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Coding and Decoding

13 minbeginnerModule 4: Analytical ReasoningContinues from hat-relations-and-directions
13 min · Module 4: Analytical Reasoning · Mechanical patterns

Why This Matters

Coding items are the most mechanical questions on the analytical section: a rule is demonstrated on one word, and you apply it to another. There is no reasoning to do and no diagram to draw — only a transformation to name. That makes them the fastest marks in the section when you know the catalogue, and a five-minute dead end when you do not.

The skill is recognition: compare the given pairs letter by letter, and the transformation announces itself in the first two letters.

A Simple Model

Ask one question: what happened to each letter? Work through the catalogue in order of likelihood and stop at the first match.

  1. Shift: is every letter moved by the same number of places? (CAT to DBU is +1.)
  2. Reversal: is the word written backwards? (MOTHER to REHTOM.)
  3. Shift and reverse together.
  4. Position arithmetic: are letters replaced by their numbers, or by sums and differences of numbers?
  5. Substitution: a fixed mapping, such as vowels shifted and consonants kept.
  6. Word-level code: whole words replaced by invented words, solved by intersecting two sentences.

Write the alphabet with its positions at the top of your rough sheet before the section starts. That single line converts every shift question into counting rather than recall.

The Actual Detail

The alphabet strip you should write out

A  B  C  D  E  F  G  H  I  J  K  L  M
1  2  3  4  5  6  7  8  9  10 11 12 13
N  O  P  Q  R  S  T  U  V  W  X  Y  Z
14 15 16 17 18 19 20 21 22 23 24 25 26

Remember EJOTY as a shortcut: E is 5, J is 10, O is 15, T is 20, Y is 25. Any letter's position can then be found by stepping a few places from one of those anchors — Q is one before R, and R is 18, so Q is 17.

The transformations, with examples

RuleGivenCodeThen
Shift +1CATDBUDOG becomes EPH
ReverseMOTHERREHTOMFATHER becomes REHTAF
Shift +2 then reverseCATVCEDOG becomes IQF
Positions as numbersMAN13-1-14The sum for DOG is 4 + 15 + 7 = 26
Mirror (A to Z, B to Y)CATXZGDOG becomes WLT
Vowels shifted +1, consonants unchangedCATCBTDOG becomes DPG

Word-level codes (the invented-language questions)

These give whole sentences in a made-up language and ask for a word's meaning. The method is intersection, not vocabulary:

Test the shift on two different letters before committing. A shift of +1 in the first letter pair and +3 in the second means the rule is not a uniform shift; check the third pair, because the real rule is often positional (first letter +1, second +2, third +3).
Two traps. (1) Wrapping around the alphabet: shifting Z by +1 gives A, not an error. (2) Applying a mirror rule backwards — in the mirror code A and Z are partners, so mirroring twice returns the original word, which is exactly how you can check your answer.

Worked Examples

1. If CAT is coded as DBU, how is DOG coded?

Each letter has moved one place forward: C to D, A to B, T to U. So D to E, O to P, G to H: EPH.

2. If MOTHER is coded as REHTOM, how is FATHER coded?

The code is the word reversed. FATHER reversed letter by letter is REHTAF.

3. If A = 1 and Z = 26, what is the sum of the letters in DOG?

D is 4, O is 15, G is 7: 4 + 15 + 7 = 26. Notice that DOG happens to sum to 26, the number of letters in the alphabet — a coincidence of this particular word, not a rule.

4. In a certain language, "pa ta ka" means "rain comes soon" and "ta ne da" means "comes the storm". Which word means "comes"?

The two sentences share the word "comes", and the only code word shared by "pa ta ka" and "ta ne da" is ta. So ta means comes, and the dictionary entry was found by intersection rather than by guessing.

Try It

If CAT is coded as DBU, how is DOG coded?

If MOTHER is coded as REHTOM, how is FATHER coded?

If A = 1 through to Z = 26, what is the sum of the letters in DOG?

In a code, each letter is replaced by the letter as far from the end of the alphabet as it is from the start (A becomes Z). What is the code for CAT?

Check Your Understanding

Without looking back: what does EJOTY stand for, and how do you solve an invented-language code?

The answer: E is 5, J is 10, O is 15, T is 20 and Y is 25, giving anchors for letter positions; and word-level codes are solved by intersecting two sentences to find the shared word.

In the mirror code, A is paired with . The memory trick EJOTY gives the positions 5, 10, 15, 20 and . If every letter is moved one place forward, CAT becomes . Shared code words between two coded sentences are found by .

Apply It

A code works like this: the first letter moves one place forward, the second two places forward, the third three places forward, and so on. What is the code for CAT, and what is the code for AB?

Show the reasoning

For CAT: C +1 = D, A +2 = C, T +3 = W, giving DCW. The positional rule is the giveaway when a uniform shift fails: if the first letter looks like +1 and the second like +2, the shift is positional, not constant.

For AB: A +1 = B, B +2 = D, giving BD. The rule works the same for any word length, which is the practical test of whether you have identified it correctly — apply it to a second known pair before answering.

Notice also the wrap-around: if a letter crosses Z it continues at A. That is why practising with letters near the end of the alphabet, such as Y and Z, is worth doing before the paper.

Connect

Patterns are done. The next lesson turns to a habit that saves marks across the whole quantitative and analytical sections: deciding whether the information you have is actually enough to answer — and being willing to choose "cannot be determined".