BFP Entrance Exam Analytical Ability — Logical ReasoningExam Answer Templates

Marks

3

Topic

Types of Logical Reasoning

Difficulty

easy

Template Id

T1

Examiner Tip

Always provide concrete examples to illustrate abstract logical concepts - this shows deeper understanding

Model Answer

Logical reasoning is the process of using a given set of facts or premises to deduce other facts by reasoning logically and drawing valid conclusions. Deductive reasoning starts with general statements (premises) to reach specific conclusions. If the premises are true, the conclusion must be true. It follows a 'top-down' approach. Example: All mammals have hearts. Dogs are mammals. Therefore, dogs have hearts. Inductive reasoning starts from specific observations to form broad generalizations. The conclusion is probably supported by the premises but not guaranteed to be true. It follows a 'bottom-up' approach. Example: Most observed swans are white. Therefore, all swans are probably white.

Question Type

short_answer

Answer Structure

• Line 1: Define logical reasoning [1 mark]
• Lines 2-3: Define deductive reasoning with example [1 mark]
• Lines 4-5: Define inductive reasoning with example [1 mark]

Scoring Breakdown

Common Mark Deductions

• Confusing deductive and inductive
• Missing examples
• Incorrect use of terminology
• Not explaining the direction of reasoning

Key Phrases To Include

• logical reasoning
• deductive
• inductive
• premises
• conclusion
• top-down
• bottom-up
• general to specific
• specific to general

Marks

2

Topic

Argument Analysis

Difficulty

medium

Template Id

T2

Examiner Tip

Distinguish between validity (logical structure) and truth (factual accuracy of premises)

Model Answer

This is a valid deductive argument following the categorical syllogism format. Premise 1: All Filipinos are Asians (major premise) Premise 2: Maria is a Filipino (minor premise) Conclusion: Therefore, Maria is an Asian The argument is VALID because if both premises are true, the conclusion must necessarily be true. The logical structure follows the pattern: All A are B, X is A, therefore X is B.

Question Type

short_answer

Answer Structure

• Line 1: Identify argument type and validity [1 mark]
• Lines 2-4: Break down premises and conclusion with logical analysis [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not identifying argument type
• Confusing validity with truth
• Missing logical structure analysis

Key Phrases To Include

• valid
• deductive argument
• categorical syllogism
• premises
• conclusion
• necessarily true

Marks

5

Topic

Venn Diagrams and Set Logic

Difficulty

medium

Template Id

T3

Examiner Tip

Always explain what each part of your Venn diagram represents and how the relationships lead to your conclusion

Model Answer

Let me analyze this using Venn diagrams: Given statements: 1. Some students are athletes 2. All athletes are disciplined [Venn Diagram Analysis] Set S = Students, Set A = Athletes, Set D = Disciplined people From statement 1: 'Some students are athletes' means the circles S and A overlap partially. From statement 2: 'All athletes are disciplined' means circle A is completely inside circle D. Combining both diagrams: The overlapping portion of S and A (students who are athletes) must be inside circle D (disciplined people). Conclusion: Some students are disciplined. This conclusion is valid because the students who are also athletes must be disciplined (from premise 2), so at least some students have the disciplined property.

Question Type

diagram_based

Answer Structure

• Line 1: State the approach using Venn diagrams [1 mark]
• Lines 2-3: Identify and list given statements [1 mark]
• Lines 4-6: Draw and explain individual Venn relationships [1 mark]
• Lines 7-8: Combine diagrams and show logical connection [1 mark]
• Lines 9-10: State valid conclusion with justification [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incorrect Venn diagram interpretation
• Missing diagram analysis
• Invalid conclusion
• Not showing logical connections

Key Phrases To Include

• Venn diagram
• some students
• all athletes
• overlapping
• completely inside
• valid conclusion

Marks

1

Topic

Basic Logical Concepts

Difficulty

easy

Template Id

T4

Examiner Tip

Keep 1-mark answers concise but complete - include all essential elements

Model Answer

A syllogism is a form of logical reasoning that studies two premises to make a logical conclusion.

Question Type

very_short_answer

Answer Structure

• Single line: Complete definition of syllogism [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incomplete definition
• Confusing with other logical terms
• Not mentioning premises or conclusion

Key Phrases To Include

• syllogism
• two premises
• logical conclusion

Marks

3

Topic

Ordering and Sequencing

Difficulty

medium

Template Id

T5

Examiner Tip

Use symbols (>, <) or diagrams to make relationships visually clear

Model Answer

Let me solve this step by step using height ordering: Given information: - Ana is taller than Ben but shorter than Carlo: Carlo > Ana > Ben - Diana is shorter than Ben but taller than Emma: Ben > Diana > Emma Combining the information: Carlo > Ana > Ben > Diana > Emma Therefore: Tallest person: Carlo Shortest person: Emma

