Analyzing the Coding and Decoding Puzzle

This question involves a word-number coding system where a sentence or phrase is represented by a sequence of numbers. We are given two examples of this coding and need to find the code for a third phrase based on the discovered pattern.

Step 1: Examine the Given Statements and Codes

We have the following information:

• 'School education is free in India' is coded as 692425.
• 'College education is costly' is coded as 7926.

We need to find the code for 'I want to become graduate'.

Step 2: Identify Common Words and Corresponding Codes

Let's list the words and the sequence of digits given for each statement:

Statement 1: School education is free in India

Codes 1: 6 9 2 4 2 5

Statement 2: College education is costly

Codes 2: 7 9 2 6

Common words in both statements are 'education' and 'is'.

The digits that appear in both code sequences (692425 and 7926) are 9, 2, and 6.

A standard approach is that common words correspond to common codes. However, we have two common words ('education', 'is') and three common digits (9, 2, 6). This suggests that the mapping might not be a simple one-to-one correspondence for all common elements, or that the order of the digits in the code sequence directly corresponds to the order of the words in the sentence.

Step 3: Test the Hypothesis of Ordered Mapping

Let's assume the digits in the code sequence correspond to the words in the sentence in the given order:

From 'School education is free in India' = 692425:

• School → 6
• education → 9
• is → 2
• free → 4
• in → 2
• India → 5

From 'College education is costly' = 7926:

• College → 7
• education → 9
• is → 2
• costly → 6

Let's check for consistency with this ordered mapping:

• 'education' is coded as 9 in both statements. This is consistent.
• 'is' is coded as 2 in both statements. This is consistent.
• 'in' is coded as 2 in Statement 1. This means 'is' and 'in' share the same code 2. This is a possible pattern.
• 'School' is coded as 6 in Statement 1, and 'costly' is coded as 6 in Statement 2. This means 'School' and 'costly' share the same code 6. This is another possible pattern, similar to 'is' and 'in'.

This ordered mapping, while showing some shared codes, is consistent with the given code sequences:

• Codes for 'School education is free in India' are {6, 9, 2, 4, 2, 5}, which matches 692425.
• Codes for 'College education is costly' are {7, 9, 2, 6}, which matches 7926.

Therefore, it seems the coding follows the order of the words, and different words can indeed share the same numerical code.

Step 4: Consolidate the Word-to-Code Mappings

Based on the consistent ordered mapping, we have the following codes for the words encountered:

We observe that:

• Code 2 is used for 'is' and 'in'.
• Code 6 is used for 'School' and 'costly'.

Step 5: Determine the Code for the Target Phrase

We need to find the code for 'I want to become graduate'. This phrase has 5 words.

Let's look at the given options, which are 5-digit numbers, suggesting an ordered mapping for this phrase as well:

1. 54268
2. 15426
3. 14268
4. 23586

Let's examine the digits in the correct option (Option 3: 14268) and assume this is the code sequence for 'I want to become graduate':

• I → 1
• want → 4
• to → 2
• become → 6
• graduate → 8

Let's check if these new assignments fit the pattern of shared codes we discovered:

• 'want' is coded as 4. This code was previously assigned to 'free'. This fits the pattern of shared codes. So, 'free' and 'want' share code 4.
• 'to' is coded as 2. This code was previously assigned to 'is' and 'in'. This also fits the pattern. So, 'is', 'in', and 'to' share code 2.
• 'become' is coded as 6. This code was previously assigned to 'School' and 'costly'. This fits the pattern. So, 'School', 'costly', and 'become' share code 6.
• 'I' is coded as 1. This is a new code.
• 'graduate' is coded as 8. This is a new code.

This assignment is consistent with the observed coding logic where certain codes are shared between multiple words. The codes for 'I', 'want', 'to', 'become', 'graduate' are 1, 4, 2, 6, 8 respectively, in order.

Conclusion

Following the established pattern where digits correspond to words in order and some codes are shared, the code for 'I want to become graduate' is 14268.

Revision Table: Word to Code Mapping

Additional Information on Coding-Decoding

Coding-decoding questions test your ability to identify patterns and rules in coded messages. Common types include:

• Letter Coding: Letters are replaced by other letters based on a sequence (e.g., shifting letters in the alphabet) or a specific pattern.
• Number Coding: Words are represented by numbers based on letter positions in the alphabet, counting letters, or assigning arbitrary numbers as seen in this problem.
• Symbol Coding: Words are represented by symbols.
• Mixed Coding: A mix of letters, numbers, and symbols is used.
• Sentence Coding: As in this problem, entire sentences are coded, and the pattern is often found by comparing common words and common codes between different sentences. Look for words that appear in multiple sentences and the numbers/codes that appear in their corresponding coded forms.

When solving sentence coding problems:

1. List the words and codes for each sentence.
2. Identify words common to two or more sentences.
3. Identify codes common to the corresponding coded sentences.
4. Match the common words to common codes. This might require trial and error or looking for uniquely appearing words/codes.
5. Once some mappings are established, use them to decode unique words and find codes for the target phrase.
6. Be aware that patterns can be complex, including shared codes (as in this problem) or codes based on letter position, count, etc., although shared codes based on comparison is a common pattern.