In a certain code language, ‘WATER’ is coded as ‘4267229’. How will ‘PURITY’ be coded in that language?

Question

In a certain code language, &lsquo;WATER&rsquo; is coded as &lsquo;4267229&rsquo;. How will &lsquo;PURITY&rsquo; be coded in that language?

Prepp Team · Accepted Answer

Understanding the Coding Language Logic

This problem requires us to decode a rule used to convert a word into a numerical sequence. We are given the example 'WATER' is coded as '4267229'. We need to apply the same logic to find the code for 'PURITY'.

Analyzing the Example: WATER to 4267229

Let's list the letters in 'WATER' and their corresponding positions in the English alphabet (A=1, B=2, ..., Z=26):

Letter	Alphabetical Position
W	23
A	1
T	20
E	5
R	18

The code given is '4267229'. Let's try to split this code into segments corresponding to the letters in 'WATER'. A plausible split based on the sequence and length is 42, 6, 7, 22, 9.

Letter	Alphabetical Position	Assigned Code Segment
W	23	42
A	1	6
T	20	7
E	5	22
R	18	9

Now, let's look for a relationship between the Alphabetical Position and the Assigned Code Segment. Let's consider the Reverse Alphabetical Position (where A=26, B=25, ..., Z=1). The Reverse Alphabetical Position for a letter at Position 'P' is calculated as 27 - P.

Letter	Alphabetical Position (P)	Reverse Alphabetical Position (27 - P)	Assigned Code Segment
W	23	$27 - 23 = 4$	42
A	1	$27 - 1 = 26$	6
T	20	$27 - 20 = 7$	7
E	5	$27 - 5 = 22$	22
R	18	$27 - 18 = 9$	9

By comparing the Reverse Alphabetical Position with the Assigned Code Segment, we observe a pattern:

For letters T(7), E(22), and R(9), the Assigned Code Segment is exactly equal to their Reverse Alphabetical Position.
For letter A(26), the Assigned Code Segment is 6. This is an exception to the rule.
For letter W(4), the Assigned Code Segment is 42. This is another exception.

So, the coding rule is primarily based on the Reverse Alphabetical Position, with specific assigned codes for 'A' and 'W'.

Applying the Logic to PURITY

Now, let's apply this logic to the word 'PURITY'. First, find the Alphabetical Position and Reverse Alphabetical Position for each letter:

Letter	Alphabetical Position (P)	Reverse Alphabetical Position (27 - P)
P	16	$27 - 16 = 11$
U	21	$27 - 21 = 6$
R	18	$27 - 18 = 9$
I	9	$27 - 9 = 18$
T	20	$27 - 20 = 7$
Y	25	$27 - 25 = 2$

Now, let's determine the code for each letter based on the derived rule:

P: Alphabetical Position 16, Reverse Position 11. P is not one of the exceptions (A or W). Apply the main rule: Code = Reverse Alphabetical Position. Code for P is 11.
U: Alphabetical Position 21, Reverse Position 6. U is not one of the exceptions. Apply the main rule: Code = Reverse Alphabetical Position. Code for U is 6.
R: Alphabetical Position 18, Reverse Position 9. R is not one of the exceptions. Apply the main rule: Code = Reverse Alphabetical Position. Code for R is 9. (This matches the code for R found in the WATER example, confirming the rule).
I: Alphabetical Position 9, Reverse Position 18. I is not one of the exceptions. Apply the main rule: Code = Reverse Alphabetical Position. Code for I is 18.
T: Alphabetical Position 20, Reverse Position 7. T is not one of the exceptions. Apply the main rule: Code = Reverse Alphabetical Position. Code for T is 7. (This matches the code for T found in the WATER example, confirming the rule).
Y: Alphabetical Position 25, Reverse Position 2. Y is not one of the exceptions. Apply the main rule: Code = Reverse Alphabetical Position. Code for Y is 2.

Concatenating the codes for PURITY in order:

P (11) + U (6) + R (9) + I (18) + T (7) + Y (2) = 11691872

Conclusion

The code for 'PURITY' in this language is 11691872. This matches Option 3.

Revision Table: Coding Language Concepts

Concept	Description	Relevance to Problem
Alphabetical Position	The numerical order of a letter in the alphabet (A=1, B=2, ...).	Used as the basis for calculating Reverse Alphabetical Position.
Reverse Alphabetical Position	The numerical order of a letter counting backwards from Z (Z=1, Y=2, ... A=26 or 27-Position).	The primary rule for coding most letters in this specific problem.
Pattern Recognition	Identifying recurring relationships or rules in data.	Crucial skill needed to decipher the coding logic from the example.
Exception Handling	Identifying elements that do not follow the general rule.	Necessary because letters 'A' and 'W' have specific, non-standard codes.

Additional Information: Types of Word Coding

Word coding problems are common in reasoning sections of competitive exams. They test your ability to identify patterns and apply logical rules. Here are a few common types:

Alphabetical Position Based: Rules derived directly from the letter's position (forward or reverse), sometimes with simple arithmetic operations (+, -, *, /).
Letter Mapping: One letter is directly substituted by another letter or symbol based on a pattern (e.g., shifting letters by a fixed number, reversing the alphabet).
Word/Sentence Based: Sometimes, words or sentences are coded, and the logic might involve rearranging letters or words, substituting based on position within the word/sentence, or other complex rules.
Mixed Logic: Problems often combine multiple rules, like different rules for vowels and consonants, or rules that change based on the letter's position within the word.

To solve these problems, practice is key. Always start by writing down the given information clearly, like the letters, their positions, and the codes. Then, systematically test different possible relationships and patterns.