Decoding the Code: Finding the Pattern in RACER and USAGE

This question asks us to find a hidden rule or pattern used to convert words into numbers in a specific code language. We are given two examples: 'RACER' is coded as '46', and 'USAGE' is coded as '54'. Our task is to use these examples to figure out the coding logic and then apply it to find the code for the word 'ESSAY'.

Analyzing the Given Codes and Words

Let's look at the letters in the words and their numerical values. A common approach in such coding-decoding problems is to use the alphabetical position of each letter (A=1, B=2, C=3, ..., Z=26).

Let's analyze the first example: 'RACER' coded as '46'.

• R is the 18th letter.
• A is the 1st letter.
• C is the 3rd letter.
• E is the 5th letter.
• R is the 18th letter.

Let's sum these positions: $18 + 1 + 3 + 5 + 18 = 45$.

The coded value is 46. The sum we got is 45. The difference is $46 - 45 = 1$. This suggests the rule might involve summing the alphabetical positions and then adding 1.

Testing the Pattern with the Second Example: USAGE

Let's apply the potential rule (sum of alphabetical positions + 1) to the second example: 'USAGE' coded as '54'.

• U is the 21st letter.
• S is the 19th letter.
• A is the 1st letter.
• G is the 7th letter.
• E is the 5th letter.

Let's sum these positions: $21 + 19 + 1 + 7 + 5 = 53$.

The coded value is 54. The sum we got is 53. The difference is $54 - 53 = 1$. This matches the pattern observed with 'RACER'. The logic seems to be correct: sum the alphabetical positions of all letters in the word and add 1 to the total.

Applying the Coding Logic to ESSAY

Now, let's apply this established rule to find the code for the word 'ESSAY'.

• E is the 5th letter.
• S is the 19th letter.
• S is the 19th letter.
• A is the 1st letter.
• Y is the 25th letter.

Let's sum the alphabetical positions of the letters in 'ESSAY':

$5 + 19 + 19 + 1 + 25$

Adding these values:

$5 + 19 = 24$

$24 + 19 = 43$

$43 + 1 = 44$

$44 + 25 = 69$

The sum of the alphabetical positions is 69.

According to the pattern, we need to add 1 to this sum:

$69 + 1 = 70$

So, the code for 'ESSAY' is 70.

Conclusion on the ESSAY Code

Based on the coding pattern observed in the examples 'RACER' (46) and 'USAGE' (54), the code for 'ESSAY' is calculated to be 70. The pattern involves summing the alphabetical positions of the letters in the word and adding 1 to the total sum.

Revision Table: Alphabetical Positions Used

Additional Information on Coding-Decoding Patterns

Coding-decoding questions in reasoning tests can use various patterns. Besides the sum of alphabetical positions, other common patterns include:

• Sum of Reverse Alphabetical Positions: Z=1, Y=2, ..., A=26.
• Difference or Sum of Positions with Modification: Adding/subtracting a fixed number, multiplying/dividing the sum.
• Position of Vowels/Consonants: Separate rules for vowels and consonants, or counting their numbers.
• Specific Letter Values: Assigning arbitrary values to specific letters.
• Combination of Rules: Using more than one rule based on position, type of letter, etc.

Always look for consistency across the given examples to confirm the identified pattern before applying it to the word in question.