In a certain code language, 'PAR' is coded as ‘35' and 'GAT' is coded as ‘28'. How will 'FOM' be coded in that language?
34
Understanding the Code Language Pattern
The question asks us to decode a certain language pattern based on two examples: 'PAR' is coded as '35', and 'GAT' is coded as '28'. We need to apply this same logic to find the code for 'FOM'.
Let's analyze the given examples to find the underlying rule. A common method in coding-decoding problems is to look at the positional values of the letters in the English alphabet (A=1, B=2, ..., Z=26).
Analyzing the Coding for 'PAR'
Let's find the positional values for each letter in 'PAR':
- P is the 16th letter, so its value is 16.
- A is the 1st letter, so its value is 1.
- R is the 18th letter, so its value is 18.
Now let's see if combining these values gives us 35. Let's try summing them up:
\( 16 + 1 + 18 = 35 \)
This matches the given code for 'PAR'. This suggests that the pattern might be the sum of the positional values of the letters.
Analyzing the Coding for 'GAT'
Let's verify this pattern with the second example, 'GAT', which is coded as '28'.
Find the positional values for each letter in 'GAT':
- G is the 7th letter, so its value is 7.
- A is the 1st letter, so its value is 1.
- T is the 20th letter, so its value is 20.
Now, let's sum these values:
\( 7 + 1 + 20 = 28 \)
This also matches the given code for 'GAT'. The pattern seems to be consistently the sum of the positional values of the letters in the word.
Applying the Pattern to Code 'FOM'
Now we will apply the same pattern to find the code for 'FOM'.
Find the positional values for each letter in 'FOM':
- F is the 6th letter, so its value is 6.
- O is the 15th letter, so its value is 15.
- M is the 13th letter, so its value is 13.
Sum these positional values:
\( 6 + 15 + 13 \)
\( 6 + 15 = 21 \)
\( 21 + 13 = 34 \)
So, 'FOM' should be coded as 34.
Summary of Letter Values and Calculation
| Word | Letters | Positional Values | Sum | Coded Value |
|---|---|---|---|---|
| PAR | P, A, R | 16, 1, 18 | 16 + 1 + 18 = 35 | 35 |
| GAT | G, A, T | 7, 1, 20 | 7 + 1 + 20 = 28 | 28 |
| FOM | F, O, M | 6, 15, 13 | 6 + 15 + 13 = 34 | 34 |
The coded value for 'FOM' is 34.
Revision Table: Key Concepts
| Concept | Description | Relevance to Problem |
|---|---|---|
| Coding-Decoding | Problems where words/numbers are coded based on a specific rule, and the rule must be identified to decode a new word/number. | The core type of problem presented in the question. |
| Positional Values | Assigning a numerical value to each letter based on its position in the alphabet (A=1, B=2, ...). | The key method used to solve this specific coding pattern. |
| Pattern Recognition | Identifying the consistent rule or logic applied across the given examples. | Essential skill required to solve coding-decoding questions. |
Additional Information on Coding Patterns
Coding-decoding questions can use various patterns. Besides summing positional values, other common patterns include:
- Difference of Positional Values: Sometimes, the code might be the difference between the values of letters.
- Sum of Reverse Positional Values: Using values like A=26, B=25, etc.
- Pattern based on Vowels/Consonants: Separate rules might apply to vowels and consonants.
- Adding/Subtracting Constants: The sum or difference might then have a constant added or subtracted.
- Digit Sums: If the positional value is a two-digit number, its digits might be added (e.g., P=16, sum of digits = 1+6=7).
- Letter Shifting (Caesar Cipher): Each letter is shifted a certain number of places forward or backward in the alphabet.
To solve coding-decoding problems, it's important to analyze the given examples carefully and test different potential patterns involving letter positions or other properties until a consistent rule is found.
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