In a certain code language, ‘HAMMER’ is written as ‘ICPQJX’. How will ‘WRENCH’ be written as in that language?
XTHRHN
This question is a classic example of a coding-decoding problem often found in logical reasoning sections. The goal is to identify the rule or pattern used to convert one word into a coded form and then apply that same rule to another word.
Let's look at the correspondence between the letters in the original word 'HAMMER' and its coded form 'ICPQJX'. We can examine the position of each letter in the English alphabet.
| Original Word | Coded Word | Alphabetical Position (Original) | Alphabetical Position (Coded) | Shift |
|---|---|---|---|---|
| H | I | 8 | 9 | $+9 - 8 = +1$ |
| A | C | 1 | 3 | $+3 - 1 = +2$ |
| M | P | 13 | 16 | $+16 - 13 = +3$ |
| M | Q | 13 | 17 | $+17 - 13 = +4$ |
| E | J | 5 | 10 | $+10 - 5 = +5$ |
| R | X | 18 | 24 | $+24 - 18 = +6$ |
From the table, we can clearly see a pattern in the shift applied to each successive letter:
So, the rule is to shift the 1st letter by +1, 2nd by +2, 3rd by +3, 4th by +4, 5th by +5, and 6th by +6.
Now, let's apply this same pattern to the word 'WRENCH'. The word 'WRENCH' also has six letters, just like 'HAMMER'. We will apply the corresponding shifts to each letter of 'WRENCH'.
| Original Word (WRENCH) | Alphabetical Position | Shift Rule | Calculation | Coded Letter Position | Coded Letter |
|---|---|---|---|---|---|
| W | 23 | $+1$ | $23 + 1 = 24$ | 24 | X |
| R | 18 | $+2$ | $18 + 2 = 20$ | 20 | T |
| E | 5 | $+3$ | $5 + 3 = 8$ | 8 | H |
| N | 14 | $+4$ | $14 + 4 = 18$ | 18 | R |
| C | 3 | $+5$ | $3 + 5 = 8$ | 8 | H |
| H | 8 | $+6$ | $8 + 6 = 14$ | 14 | N |
Combining the coded letters, we get 'XTHRHN'.
Based on the coding pattern observed in 'HAMMER' becoming 'ICPQJX', the word 'WRENCH' is coded as 'XTHRHN'.
Let's check the given options:
Our calculated code 'XTHRHN' matches Option 1.
| Concept | Description |
|---|---|
| Letter Coding | Replacing each letter of a word with another letter or symbol based on a specific rule. |
| Position Shift | A common rule where letters are replaced by letters a fixed number of positions forward or backward in the alphabet. |
| Sequential Shift | The shift amount changes sequentially for each letter, as seen in this problem (+1, +2, +3, ...). |
| Decoding | The process of converting the coded form back to the original word. |
Coding-decoding problems can involve various patterns. Some common types include:
Practicing different types helps in quickly identifying the pattern during exams.
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