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Logical Reasoning: Coding & Decoding

1. Alphabet Reference Chart

In coding/decoding questions, letters are mapped to numbers. Memorizing the forward and backward ranks of alphabets is essential.

EJOTY Shortcut

Use the word EJOTY to remember key forward positions (multiples of 5):

  • E = 5
  • J = 10
  • O = 15
  • T = 20
  • Y = 25

Forward & Reverse Positions

For any letter: $$\text{Forward Rank} + \text{Reverse Rank} = 27$$

Reverse Pairs (Opposite Letters)

Opposite letters are pairs that sum to 27:

  • A – Z (AZ)
  • B – Y (BY)
  • C – X (CruX)
  • D – W (DeW)
  • E – V (EVen)
  • F – U (FUll)
  • G – T (GT Road)
  • H – S (High School)
  • I – R (Indian Railway)
  • J – Q (Jack & Queen)
  • K – P (KP Tower)
  • L – O (LOve)
  • M – N (MaN)

2. Common Coding Patterns

  1. Letter Shifting: Shifting letters forward/backward by a fixed value. E.g., CAT $\to$ DBU (shift of $+1$).
  2. Reverse/Opposite Coding: Replacing letters with their opposites. E.g., BAG $\to$ YZT.
  3. Cross-Shifting: Splitting a word in half and crossing the letters.
  4. Number Coding: Mapping words to numbers using their place value sums.
  5. Substitution (Chinese Coding): Grouping sentences and codes together to solve by word elimination.

3. Practice Problems

Problem 1 (Letter Shift)

In a certain code language, COMPUTER is written as RFUVQNPC. How will MEDICINE be written in that same code language?

Problem 2 (Number Coding)

If BAT $= 23$ and CAT $= 24$, find the value of BALL.

Problem 3 (Substitution Coding)

In a code language:

  • "sky is blue" is written as "mud pot ko"
  • "blue color pen" is written as "ko ra ze"
  • "sky has color" is written as "mud ra pi" What is the code for the word "has"?

Problem 4 (Opposite Letter Coding)

In a certain code language, PRISM is written as KIRHN. How will LIGHT be written in that same code language?

Problem 5 (Cross-Shifting)

In a certain code language, BREAKING is written as AERBGNIK. How will COMPUTER be written in that same code language?

Problem 6 (Number Coding)

If WORK is coded as 4-12-9-16, how will PLAY be coded?

Problem 7 (Substitution Coding)

In a certain code:

  • "truth is eternal" is written as "3a 2b 7c"
  • "enmity is temporary" is written as "7c 9a 8b"
  • "truth and enmity" is written as "1a 2b 8b" Which code represents the word "eternal"?

Problem 8 (Continuous Shifts)

If GOLD is written as IQNF, how will WIND be written in that same code language?

Problem 9 (Mixed Letter & Number Coding)

If DANGER is coded as 8-2-28-14-10-36, how will SAFETY be coded in that same code language?

Problem 10 (Substitution Coding)

In a certain code language:

  • "study hard get success" is written as "ka la ma ta"
  • "success is very important" is written as "ta na pa ra"
  • "hard work is important" is written as "ka sa na pa"
  • "study work get rewards" is written as "la ma sa da" What is the code for the word "rewards"?

4. Step-by-Step Solutions

Solution 1

  1. Analyze the pattern in COMPUTER $\to$ RFUVQNPC:
    • Split the word into individual letters and notice the first and last letters:
      • The first letter C goes to the end C.
      • The last letter R goes to the beginning R.
    • Now check the inner letters: O M P U T E $\to$ F U V Q N P (written in reverse order):
      • O $+ 1 = $ P (placed second to last).
      • M $+ 1 = $ N (placed third to last).
      • P $+ 1 = $ Q (placed fourth to last).
      • U $+ 1 = $ V.
      • T $+ 1 = $ U.
      • E $+ 1 = $ F (placed second).
    • Summary: Reverse the word, then add $+1$ to all middle letters while keeping original first/last letters.
  2. Apply the pattern to MEDICINE:
    • First and last letters: Swap M and E $\to$ Starts with E, ends with M.
    • Reverse the inner letters E D I C I N $\to$ N I C I D E.
    • Add $+1$ to each of these reversed inner letters:
      • N $+ 1 = $ O
      • I $+ 1 = $ J
      • C $+ 1 = $ D
      • I $+ 1 = $ J
      • D $+ 1 = $ E
      • E $+ 1 = $ F
  3. Assemble the final code:
    • E + O J D J E F + M = EOJDJEFM.
  4. Answer: EOJDJEFM.

Solution 2

  1. Check place values:
    • BAT $= B(2) + A(1) + T(20) = 23$.
    • CAT $= C(3) + A(1) + T(20) = 24$.
    • The code is simply the sum of forward alphabetical ranks.
  2. Calculate value for BALL:
    • BALL $= B(2) + A(1) + L(12) + L(12) = 27$.
  3. Answer: The value is 27.

Solution 3

  1. Compare sentences to isolate words:
    • Compare "sky is blue" ("mud pot ko") and "blue color pen" ("ko ra ze").
      • Common word: "blue". Common code: "ko".
      • Thus, blue = ko.
    • Compare "blue color pen" ("ko ra ze") and "sky has color" ("mud ra pi").
      • Common word: "color". Common code: "ra".
      • Thus, color = ra.
    • Compare "sky is blue" ("mud pot ko") and "sky has color" ("mud ra pi").
      • Common word: "sky". Common code: "mud".
      • Thus, sky = mud.
  2. Find the code for "has":
    • Look at the third sentence: "sky has color" coded as "mud ra pi".
    • We know sky = mud and color = ra.
    • The remaining word is "has" and the remaining code is "pi".
    • Therefore, has = pi.
  3. Answer: The code is pi.

