9.7 Odd-One-Out, Classification, and Logic Puzzles

Adamson University College Entrance Test AdUCET

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1 Introduction & Exam Overview

1.1 AdUCET Overview, Format, and Admission Process 1.2 Test-Taking and Time-Management Strategies

2 Chapter 2: Mathematics I — Numbers, Algebra, and Functions

2.1 Number Sense, Operations, and Fraction–Decimal–Percent Conversions 2.2 Algebra, Polynomials, and Linear/Quadratic Equations 2.3 Inequalities, Absolute Value, and Systems of Equations 2.4 Radicals, Rational Expressions, and Scientific Notation 2.5 Coordinate Geometry, Lines, and Functions

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4 Chapter 4: Mathematics III — Sequences, Proportion, and Data

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5 Chapter 5: English I — Reading Comprehension and Vocabulary

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6 Chapter 6: English II — Grammar, Usage, and Written Expression

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8 Chapter 8: General Science II — Physics and Earth Science

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9 Chapter 9: Aptitude and Abstract Reasoning

9.1 Figure Series and Pattern Progression 9.2 Matrix Reasoning and Figural Analogies 9.3 Spatial Reasoning: Rotation, Reflection, and Chirality 9.4 Paper Folding, Cube Nets, and Orthographic Views 9.5 Deductive Reasoning, Syllogisms, and Venn Diagrams 9.6 Number, Letter, and Alphanumeric Series 9.7 Odd-One-Out, Classification, and Logic Puzzles

9.7 Odd-One-Out, Classification, and Logic Puzzles

Key Takeaways Explain This Topic AI

A valid odd-one-out property must hold for exactly all but one item, so a property that splits a five-item set three against two is never the intended rule.

When two properties each isolate a different member, choose the more specific one — 'prime' outranks 'odd', so in 2, 3, 5, 7, 9 the answer is 9 and not 2.

In a logic grid, a confirmed match crosses out every remaining cell in its row and in its column, and that fact then transfers to every other sub-grid.

'Only two examinees scored higher than Nena' places Nena third from the top, and third from the bottom of seven means fifth from the top.

Seated in a circle facing the centre, a person's right-hand side runs anticlockwise as seen from above, and facing outward reverses that direction.

Last updated: August 2026

9.7 Odd-One-Out, Classification, and Logic Puzzles

Classification items look casual and are not. Every well-built odd-one-out question hides exactly one property that all but one member share, and the wrong answers are built from properties that almost work. Puzzle items go further and ask you to hold several constraints in your head at once. Both reward method over speed.

The odd-one-out method

Read every option before theorising. The first pattern that occurs to you is usually the one the examiner planted as a decoy.

Name a candidate property that at least three members clearly share.

Count. In a set of n n n items the defining property must hold for exactly n − 1 n-1 n − 1 of them. A property that splits a five-item set three against two is not the rule.

Test at least two more candidate properties before committing. If two survive and point at different members, apply the disambiguation conventions below.

Numerical classification

Criterion How to test it Sample set Odd member
Prime versus composite Look for a divisor other than 1 and itself 13, 17, 21, 29 21, since 21 = 3 x 7
Perfect square Take the square root 36, 49, 60, 81 60
Perfect cube Take the cube root 27, 64, 100, 125 100
Parity Divide by 2 14, 22, 33, 46 33
Divisibility Use the shortcut tests 24, 36, 42, 55 55, the only one not divisible by 3
Digit sum Add the digits 18, 27, 45, 52 52, whose digits total 7 rather than 9
Palindrome Read it backwards 121, 232, 245, 343 245

The divisibility shortcuts are worth memorising because they turn a slow division into a glance:

2 — the last digit is even.

3 — the digit sum is divisible by 3.

4 — the last two digits form a multiple of 4.

5 — the number ends in 0 or 5.

6 — it passes both the 2 test and the 3 test.

9 — the digit sum is divisible by 9.

11 — the alternating sum of the digits is divisible by 11.

Worked example. Which number does not belong: 34, 55, 68, 85, 102?

Parity. Even members are 34, 68 and 102; odd members are 55 and 85. That is a three-against-two split, so by step 3 the property is discarded.

Digit sums. They are 7, 10, 14, 13 and 3 — no four-against-one split.

