Understanding the Coding Language Pattern

This type of question involves identifying a hidden pattern or logic used to code words into numbers. We are given two examples to help us figure out the rule: 'CURSOR' is coded as '564' and 'BOY' is coded as '126'. Our goal is to apply this logic to find the code for 'FREE'.

Analyzing the Examples

Let's look at the first example:

Word: CURSOR

• Number of letters: 6
• Coded value: 564

Now, let's look at the second example:

Word: BOY

• Number of letters: 3
• Coded value: 126

The coded values seem relatively large compared to the number of letters. Let's consider the alphabetical position of each letter (A=1, B=2, ..., Z=26).

Calculating Letter Positions and Sums

For 'CURSOR':

Sum of positions for CURSOR = \({3 + 21 + 18 + 19 + 15 + 18 = 94}\).

For 'BOY':

Sum of positions for BOY = \({2 + 15 + 25 = 42}\).

Discovering the Coding Logic

Let's see if there's a relationship between the sum of positions, the number of letters, and the coded value.

• For CURSOR: Sum = 94, Number of letters = 6, Coded value = 564. Is there a link between 94, 6, and 564? Let's try multiplying the sum by the number of letters: \({94 \times 6 = 564}\). This matches the coded value!
• For BOY: Sum = 42, Number of letters = 3, Coded value = 126. Let's apply the same logic: \({42 \times 3 = 126}\). This also matches the coded value!

The logic appears to be consistent across both examples.

The coding rule is: Coded Value = (Sum of alphabetical positions of letters) × (Number of letters in the word).

Applying the Logic to 'FREE'

Now we will apply this rule to the word 'FREE'.

Word: FREE

• Number of letters: 4

Let's find the alphabetical position for each letter in 'FREE':

Sum of positions for FREE = \({6 + 18 + 5 + 5 = 34}\).

Now, apply the coding rule:

Coded value for FREE = (Sum of positions) × (Number of letters)

Coded value for FREE = \({34 \times 4}\)

Coded value for FREE = \({136}\)

So, 'FREE' will be written as '136' in that code language.

Conclusion

Based on the pattern observed in the examples 'CURSOR' and 'BOY', the word 'FREE' is coded as '136'.

Revision Table: Coding Logic Summary

Additional Information: Solving Coding Problems

Coding and decoding questions are common in logical reasoning and aptitude tests. They require you to identify a specific rule or pattern used to transform one set of information (like words) into another (like numbers or other words). Here are some common patterns to look for:

• Letter Position: Using the alphabetical order (A=1, B=2, etc.). The pattern might involve the sum, difference, product, or individual digits of these positions.
• Number of Letters: The coded value might be directly related to the count of letters.
• Consonants and Vowels: The pattern might differentiate between consonants and vowels, assigning different values or rules to them.
• Reverse Alphabetical Position: Using Z=1, Y=2, etc.
• Difference/Sum of Positions: The difference or sum of positions of the first and last letter, or other specific letters.
• Skipping/Adding Letters: Shifting letters by a fixed number of steps forward or backward in the alphabet (like in a Caesar cipher, though this is a numerical code).
• Combination of Rules: Often, the pattern is a combination of several simpler rules, as seen in this problem (sum of positions combined with the number of letters).

Solving these problems effectively often involves:

• Carefully analyzing the given examples.
• Testing different potential patterns systematically.
• Performing calculations accurately.