Solution 4

  1. Understand the opposite letter mapping:
    • Check the mapping of PRISM to KIRHN:
      • P opposite is K (16 + 11 = 27)
      • R opposite is I (18 + 9 = 27)
      • I opposite is R (9 + 18 = 27)
      • S opposite is H (19 + 8 = 27)
      • M opposite is N (13 + 14 = 27)
    • The pattern is replacing each letter with its opposite letter in the alphabet.
  2. Apply to LIGHT:
    • L opposite is O
    • I opposite is R
    • G opposite is T
    • H opposite is S
    • T opposite is G
  3. Answer: ORTSG.

Solution 5

  1. Analyze the pattern in BREAKING $\to$ AERBGNIK:
    • Split the 8-letter word in half: BREA and KING.
    • Reverse the first half: BREA $\to$ AERB.
    • Reverse the second half: KING $\to$ GNIK.
    • Combine the two halves: AERBGNIK.
  2. Apply to COMPUTER:
    • Split in half: COMP and UTER.
    • Reverse the first half: COMP $\to$ PMOC.
    • Reverse the second half: UTER $\to$ RETU.
    • Combine: PMOCRETU.
  3. Answer: PMOCRETU.

Solution 6

  1. Analyze the code for WORK:
    • W: Forward rank = 23, Reverse rank = 27 - 23 = 4
    • O: Forward rank = 15, Reverse rank = 27 - 15 = 12
    • R: Forward rank = 18, Reverse rank = 27 - 18 = 9
    • K: Forward rank = 11, Reverse rank = 27 - 11 = 16
    • The code is formed by the reverse ranks of the letters separated by hyphens.
  2. Apply to PLAY:
    • P: Forward rank = 16, Reverse rank = 27 - 16 = 11
    • L: Forward rank = 12, Reverse rank = 27 - 12 = 15
    • A: Forward rank = 1, Reverse rank = 27 - 1 = 26
    • Y: Forward rank = 25, Reverse rank = 27 - 25 = 2
  3. Assemble the code:
    • 11-15-26-2
  4. Answer: 11-15-26-2.

Solution 7

  1. Compare sentences to identify words:
    • Compare "truth is eternal" ("3a 2b 7c") and "enmity is temporary" ("7c 9a 8b").
      • Common word: "is". Common code: "7c".
      • Thus, is = 7c.
    • Compare "truth is eternal" ("3a 2b 7c") and "truth and enmity" ("1a 2b 8b").
      • Common word: "truth". Common code: "2b".
      • Thus, truth = 2b.
  2. Find the code for "eternal":
    • The first sentence "truth is eternal" is coded as "3a 2b 7c".
    • We know truth = 2b and is = 7c.
    • The remaining word "eternal" must correspond to the remaining code 3a.
  3. Answer: The code is 3a.

Solution 8

  1. Analyze the pattern in GOLD $\to$ IQNF:
    • G $+ 2 = $ I
    • O $+ 2 = $ Q
    • L $+ 2 = $ N
    • D $+ 2 = $ F
    • The pattern is a shift of $+2$ for all letters.
  2. Apply to WIND:
    • W $+ 2 = $ Y
    • I $+ 2 = $ K
    • N $+ 2 = $ P
    • D $+ 2 = $ F
  3. Answer: YKPF.

Solution 9

  1. Analyze the pattern in DANGER $\to$ 8-2-28-14-10-36:
    • Write down the forward ranks of the letters in DANGER:
      • D = 4, A = 1, N = 14, G = 7, E = 5, R = 18.
    • Multiply each forward rank by 2:
      • D: $4 \times 2 = 8$
      • A: $1 \times 2 = 2$
      • N: $14 \times 2 = 28$
      • G: $7 \times 2 = 14$
      • E: $5 \times 2 = 10$
      • R: $18 \times 2 = 36$
    • Combine with hyphens: 8-2-28-14-10-36.
  2. Apply the pattern to SAFETY:
    • Write down the forward ranks:
      • S = 19, A = 1, F = 6, E = 5, T = 20, Y = 25.
    • Multiply each rank by 2:
      • S: $19 \times 2 = 38$
      • A: $1 \times 2 = 2$
      • F: $6 \times 2 = 12$
      • E: $5 \times 2 = 10$
      • T: $20 \times 2 = 40$
      • Y: $25 \times 2 = 50$
  3. Assemble the code:
    • 38-2-12-10-40-50
  4. Answer: 38-2-12-10-40-50.

Solution 10

  1. Compare sentences to isolate words and their codes:
    • Compare "study hard get success" ("ka la ma ta") and "hard work is important" ("ka sa na pa").
      • Common word: "hard". Common code: "ka". Thus, hard = ka.
    • Compare "study hard get success" ("ka la ma ta") and "success is very important" ("ta na pa ra").
      • Common word: "success". Common code: "ta". Thus, success = ta.
    • Compare "hard work is important" ("ka sa na pa") and "study work get rewards" ("la ma sa da").
      • Common word: "work". Common code: "sa". Thus, work = sa.
  2. Determine "rewards" from the fourth sentence:
    • Sentence 4: "study work get rewards" $\to$ "la ma sa da".
    • We know work = sa.
    • Comparing Sentence 1 "study hard get success" ("ka la ma ta") and Sentence 4 "study work get rewards" ("la ma sa da"), the common words are "study" and "get", and their common codes are "la" and "ma".
    • Therefore, {"study", "get"} corresponds to {"la", "ma"}.
    • The remaining word in Sentence 4 is "rewards" and the remaining code is "da".
  3. Answer: The code for "rewards" is da.