Common factor. 34 = 17 x 2, 68 = 17 x 4, 85 = 17 x 5 and 102 = 17 x 6, but 55 = 5 x 11. Four members are multiples of 17 and one is not.

Answer: 55. Notice that the parity check, which most candidates try first, produces nothing usable — it is the counting rule in step 3 that saves you from guessing.

Verbal classification

Criterion Question to ask Sample set Odd member

Category membership Are these all the same kind of thing? Lanzones, Rambutan, Chico, Malunggay Malunggay, a leafy vegetable among fruits

Function What is each one for ? Hammer, Saw, Chisel, Nail Nail, a fastener rather than a tool

Part and whole Is one of them the whole object? Engine, Windshield, Steering wheel, Jeepney Jeepney, the vehicle itself

Origin Where does each one come from? Adobo, Sinigang, Kare-kare, Sushi Sushi, which is Japanese

Level of a hierarchy Are these at the same rank? Manila, Cebu City, Davao City, Luzon Luzon, an island among cities

Figural classification (1) equilateral (2) square (3) regular (4) circle
triangle pentagon

/\ +------+ /\ .----.

/ \ | | / \ / \
/ \ | | | | | |
/______\ +------+ \____/ \ /
'----'
straight sides 3 4 5 0
axes of symmetry 3 4 5 unlimited
made of lines lines lines curve

For figures, run through this fixed list of properties: number of sides or vertices , number of axes of line symmetry , order of rotational symmetry , open versus closed outline, convex versus concave (does any interior angle exceed 180 degrees?), curved versus straight edges, and shading or fill . In the row above, the odd figure is the circle: it is the only shape with no straight sides, and it is the only one whose axis count does not equal its side count.

When two answers both look right

Genuine ambiguity is common in poorly written practice material and rare in a properly edited examination. Three conventions resolve it.

The exactly-all-but-one rule. For guitar, violin, cello and flute, 'string instrument' holds for three of the four, so the flute is odd. A candidate might object that the violin and cello are bowed while the guitar is plucked — but 'bowed' holds for only two of four, so it cannot be the defining property.

The most-specific-property rule. When two properties each isolate a different member, choose the one satisfied by the tighter, more structured class. In 2, 3, 5, 7, 9, the property 'even' isolates 2 while the property 'prime' isolates 9. Being prime is a far more restrictive classification than mere parity, so the intended answer is 9 , and the number 2 is the planted decoy.

Meaning beats spelling. Prefer a property about what the items are over an accident of how they are written, such as letter count or first letter.

Logic-grid puzzles

A logic grid matches a set of entities against two or more attributes. Build one sub-grid for each entity-attribute pairing, use a tick for a confirmed match and a cross for an exclusion, and obey three mechanical rules:

Elimination rule. A tick in a cell forces a cross into every other cell in its row and every other cell in its column.

Last-cell rule. If a row or a column has exactly one cell left uncrossed, that cell is a tick.

Transfer rule. Facts move between sub-grids. If Bernard is in Room 201 and the Room 201 examinee takes Psychology, then Bernard takes Psychology.

Clue wording Grid action
'X is not the one who …' one cross
'The one who did A also did B' link the sub-grids; A and B belong to the same person
'Neither X nor Y is Z' two crosses in the Z column
'X is either P or Q' cross out everything in X's row except P and Q
'A ranks above B' A is not the lowest, B is not the highest, and A is not B
'A sat immediately left of B' an ordered adjacent pair; test each placement
A fully worked grid

Four applicants — Althea, Bernard, Carmela and Dario — sat the AdUCET in Rooms 201, 202, 203 and 204. Each came from a different senior high school strand (ABM, GAS, HUMSS, STEM) and each named a different target course (Accountancy, Architecture, Chemical Engineering, Psychology).

Bernard sat in Room 201.

The examinee in Room 201 named Psychology.

The examinee who named Chemical Engineering sat in Room 204.

Dario sat in a lower-numbered room than Althea, and Althea sat in a lower-numbered room than the Chemical Engineering examinee.

The STEM examinee sat in Room 201.

The HUMSS examinee named Architecture.

Carmela is not from the GAS strand.

Dario did not name Architecture.

Deduction order.

