Analysing the Odd One Out: Letter Coding Puzzle

This question requires identifying the pair that does not follow the same logical pattern as the other four pairs. We need to analyze the relationship between the letters in the first word and the second word of each pair.

Analysing the Pattern in Each Pair

We will determine the pattern by calculating the shift in the alphabetical position for each letter from the original word to the coded word. We use modular arithmetic (modulo 26) for wrap-around cases (e.g., A following Z).

1. DATE: EXWH

• D (4th letter) \(\to\) E (5th letter): Shift = \(5 - 4 = +1\)
• A (1st letter) \(\to\) X (24th letter): Shift = \(24 - 1 = +23 \equiv -3 \pmod{26}\)
• T (20th letter) \(\to\) W (23rd letter): Shift = \(23 - 20 = +3\)
• E (5th letter) \(\to\) H (8th letter): Shift = \(8 - 5 = +3\)

The pattern for DATE is (+1, -3, +3, +3).

2. READ: SFBC

• R (18th letter) \(\to\) S (19th letter): Shift = \(19 - 18 = +1\)
• E (5th letter) \(\to\) F (6th letter): Shift = \(6 - 5 = +1\)
• A (1st letter) \(\to\) B (2nd letter): Shift = \(2 - 1 = +1\)
• D (4th letter) \(\to\) C (3rd letter): Shift = \(3 - 4 = -1\)

The pattern for READ is (+1, +1, +1, -1).

3. FISH: GJTID

Assuming the pattern applies to the first four letters (F, I, S, H) corresponding to G, J, T, I:

• F (6th letter) \(\to\) G (7th letter): Shift = \(7 - 6 = +1\)
• I (9th letter) \(\to\) J (10th letter): Shift = \(10 - 9 = +1\)
• S (19th letter) \(\to\) T (20th letter): Shift = \(20 - 19 = +1\)
• H (8th letter) \(\to\) I (9th letter): Shift = \(9 - 8 = +1\)

The pattern for FISH is (+1, +1, +1, +1).

4. BOOK: CPQL

• B (2nd letter) \(\to\) C (3rd letter): Shift = \(3 - 2 = +1\)
• O (15th letter) \(\to\) P (16th letter): Shift = \(16 - 15 = +1\)
• O (15th letter) \(\to\) Q (17th letter): Shift = \(17 - 15 = +2\)
• K (11th letter) \(\to\) L (12th letter): Shift = \(12 - 11 = +1\)

The pattern for BOOK is (+1, +1, +2, +1).

5. CARD: DBSE

• C (3rd letter) \(\to\) D (4th letter): Shift = \(4 - 3 = +1\)
• A (1st letter) \(\to\) B (2nd letter): Shift = \(2 - 1 = +1\)
• R (18th letter) \(\to\) S (19th letter): Shift = \(19 - 18 = +1\)
• D (4th letter) \(\to\) E (5th letter): Shift = \(5 - 4 = +1\)

The pattern for CARD is (+1, +1, +1, +1).

Identifying the Outlier Group

Let's summarize the observed patterns:

We are looking for a group of four items that share a common characteristic. Let's examine the patterns:

• CARD, FISH, and READ primarily use shifts of magnitude 1 (+1 or -1).
• BOOK uses shifts of magnitude 1, with one instance of magnitude 2 (+2).
• DATE uses shifts of magnitude 1 (+1), but also involves shifts of magnitude 3 (+3) and a negative shift of magnitude 3 (-3).

The common characteristic among READ, FISH, BOOK, and CARD is that their transformation patterns involve shifts primarily of magnitude 1, with only minor exceptions (one -1 shift in READ, one +2 shift in BOOK). The pattern for DATE, containing shifts of -3 and +3, deviates significantly in terms of the magnitude and sign of these shifts compared to the others.

Therefore, DATE: EXWH is the one that does not belong to the group.