In a code language, 'SPACE' is written as '5-91' and 'ROTTEN' is written as '6-70'. How will 'MEAN' be written in that language?
Understanding the Code Language Pattern
The problem presents a coding language where words are transformed into a code consisting of a number, a hyphen, and another number. We are given two examples: 'SPACE' coded as '5-91' and 'ROTTEN' coded as '6-70'. We need to find the code for 'MEAN' using the same logic.
Let's analyze the given examples to figure out the rule:
- For 'SPACE': The code is '5-91'. The word 'SPACE' has 5 letters. This matches the first number in the code. So, the first part of the code might be the total number of letters in the word.
- For 'ROTTEN': The code is '6-70'. The word 'ROTTEN' has 6 letters. This also matches the first number, confirming that the first part of the code is likely the count of letters.
Now let's analyze the second part of the code: '91' for 'SPACE' and '70' for 'ROTTEN'. This part is likely derived from the letters themselves, perhaps their numerical positions or a variation of them.
Let's consider the alphabetical position of each letter (A=1, B=2, ..., Z=26) and the reverse alphabetical position (A=26, B=25, ..., Z=1, which is equivalent to $27 - \text{position}$).
Analyzing 'SPACE' (Code: 5-91)
Word: SPACE
| Letter | Alphabetical Position | Reverse Position (27 - Position) |
|---|---|---|
| S | 19 | $27 - 19 = 8$ |
| P | 16 | $27 - 16 = 11$ |
| A | 1 | $27 - 1 = 26$ |
| C | 3 | $27 - 3 = 24$ |
| E | 5 | $27 - 5 = 22$ |
Let's calculate the sum of the reverse positions: $8 + 11 + 26 + 24 + 22 = 91$.
This sum matches the second part of the code for 'SPACE'.
Analyzing 'ROTTEN' (Code: 6-70)
Word: ROTTEN
| Letter | Alphabetical Position | Reverse Position (27 - Position) |
|---|---|---|
| R | 18 | $27 - 18 = 9$ |
| O | 15 | $27 - 15 = 12$ |
| T | 20 | $27 - 20 = 7$ |
| T | 20 | $27 - 20 = 7$ |
| E | 5 | $27 - 5 = 22$ |
| N | 14 | $27 - 14 = 13$ |
Let's calculate the sum of the reverse positions: $9 + 12 + 7 + 7 + 22 + 13 = 70$.
This sum matches the second part of the code for 'ROTTEN'.
The rule is confirmed: The code is formed by the number of letters in the word, followed by a hyphen, and then the sum of the reverse alphabetical positions of all letters in the word.
Applying the Rule to 'MEAN'
Word: MEAN
First part of the code: Number of letters in 'MEAN'. 'MEAN' has 4 letters. So the first part is 4.
Second part of the code: Sum of the reverse alphabetical positions of the letters in 'MEAN'.
| Letter | Alphabetical Position | Reverse Position (27 - Position) |
|---|---|---|
| M | 13 | $27 - 13 = 14$ |
| E | 5 | $27 - 5 = 22$ |
| A | 1 | $27 - 1 = 26$ |
| N | 14 | $27 - 14 = 13$ |
Sum of reverse positions: $14 + 22 + 26 + 13 = 75$.
The second part of the code is 75.
Combining the two parts, the code for 'MEAN' is '4-75'.
Comparing with Options
- Option 1: 4-75
- Option 2: 4-74
- Option 3: 4-73
- Option 4: 4-76
Our calculated code '4-75' matches Option 1.
Revision Table: Key Concepts
| Concept | Description | Application in Problem |
|---|---|---|
| Coding-Decoding | A type of reasoning question where a word, number, or series is coded according to a specific rule, and you need to decode another item using the same rule. | Identifying the rule used to code 'SPACE' and 'ROTTEN' to apply it to 'MEAN'. |
| Alphabetical Position | The standard numerical order of letters (A=1, B=2, ..., Z=26). | Used as the basis for calculating reverse position. |
| Reverse Alphabetical Position | Assigning numerical values in reverse order (A=26, B=25, ..., Z=1). Can be calculated as $27 - \text{Alphabetical Position}$. | The sum of these values formed the second part of the code. |
| Pattern Recognition | Identifying the underlying rule or logic in a sequence or transformation. | Crucial for determining how 'SPACE' and 'ROTTEN' were coded. |
Additional Information: Types of Coding-Decoding
Coding-decoding problems are common in reasoning sections of competitive exams. They test your ability to identify patterns and apply logical rules. Some common types include:
- Letter Coding: Letters are replaced by other letters based on a shift in position or a specific pattern.
- Number Coding: Words are coded into numbers based on letter positions, sum of positions, or other calculations. This problem is an example of letter-to-number coding.
- Symbol Coding: Letters or words are replaced by symbols.
- Mixed Coding: A mix of letters, numbers, and symbols is used.
- Sentence Coding: Rules are applied to entire sentences or phrases.
To solve these problems effectively, it's helpful to know the alphabetical positions of letters and practice identifying various patterns involving shifts, sums, reverse orders, etc.
Important Questions from Operations on Place Value
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In a certain code language, GRAPES is written as 66. How will PRAISE be written in the same language?
In the following question, some group of letters is given, all of which, except one, share a common similarity while one is different. Choose the odd one out:
