you know only these two facts:

Fact 1: Every member of the school orchestra attends the Friday rehearsal.Fact 2: Carlo is a member of the school orchestra.

Now consider this claim:

Claim: Carlo attends the Friday rehearsal.

Yes, the conclusion follows. Fact 1 covers every orchestra member. Fact 2 tells us Carlo is one of those members. The facts leave no possible case in which Carlo is an orchestra member but does not attend.

Now consider a different claim:

Claim: Carlo plays the violin.

No, the conclusion does not follow. It may be true, but neither fact identifies Carlo’s instrument. He could play the drums, flute, or cello.

The ACET distinction: “Could be true” is not the same as “must be true.” Logical reasoning questions reward only the conclusion supported by the stated facts.

DO IT FAST

Use FACT → LINK → LIMIT

1. FACT: Underline exactly what each statement tells you. Do not improve or reinterpret it.
2. LINK: Find the person, object, or group that appears in more than one statement.
3. LIMIT: Ask whether the proposed conclusion says more than the facts allow.

One-question test: “Can I invent even one situation where all the facts are true but this conclusion is false?” If yes, the conclusion does not necessarily follow.

WORKED EXAMPLES

Five forms you must recognize

1. Direct group link

Every mangrove guide has completed first-aid training.Nica is a mangrove guide.Conclusion: Nica completed first-aid training.

1. Fact: The first statement covers every mangrove guide.
2. Link: Nica belongs to that group.
3. Limit: The conclusion repeats only what group membership guarantees.

Follows.

2. The reversed conclusion

Every mangrove guide has completed first-aid training.Paolo completed first-aid training.Conclusion: Paolo is a mangrove guide.

First-aid training may be completed by teachers, athletes, nurses, and many other people. The fact gives one direction only: guide → trained.

Does not follow. The conclusion reverses the relationship.

3. “Some” means at least one

Some campus volunteers are architecture students.Conclusion: At least one architecture student is a campus volunteer.

The statement guarantees an overlap. It does not tell us how large that overlap is.

Follows.

Do not upgrade “some” to “most” or “all.”

4. Two facts that do not connect enough

All ceramic pieces in Cabinet A are insured.Some museum donations are insured.Conclusion: Some museum donations are ceramic pieces in Cabinet A.

The two facts mention insured objects, but they may refer to entirely different insured objects.

Does not follow. Sharing a description does not prove the groups overlap.

5. A valid two-step chain

All field researchers carry identification.Everyone carrying identification may enter the records room.Lea is a field researcher.Conclusion: Lea may enter the records room.

Lea is a researcher → researchers carry identification → identification permits entry.

Follows through a complete chain.

GUIDED TRY

Try one with the steps still visible

No vehicles using diesel may enter Zone C.Van R uses diesel.Does this follow? Van R may not enter Zone C.

1. Which rule applies to diesel vehicles?
2. Does Van R belong to that group?
3. Does the conclusion say anything beyond the rule?

Yes, it follows. The first fact excludes every diesel vehicle from Zone C. The second fact places Van R in that excluded group. The conclusion makes no additional claim.

COMMON TRAPS

Why believable answers can still be wrong

Reversing: All painters are artists does not mean all artists are painters.

Adding knowledge: A claim may be true in real life but absent from the facts.

Upgrading quantity: Some does not mean most; most does not mean all.

Inventing overlap: Two groups sharing one trait need not share members.

Assuming existence: “All dragons in the room are green” does not prove there are dragons.

Skipping a broken link: Every step in a chain must be supported.

FIVE-FORM SKILL CHECK

Do you need Foundations or Core Practice?

CHOOSE YOUR PRACTICE

Build the skill in stages

Foundations

Direct links and obvious overclaims.

Core

Some, no, group overlap, and short chains.

ACET Transfer

Dense wording and tempting distractors.

FRESH MASTERY CHECK

Can you decide without the scaffolding?

Score 5/5 to verify this competency. If not, a fresh set loads.

QUICK ANSWERS

Statements and Conclusions FAQ

What does “the conclusion follows” mean?

It means the stated facts make the conclusion unavoidable. If the conclusion could be false while every fact remains true, it does not necessarily follow.

Can I use facts that I know from real life?

No. Treat the statements as the complete world of the question. Outside knowledge can make an unsupported choice appear attractive.

Does “some” mean more than one?

Not in formal reasoning. “Some” guarantees at least one. It does not tell you whether the number is one, several, most, or all.

Does “all A are B” mean “all B are A”?

No. All nurses may be trained, but not everyone who is trained must be a nurse. Reversing the direction is one of the most common traps.

What should I do when two choices seem possible?

Try to build a counterexample for each choice. The required answer survives every situation permitted by the facts; a merely possible answer does not.

How fast should I answer these in the ACET?

Learn the method without rushing first. Once accurate, practise FACT → LINK → LIMIT and leave an unusually dense item for later rather than losing time on one conclusion.

RELATED LOGICAL REASONING COMPETENCIES

Continue the reasoning pathway

Conditionals: if, only if, unlessCertainty levelsSyllogisms and quantifiersNecessary and sufficient conditionsValid and invalid deductionsTimed mixed reasoning

NEED A STUDY PLAN?

Use your diagnostic result to decide what to review next

If Logical Reasoning was one of your lowest sections, complete the reviewer pathway in order and retake a timed mixed set only after the individual competencies are secure.

Ask Teacher Abi for guidance

REVIEW DASHBOARD

Choose your next step

Next competency: Conditionals: if, only if, and unless

Return to the ACET Student Hub Take or retake the diagnostic