Question Type

short_answer

Answer Structure

• Line 1: State systematic approach [0.5 marks]
• Lines 2-4: Break down given relationships [1 mark]
• Line 5: Combine into complete order [1 mark]
• Lines 6-7: State final answers clearly [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Incorrect ordering
• Missing intermediate steps
• Not clearly stating final answers

Key Phrases To Include

• step by step
• height ordering
• combining
• tallest
• shortest

Marks

2

Topic

Types of Syllogisms

Difficulty

medium

Template Id

T6

Examiner Tip

Always explain why it's that specific type of syllogism by showing the characteristic pattern

Model Answer

This is a disjunctive syllogism. Structure analysis: - Major premise: The book is either fiction or non-fiction (presents two exclusive options) - Minor premise: The book is not fiction (eliminates one option) - Conclusion: Therefore, the book is non-fiction (accepts the remaining option) The argument follows the format: A is either B or C, A is not C, therefore A is B.

Question Type

short_answer

Answer Structure

• Line 1: Identify the syllogism type [1 mark]
• Lines 2-5: Analyze structure and format [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incorrect syllogism type
• Missing structural analysis
• Not explaining the logical process

Key Phrases To Include

• disjunctive syllogism
• exclusive options
• eliminates one option
• major premise
• minor premise

Marks

1

Topic

Inductive Reasoning

Difficulty

easy

Template Id

T7

Examiner Tip

For True/False questions, always add a brief explanation to ensure full marks

Model Answer

False. In inductive reasoning, the conclusion is probable but not certain.

Question Type

very_short_answer

Answer Structure

• Single line: State False with brief explanation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Answering True
• Not providing explanation
• Confusing with deductive reasoning

Key Phrases To Include

• False
• probable
• not certain

Marks

3

Topic

Conditional Syllogisms

Difficulty

hard

Template Id

T8

Examiner Tip

Learn to recognize the four main conditional argument forms: modus ponens, modus tollens, affirming consequent, denying antecedent

Model Answer

This is a valid conditional syllogism using the modus tollens form. Structure: - Major premise: If it rains, then the ground gets wet (If P, then Q) - Minor premise: The ground is not wet (not Q) - Conclusion: Therefore, it did not rain (not P) This follows the valid logical pattern: If P then Q, not Q, therefore not P. The argument is logically sound because when the consequent is false, the antecedent must also be false to maintain the conditional relationship.

Question Type

short_answer

Answer Structure

• Line 1: Identify as conditional syllogism and modus tollens [1 mark]
• Lines 2-4: Break down the logical structure [1 mark]
• Lines 5-6: Explain validity and logical pattern [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not recognizing modus tollens
• Incorrect logical analysis
• Missing validity explanation

Key Phrases To Include

• conditional syllogism
• modus tollens
• antecedent
• consequent
• valid logical pattern

Marks

5

Topic

Complex Ordering Problems

Difficulty

hard

Template Id

T9

Examiner Tip

Always verify your final answer by checking it against each original constraint - this prevents careless errors

Model Answer

Let me solve this step by step using the given constraints: Given constraints: 1. A is not first or last 2. B is immediately before C 3. D is at one end 4. E is between A and C Analysis: From constraint 3: D is either first or last position From constraint 2: B and C are consecutive with B before C (BC pattern) From constraint 4: The order involving A, E, C is A-E-C From constraint 1: A cannot be in position 1 or 5 Testing possibilities: If D is first: D _ _ _ _ We need to fit A-E-C pattern and B immediately before C Since B comes before C, and E is between A and C, we have A-E-B-C With A not first: D-A-E-B-C Verification: - A is not first or last ✓ (position 2) - B is immediately before C ✓ (positions 4-5) - D is at one end ✓ (position 1) - E is between A and C ✓ (position 3) Therefore, the order is: D-A-E-B-C

Question Type

long_answer

Answer Structure

• Line 1: State systematic approach [0.5 marks]
• Lines 2-5: List all constraints clearly [1 mark]
• Lines 6-9: Analyze constraints and their implications [1.5 marks]
• Lines 10-12: Test possible arrangements [1 mark]
• Lines 13-16: Verify solution against all constraints [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not listing all constraints
• Random guessing without systematic approach
• Incorrect final arrangement
• Not verifying solution

Key Phrases To Include

• step by step
• constraints
• systematic analysis
• testing possibilities
• verification

Marks

2

Topic

Argument Evaluation

Difficulty

medium

Template Id

T10

Examiner Tip

Remember: validity is about form, soundness is about form plus content

Model Answer

Validity refers to the logical structure of an argument - whether the conclusion follows logically from the premises. An argument is valid if the conclusion must be true when the premises are true, regardless of whether the premises are actually true. Soundness requires both validity and true premises. A sound argument has correct logical structure AND all premises are factually true, guaranteeing a true conclusion.

