11.2 Coding-Decoding, Classification, and Logical Reasoning
Key Takeaways
- In a Caesar letter-shift code, every letter moves the same number of places — CAT encoded with a +1 shift becomes DBU, and decoding means shifting back
- Always crack the code from the given example first: align the original and coded words letter by letter before touching the question word
- Classification items are won by finding one property shared by all options except one — test meaning first, then spelling, letter count, or number properties
- In logic, 'if P then Q' guarantees Q when P happens and guarantees not-P when Q fails — but P is never proven by Q alone
- Direction-sense puzzles are right-triangle problems in disguise: 3 km north then 4 km east puts you 5 km from the start
Why Coding and Logic Items Matter
The same Abstract Reasoning portion of the PUPCET that tests spatial skills also tests verbal-symbolic reasoning: coded words, odd-one-out sets, and short logical deductions. These items look like games, but they measure exactly what college coursework demands — following a rule precisely and drawing only the conclusions the rule allows. The good news: every coding-decoding item is solved by the same opening move. Crack the rule from the example given, then apply it mechanically. Never jump to the question word first.
Letter-Shift (Caesar) Codes
In a Caesar cipher, every letter shifts forward (or backward) by a fixed number of alphabet positions. Align the example word with its code, letter by letter, to find the shift.
Worked encoding: 'In a certain code, CAT is written as DBU. How is DOG written?' Align C to D, A to B, T to U — each letter moves +1. Apply +1 to DOG: D becomes E, O becomes P, G becomes H, so DOG is written EPH.
Worked decoding: 'In the same code, UFTU is written. What is the original word?' Decoding reverses the shift: move -1. U becomes T, F becomes E, T becomes S, U becomes T — the original word is TEST. The lesson: write the alphabet positions if you must (A=1, B=2, ... Z=26) and do the arithmetic on paper. Watch for wrap-around: Z shifted +1 becomes A, so BUZZ with a +1 shift becomes CVAA.
Number-Substitution and Symbol Codes
Other code families you will meet:
| Code type | How it works | Example |
|---|---|---|
| Letter shift | Each letter +n or -n positions | CAT becomes DBU (shift +1) |
| Position number | A=1 ... Z=26 (or reversed A=26) | CAB becomes 3-1-2 |
| Symbol substitution | Each letter maps to a symbol | star=A, hash=B, and so on |
| Reversed word | Word spelled backward | REWARD becomes DRAWER |
| Position swap | Letters trade places by a fixed rule | FIRST and LAST letters swap |
Worked symbol example: 'If MANGO is coded as 13-1-14-7-15, how is APPLE coded?' The example tells you the rule is simple position numbering: M=13, A=1, N=14, G=7, O=15. So APPLE is A=1, P=16, P=16, L=12, E=5, or 1-16-16-12-5. Worked reversal: 'If STUDENT is written as TNEDUTS, how is SCHOLAR written?' The rule is full reversal, so SCHOLAR becomes RALOHCS. Position-swap variant: 'If TABLE is written as EABLT (first and last letters swapped, middle reversed)' — identify the swap from the example before applying; never assume the rule is reversal when only the outer letters moved.
Classification: Odd-One-Out Items
Classification items give four or five options and ask which one does not belong. The winning habit is to state, in one sentence, the property that the majority shares — then find the option lacking it. Attack in this order:
- Meaning (semantic): Are they all fruits, all land vehicles, all provinces? Example: mango, banana, apple, carrot — the first three are fruits, so carrot (a vegetable) is out.
- Structure: Count letters, vowels, or syllables; check starting and ending letters; look for anagrams. Example: STOP, POTS, SPOT, MEAL — the first three are all rearrangements of the same four letters, so MEAL is out.
- Number properties: even vs odd, prime vs composite, perfect square or cube, divisibility. Example: 8, 27, 64, 30 — the first three are perfect cubes (2^3, 3^3, 4^3), so 30 is out.
Worked example: 'Choose the odd one out: 121, 144, 169, 180.' Check the number properties: 121 = 11^2, 144 = 12^2, 169 = 13^2, but 180 is not a perfect square — 180 is the answer. Common traps: (1) picking a property that splits the set 2-against-2 instead of 3-against-1 — a valid odd-one-out rule must isolate exactly one option; (2) settling for the first difference you spot when a stronger one exists. If two answers seem possible, prefer the rule that uses an objective property (mathematical or dictionary category) over a subjective one.
Philippine-context drill: 'Odd one out: Mayon, Taal, Apo, Pasig.' Mayon, Taal, and Apo are volcanoes or mountains; Pasig is a river — that is the semantic split PUPCET writers favor, so brush up on basic Philippine geography alongside your logic drills.
Logical Reasoning: Syllogisms and If-Then Statements
A syllogism draws a conclusion from two premises. The valid chain: 'All honor students are diligent. All diligent students pass their classes. Therefore, all honor students pass their classes.' The chain works because the middle term (diligent) links the two. The classic invalid form reverses an 'all' statement: 'All PUPCET takers are Grade 12 students' does NOT imply 'All Grade 12 students are PUPCET takers.' On the exam, accept a conclusion only if it MUST be true in every case the premises allow.
If-Then Logic: Necessary vs Sufficient
'If it rains, then the ground gets wet' gives you exactly two valid moves:
| Given information | Valid conclusion | Name |
|---|---|---|
| It rained | The ground is wet | Affirming the condition |
| The ground is not wet | It did not rain | Denying the result |
| The ground is wet | (nothing — a sprinkler works too) | Invalid: affirming the result |
| It did not rain | (nothing — the ground could still be wet) | Invalid: denying the condition |
A sufficient condition guarantees the result (rain is sufficient for wet ground); a necessary condition must hold for the result but does not guarantee it (passing the PUPCET is necessary for admission through the test route, but the College Qualifying Score also weighs your grades, so it is not sufficient by itself).
Direction Sense
Draw the path. Worked example: 'Juan walks 3 km north, turns right and walks 4 km. How far is he from the start?' Right of north is east. His path forms the legs of a right triangle, so the straight-line distance is sqrt(3^2 + 4^2) = sqrt(25) = 5 km, northeast of the start. Always track turns relative to the walker's current facing, not to the page.
Blood Relations
Decode from the anchor person outward. Worked example: 'Pointing to a man, Liza says: he is the son of my grandfather's only son. How is the man related to Liza?' Grandfather's only son is Liza's father; the son of Liza's father is Liza's brother. Sketch a mini family tree with squares for males and circles for females — ten seconds of drawing beats two minutes of re-reading. Trap: 'only son of my grandfather' is the father, but 'only grandson of my grandfather' could be the person himself or a cousin, so parse each phrase literally before drawing.
In a certain code, MANGO is written as NBOHP. Using the same code, how is APPLE written?
Pointing to a photograph, Maria says, 'He is the son of my grandfather's only son.' How is the man in the photograph related to Maria?