1. Logical Reasoning Fundamentals 🧠
USTET Critical Thinking tests your ability to analyze arguments, identify patterns, and draw valid conclusions. Master these reasoning types!
Types of Logical Reasoning
| Type | Direction | Description | Example |
|---|---|---|---|
| Deductive | General → Specific | If premises are true, conclusion MUST be true | All mammals are warm-blooded. Dogs are mammals. ∴ Dogs are warm-blooded. |
| Inductive | Specific → General | Conclusion is PROBABLY true based on evidence | I've seen 1000 swans, all white. ∴ All swans are probably white. |
| Abductive | Effect → Best Explanation | Finding the most likely explanation for observations | The grass is wet. It probably rained. |
Syllogisms - The Core of Deductive Logic
Valid Syllogism Structure
Major Premise: All A are B
Minor Premise: C is A
Conclusion: ∴ C is B
Example: All Thomasians wear yellow. Juan is a Thomasian. ∴ Juan wears yellow.
Invalid Syllogism (Watch Out!)
All A are B
C is B
∴ C is A (INVALID!)
Example: All cats have tails. Rex has a tail. ∴ Rex is a cat. (No! Rex could be a dog!)
Common Logical Fallacies to Spot
- Ad Hominem: Attacking the person instead of the argument
- Straw Man: Misrepresenting someone's argument to make it easier to attack
- False Dilemma: Presenting only two options when more exist
- Circular Reasoning: Using the conclusion as a premise
- Hasty Generalization: Drawing broad conclusions from limited examples
- Appeal to Authority: Claiming something is true because an authority says so
2. Number & Letter Series 🔢
Pattern recognition in sequences. Find the rule, predict the next term!
Number Series Patterns
| Pattern Type | Example Series | Rule | Next Term |
|---|---|---|---|
| Arithmetic (+/- constant) | 2, 5, 8, 11, 14, ? | Add 3 | 17 |
| Geometric (×/÷ constant) | 3, 6, 12, 24, 48, ? | Multiply by 2 | 96 |
| Fibonacci-like | 1, 1, 2, 3, 5, 8, ? | Add previous two | 13 |
| Squares | 1, 4, 9, 16, 25, ? | n² | 36 |
| Cubes | 1, 8, 27, 64, 125, ? | n³ | 216 |
| Alternating | 1, 3, 2, 4, 3, 5, ? | Two interleaved sequences | 4 |
| Prime Numbers | 2, 3, 5, 7, 11, 13, ? | Next prime | 17 |
Letter Series Patterns
Remember the Alphabet Positions!
A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9, J=10, K=11, L=12, M=13
N=14, O=15, P=16, Q=17, R=18, S=19, T=20, U=21, V=22, W=23, X=24, Y=25, Z=26
Letter Series Examples
- A, C, E, G, ? → I (skip 1 letter)
- Z, X, V, T, ? → R (skip 1 backward)
- B, D, G, K, ? → P (+2, +3, +4, +5)
- AZ, BY, CX, DW, ? → EV (first +1, last -1)
Strategy
- Convert letters to numbers
- Find the differences between consecutive terms
- Look for second-level differences
- Check for alternating patterns
3. Analogies - Word Relationships 🔗
Understand the relationship between the first pair, then apply it to the second pair.
Common Analogy Types
| Relationship Type | Example | Explanation |
|---|---|---|
| Synonyms | Happy : Joyful :: Sad : ? | Melancholy (similar meaning) |
| Antonyms | Hot : Cold :: Light : ? | Dark (opposite meaning) |
| Part to Whole | Wheel : Car :: Key : ? | Piano (part of the whole) |
| Tool to User | Stethoscope : Doctor :: Gavel : ? | Judge (who uses it) |
| Object to Function | Knife : Cut :: Pen : ? | Write (what it does) |
| Category to Member | Fruit : Apple :: Animal : ? | Dog (member of category) |
| Degree/Intensity | Warm : Hot :: Cool : ? | Cold (more intense) |
| Cause and Effect | Fire : Smoke :: Rain : ? | Flood (effect of cause) |
| Place to Thing | Library : Books :: Armory : ? | Weapons (what's stored) |
Analogy Strategy
- Identify the relationship in the first pair
- Express it as a sentence: "A is to B as..."
- Apply the SAME relationship to find the answer
- Check if the relationship holds perfectly
- Watch for trick answers that have a different relationship type
4. Visual/Spatial Reasoning 👁️
Pattern recognition, figure completion, and mental manipulation of shapes.