Step 1 (clues 1 and 2, transfer rule). Bernard is in Room 201, so Bernard named Psychology. Cross Psychology out for everyone else.

Step 2 (clues 3 and 4). The Chemical Engineering examinee is in Room 204, and clue 4 says Dario is below Althea, who is below Room 204. Neither Dario nor Althea can therefore occupy Room 204, and Bernard already holds 201. Carmela is in Room 204.

Step 3 (clue 3, transfer rule). Carmela named Chemical Engineering.

Step 4 (clue 4 again). Only Rooms 202 and 203 remain, and Dario is below Althea, so Dario is in 202 and Althea in 203.

Step 5 (clue 8, last-cell rule). Accountancy and Architecture are the two courses left, for Dario and Althea. Dario is barred from Architecture, so Dario named Accountancy and Althea named Architecture.

Step 6 (clue 5, transfer rule). The STEM examinee is in Room 201, which is Bernard, so Bernard is STEM.

Step 7 (clue 6, transfer rule). The HUMSS examinee named Architecture, which is Althea, so Althea is HUMSS.

Step 8 (clue 7, last-cell rule). ABM and GAS remain for Carmela and Dario, and Carmela is barred from GAS, so Carmela is ABM and Dario is GAS. Room grid after Step 4 Final solution

201 202 203 204
Althea x x V x Althea 203 Architecture HUMSS
Bernard V x x x Bernard 201 Psychology STEM
Carmela x x x V Carmela 204 Chem. Eng. ABM
Dario x V x x Dario 202 Accountancy GAS

Every clue does real work here, and clue 4 is consulted twice — once to place a strand and again to fix the room. The solution is unique. If you finish a grid with a clue that never mattered, you have almost certainly made an error somewhere.

Seating arrangements

Draw the seats before you read the clues a second time, and place the absolute clues first ('at the extreme left', 'exactly in the middle of five'). Only then apply the relative clues.

Worked example. Ana, Bea, Carlo, Dina and Elmo occupy seats 1 to 5 from left to right. Carlo sits in seat 3. Elmo sits immediately to Carlo's right. Bea sits immediately to Ana's right. Dina sits at one end. From clue 2, Elmo takes seat 4. Seats 1, 2 and 5 remain, and the only adjacent pair among them is 1 and 2, so Ana takes seat 1 and Bea seat 2. Dina therefore takes seat 5, which is indeed an end. Order: Ana, Bea, Carlo, Elmo, Dina.

For circular arrangements, fix the facing convention before placing anyone. Seated facing the centre , a person's right-hand side runs anticlockwise as seen from above; seated facing outward , it runs clockwise. Getting this backwards inverts the whole answer.

Ranking puzzles

Collapse every clue into one chain of inequalities. Five examinees — Aira, Ben, Cielo, Diego and Elena. Elena scored higher than Diego; Diego scored higher than Aira; Ben scored lower than Aira; Cielo scored lowest. The chain reads Elena > Diego > Aira > Ben > Cielo, so the third-highest scorer is Aira .

Two phrasings trip candidates constantly. 'Only two examinees scored higher than Nena' puts Nena third from the top, not second. And if Nena is third from the bottom of seven, she is fifth from the top, because position from the top equals 7 − 3 + 1 7 - 3 + 1 7 − 3 + 1 .

Blood-relation puzzles

Draw a small family tree and collapse each phrase from the inside out. The key move is recognising self-references.

Worked example. Rafael, a man, said: 'Teresa's father is the only son of my father.' Work inward. 'The only son of my father' can only be Rafael himself, since Rafael is male and his father has no other son. So Teresa's father is Rafael, which makes Rafael the father of Teresa .

A second pattern: Liway, a woman, introduced a man by saying 'his wife is the only daughter of my mother'. Liway's mother's only daughter is Liway, so the man's wife is Liway and he is Liway's husband .

Common traps

Locking onto the first shared property you notice instead of counting how many members it covers.

Accepting a three-against-two split as the answer.

Forgetting to propagate a confirmed match across both the row and the column, and then into the other sub-grids.

Reading 'to the right of' as 'immediately to the right of'.

Assuming a gender in a blood-relation item that the wording never supplies.

Answering a ranking item by counting from the wrong end of the list.