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UGC NET PAPER 1 · UNIT 05 · MODULE 2: REASONING, SERIES, CODES AND RELATIONS · TOPIC 4

Coding and Decoding

The types of code, a step-by-step method and shortcuts for solving codes quickly.

  • 5 sub-topics
  • 5 min read
  • Topic 4 of 17

What this topic covers

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  1. §OverviewCoding means converting a word, number or phrase into another form using a fixed rule.
  2. 4.1Types of codingType Rule Example Fixed forward shift Every letter moves the same number of places forward MOTHER becomes NPUIFS (+1) Fixed backward shift Every letter moves backward BCD…
  3. 4.2Step-by-step methodWrite the positions of every letter of the original word and the coded word. Check whether each letter moved by the same amount. If so, it is a fixed shift. If each letter…
  4. 4.3Worked examplesExample 1 (fixed shift).
    • Example 1 (fixed shift)
    • TJTUFS
    • Example 2 (opposite letters)
    • XSZRI
    • Example 3 (increasing shift)
  5. 4.4Tricks and shortcutsCovers Mixed coding, Same length, same letters, Check the first and last letters first, Opposite-letter sanity check, Substitution chain and more.
    • Mixed coding
    • Same length, same letters
    • Opposite-letter sanity check
    • Substitution chain
    • Operator-change questions
  6. 4.5TrapsApplying the shift to the wrong end of the alphabet (forgetting that Z wraps to A). Reading the coded answer for the word name rather than for the real object in…

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§Overview#

Coding means converting a word, number or phrase into another form using a fixed rule. Decoding means finding that rule from a given example and applying it to a new word. The solving habit is always the same: write both the original and the coded form, compare them position by position, and test the rule on every letter.

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4.1Types of coding#

In brief

Type Rule Example Fixed forward shift Every letter moves the same number of places forward MOTHER becomes NPUIFS (+1) Fixed backward shift Every letter moves backward BCD…

Type Rule Example
Fixed forward shift Every letter moves the same number of places forward MOTHER becomes NPUIFS (+1)
Fixed backward shift Every letter moves backward BCD becomes ABC (-1)
Increasing shift Shifts of +1, +2, +3, +4, ... for the 1st, 2nd, 3rd letters CAT becomes DCW
Opposite-letter coding Each letter is replaced by its mirror letter (position sum 27) CAT becomes XZG
Reverse order Letters written backward CAT becomes TAC
Reverse plus shift Reverse the word, then shift combine both rules
Letter to number Letters replaced by positions CAT = 3, 1, 20
Sum or product of positions The code is the total of letter values ACE = 1 + 3 + 5 = 9
Substitution (word replacement) A word is deliberately renamed if red is called blue, then the colour of blood is named blue
Mixed coding Several coded sentences share words find common codes by elimination
Operator substitution Symbols such as +, -, x, / are given new meanings replace symbols, then solve using BODMAS

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4.2Step-by-step method#

In brief

Write the positions of every letter of the original word and the coded word. Check whether each letter moved by the same amount. If so, it is a fixed shift. If each letter…

  1. Write the positions of every letter of the original word and the coded word.

  2. Check whether each letter moved by the same amount. If so, it is a fixed shift.

  3. If each letter moved by a different amount, check for +1, +2, +3 (or -1, -2, -3) patterns.

  4. If the positions of a pair add to 27, it is opposite-letter coding.

  5. If the coded word has the same letters in reverse order, it is reverse coding.

  6. If the code is a number, test the sum, the product, and the positions side by side.

  7. Apply the rule to the new word and double-check at least two letters.

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4.3Worked examples#

In brief

Example 1 (fixed shift).

  • Example 1 (fixed shift)
  • TJTUFS
  • Example 2 (opposite letters)
  • XSZRI
  • Example 3 (increasing shift)
  • UCEPJ
  • Example 4 (substitution chain)
  • green

Example 1 (fixed shift). MOTHER is coded NPUIFS. How is SISTER coded?

  • Every letter moves +1, so SISTER becomes TJTUFS.

Example 2 (opposite letters). TABLE is coded GZYOV. Code CHAIR in the same way.

  • T (20) to G (7) is 27 - 20 = 7, so the rule is opposite-letter.

  • C becomes X, H becomes S, A becomes Z, I becomes R, R becomes I, so CHAIR becomes XSZRI.

Example 3 (increasing shift). CLOCK is coded DNRGP. How is TABLE coded?

  • C to D is +1, L to N is +2, O to R is +3, C to G is +4, K to P is +5.

  • Apply +1, +2, +3, +4, +5 to TABLE: T to U, A to C, B to E, L to P, E to J, giving UCEPJ.

Example 4 (substitution chain). In a code, red is called blue, blue is called green, green is called yellow, yellow is called white. What is the colour of the sky?

  • The sky is blue in real life. Blue is called green in the code.

  • Answer: green. Always give the code name of the real object.

Example 5 (mixed coding).

  • "mi ka ro" means "sweet red apple"

  • "ka su" means "red car"

  • "ro bi" means "sweet tea"

Steps: the word common to the first two statements is "red" and the common code is "ka", so red = ka. The word common to the first and third statements is "sweet" with the common code "ro", so sweet = ro. The remaining code in the first statement, "mi", is apple. Also car = su and tea = bi.

Example 6 (operator substitution). If + means -, - means x, x means /, and / means +, find 18 x 3 + 4 - 2 / 5.

  • Replace the symbols: 18 / 3 - 4 x 2 + 5.

  • Solve by BODMAS: 6 - 8 + 5 = 3.

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4.4Tricks and shortcuts#

In brief

Covers Mixed coding, Same length, same letters, Check the first and last letters first, Opposite-letter sanity check, Substitution chain and more.

  • Mixed coding
  • Same length, same letters
  • Opposite-letter sanity check
  • Substitution chain
  • Operator-change questions

  • Mixed coding: underline the repeating word in two statements and the repeating code in the same two statements; the pair is the answer. Repeat to find the rest.

  • Same length, same letters: if the coded word has the same letters rearranged, it is a jumbling or reverse pattern.

  • Check the first and last letters first. They reveal the type of shift fastest.

  • Opposite-letter sanity check: if the first coded letter and the original add to 27, test it on the rest.

  • Substitution chain: follow the chain exactly once, one link at a time. Do not apply it twice.

  • Operator-change questions: rewrite the whole expression with the real symbols first, and only then calculate.

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4.5Traps#

In brief

Applying the shift to the wrong end of the alphabet (forgetting that Z wraps to A). Reading the coded answer for the word name rather than for the real object in…

  • Applying the shift to the wrong end of the alphabet (forgetting that Z wraps to A).

  • Reading the coded answer for the word name rather than for the real object in substitution questions.

  • Skipping BODMAS in operator substitution questions.

  • Testing the rule on one letter only. Always confirm on at least two.

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Test yourself on Coding and Decoding

Practise with free MCQs and answer keys, then return here to fix what you got wrong.

↑ Module 2: Reasoning, Series, Codes and Relations · All 18 topics in Mathematical Reasoning · Unit overview and sample MCQs

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