Types of Visual Questions
Figure Series
- Look for rotation patterns (90°, 180°, etc.)
- Check for elements being added/removed
- Watch for color/shading changes
- Notice size changes (growing/shrinking)
- Track movement direction
Figure Matrices (3x3 Grid)
- Check patterns across rows
- Check patterns down columns
- Look for diagonal patterns
- Elements may combine or cancel out
- Each row/column may have all variations
Mirror Images
- Horizontal reflection: left ↔ right flips
- Vertical reflection: top ↔ bottom flips
- Letters like A, H, M, T stay same horizontally
- Watch for asymmetric elements
Paper Folding
- Visualize folds step by step
- Holes multiply with each fold
- Track hole positions through unfolding
- Symmetry appears along fold lines
Cube Visualization
Tips for Cube Questions
- Opposite faces: In an unfolded cube pattern, faces that are 2 squares apart are opposite
- Adjacent faces: Faces that share an edge in the pattern
- Cube counting: For stacked cubes, count systematically by layers
- Hidden cubes: Remember cubes can be hidden behind or underneath visible ones
5. Blood Relations & Directions 👨👩👧
Family tree problems and directional sense questions.
Blood Relations Key Terms
| Term | Male | Female |
|---|---|---|
| Parent's parent | Grandfather | Grandmother |
| Parent's sibling | Uncle | Aunt |
| Sibling's child | Nephew | Niece |
| Spouse's parent | Father-in-law | Mother-in-law |
| Parent's sibling's child | Cousin | |
Strategy for Blood Relations
- Draw a family tree diagram
- Use symbols: □ = male, ○ = female
- Connect with lines (— horizontal for siblings, | vertical for parent-child)
- Label each person mentioned
- Work step by step through the clues
Direction Sense
Cardinal Directions
N
NW | NE
W ----+---- E
SW | SE
S
- Right turn: Clockwise (N→E→S→W)
- Left turn: Counter-clockwise (N→W→S→E)
- Opposite: N↔S, E↔W, NE↔SW, NW↔SE
6. Coding-Decoding 🔐
Find the pattern used to encode words, then decode or encode new words.
Common Coding Patterns
Letter Shift Codes
- +1 shift: A→B, B→C, CAT→DBU
- -2 shift: A→Y, B→Z, DOG→BME
- Reverse alphabet: A↔Z, B↔Y, CAT→XZG
Other Coding Types
- Number codes: A=1, B=2... or A=26, B=25
- Word reversal: STUDY→YDUTS
- Symbol substitution: Each letter = unique symbol
Coding Example
Problem: If MANILA is coded as PDQMOD, how is CEBU coded?
Solution:
M→P (+3), A→D (+3), N→Q (+3), I→M (+4?)
Wait - let's check: M(13)→P(16)=+3, A(1)→D(4)=+3, N(14)→Q(17)=+3, I(9)→M(13)=+4, L(12)→O(15)=+3, A(1)→D(4)=+3
Pattern: Mostly +3, but position 4 is +4
CEBU: C(3)→F(6), E(5)→H(8), B(2)→F(6), U(21)→X(24)
Answer: FHFX (if simple +3 pattern)
7. Critical Thinking Tips & Practice 🎯
Exam Day Strategies
- Read Carefully: Understand exactly what's being asked
- Look for Patterns: Most questions follow recognizable patterns
- Draw It Out: Sketch diagrams for spatial and family tree questions
- Process of Elimination: Remove obviously wrong answers first
- Time Management: If stuck, mark and move on - come back later
- Trust Your First Instinct: Your brain often recognizes patterns subconsciously
- Stay Calm: Anxiety blocks logical thinking
Practice Questions
Q1: What comes next? 2, 6, 18, 54, ?
Pattern: Each number × 3. Answer: 54 × 3 = 162
Q2: Book : Read :: Song : ?
Relationship: Object : Action performed with it. Book is read, Song is sung/listened to
Q3: If all roses are flowers and some flowers fade quickly, what can be concluded?
Answer: Some roses may fade quickly (but not definitely - "some flowers" doesn't mean all or specifically roses)
Q4: A is B's brother. C is B's mother. D is C's father. How is A related to D?
D is C's father → D is B's grandfather → D is A's grandfather. Answer: A is D's grandson
Q5: Complete the series: Z, Y, W, T, P, ?
Differences: -1, -2, -3, -4, -5. Z(26)→Y(25)→W(23)→T(20)→P(16)→? = 16-5 = 11 = K