Question Type

short_answer

Answer Structure

• Lines 1-2: Define validity with focus on logical structure [1 mark]
• Lines 3-4: Define soundness as validity plus true premises [1 mark]

Scoring Breakdown

Common Mark Deductions

• Confusing validity with truth
• Not distinguishing between the two concepts
• Missing the requirement of true premises for soundness

Key Phrases To Include

• validity
• soundness
• logical structure
• true premises
• conclusion follows logically

Marks

1

Topic

Venn Diagram Basics

Difficulty

easy

Template Id

T11

Examiner Tip

Visualize the diagram in your mind - 'All A are B' means every A is also a B

Model Answer

Circle A is completely inside circle B, showing set A is a subset of set B.

Question Type

very_short_answer

Answer Structure

• Single line: Describe the Venn diagram representation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Describing overlap instead of inclusion
• Using incorrect terminology
• Reversing the relationship

Key Phrases To Include

• circle A inside circle B
• subset
• completely inside

Marks

2

Topic

Conditional Arguments

Difficulty

medium

Template Id

T12

Examiner Tip

Modus tollens is one of the most common valid argument forms - memorize its pattern

Model Answer

Using modus tollens (denying the consequent): If P (John studies hard) then Q (he will pass) Not Q (John did not pass) Therefore, not P (John did not study hard) Conclusion: John did not study hard. This is a valid logical inference.

Question Type

short_answer

Answer Structure

• Lines 1-3: Apply modus tollens structure [1 mark]
• Line 4: State conclusion and validity [1 mark]

Scoring Breakdown

Common Mark Deductions

• Using incorrect logical form
• Invalid conclusion
• Not recognizing modus tollens

Key Phrases To Include

• modus tollens
• denying the consequent
• valid logical inference

Marks

3

Topic

Truth Tables and Validity

Difficulty

hard

Template Id

T13

Examiner Tip

Truth tables must be systematic - cover all possible combinations of truth values

Model Answer

This represents modus ponens. Truth table: P | Q | If P then Q | Premise P | Conclusion Q | Valid? T | T | T | T | T | ✓ T | F | F | T | F | N/A F | T | T | F | T | N/A F | F | T | F | F | N/A The argument is valid because in all cases where both premises are true (row 1), the conclusion is also true.

Question Type

short_answer

Answer Structure

• Line 1: Identify as modus ponens [0.5 marks]
• Lines 2-6: Create complete truth table [1.5 marks]
• Line 7: Explain validity based on truth table [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incorrect truth table
• Missing analysis
• Wrong validity conclusion

Key Phrases To Include

• modus ponens
• truth table
• valid
• premises true
• conclusion true

Marks

2

Topic

Categorical Statements

Difficulty

easy

Template Id

T14

Examiner Tip

Use everyday examples that clearly illustrate the difference between 'all' and 'some'

Model Answer

'All A are B' means every member of set A is also in set B (universal statement). Example: All birds have wings - every single bird has wings without exception. 'Some A are B' means at least one but not necessarily all members of A are in B (particular statement). Example: Some students are athletes - at least one student is an athlete, but not all students are athletes.

Question Type

short_answer

Answer Structure

• Lines 1-2: Define 'All A are B' with example [1 mark]
• Lines 3-4: Define 'Some A are B' with example [1 mark]

Scoring Breakdown

Common Mark Deductions

• Confusing universal and particular
• Poor examples
• Missing key distinctions

Key Phrases To Include

• universal statement
• particular statement
• every member
• at least one
• not necessarily all

Marks

4

Topic

Sequential Ordering

Difficulty

medium

Template Id

T15

Examiner Tip

Draw a simple line or use position numbers (1,2,3,4,5) to visualize the arrangement clearly

Model Answer

Let me solve this using positional analysis: Given information: 1. A is to the right of B but left of E: B < A < E 2. C is to the left of B: C < B 3. D is at the rightmost position: D is at position 5 Step-by-step deduction: From clues 1 and 2: C < B < A < E From clue 3: D is at position 5 Since we have 5 positions and D occupies position 5: Positions: _ _ _ _ D From C < B < A < E, these four people occupy positions 1-4: C B A E D Verification: - A is to the right of B ✓ (position 3 > position 2) - A is to the left of E ✓ (position 3 < position 4) - C is to the left of B ✓ (position 1 < position 2) - D is at rightmost position ✓ (position 5) Final arrangement: C-B-A-E-D

Question Type

long_answer

Answer Structure

• Line 1: State systematic approach [0.5 marks]
• Lines 2-4: List and interpret given information [1 mark]
• Lines 5-7: Apply step-by-step logical deduction [1 mark]
• Lines 8-9: Determine positions systematically [1 mark]
• Lines 10-13: Verify solution against all constraints [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Random arrangement without logic
• Not verifying against constraints
• Incorrect interpretation of positional relationships

Key Phrases To Include

• positional analysis
• step-by-step deduction
• verification
• systematic approach