Understanding the Code Language Pattern

The question asks us to find a specific pattern or rule that converts words into numbers in a certain code language. We are given two examples: 'BOOK' is coded as '325', and 'READ' is coded as '400'. We need to use these examples to figure out the rule and then apply it to find the code for 'ABLE'. This is a common type of letter coding or word coding problem often found in reasoning tests.

Analyzing the Examples: BOOK and READ Coding

Let's look closely at the words 'BOOK' and 'READ' and their corresponding codes '325' and '400'. We need to think about how letters can be converted into numbers. Common methods involve using the alphabetical position of the letters (A=1, B=2, ..., Z=26) or perhaps reversed positions (Z=1, Y=2, ..., A=26).

Exploring Positional Values

First, let's try using the standard positional values of the letters:

• BOOK: B=2, O=15, O=15, K=11. Sum = $2+15+15+11 = 43$. The code is 325. It's not immediately obvious how 43 relates to 325.
• READ: R=18, E=5, A=1, D=4. Sum = $18+5+1+4 = 28$. The code is 400. Again, no simple relationship like direct multiplication or squaring seems to work directly with the sum of standard values.

Exploring Reversed Positional Values

Let's try using the reversed positional values. In this system, A=26, B=25, C=24, and so on, with Z=1. The reversed value of a letter can be found by subtracting its standard value from 27 (since Standard Value + Reversed Value = 27 for any letter).

Let's calculate the reversed positional values for 'BOOK':

• B: $27 - (\text{Standard value of B}) = 27 - 2 = 25$
• O: $27 - (\text{Standard value of O}) = 27 - 15 = 12$
• O: $27 - (\text{Standard value of O}) = 27 - 15 = 12$
• K: $27 - (\text{Standard value of K}) = 27 - 11 = 16$

The sum of reversed values for 'BOOK' is $25 + 12 + 12 + 16 = 65$.

Now let's see how 65 relates to the code '325'. We notice that $65 \times 5 = 325$. This looks promising. What could the multiplier '5' represent in relation to the word 'BOOK'?

'BOOK' has 4 letters. The multiplier 5 is equal to the number of letters in the word plus one ($4+1=5$).

Let's test this potential rule with the second example, 'READ', which is coded as '400'.

Calculate the reversed positional values for 'READ':

• R: $27 - (\text{Standard value of R}) = 27 - 18 = 9$
• E: $27 - (\text{Standard value of E}) = 27 - 5 = 22$
• A: $27 - (\text{Standard value of A}) = 27 - 1 = 26$
• D: $27 - (\text{Standard value of D}) = 27 - 4 = 23$

The sum of reversed values for 'READ' is $9 + 22 + 26 + 23 = 80$.

'READ' also has 4 letters. If the rule holds, the code should be the sum of reversed values multiplied by (Number of letters + 1).

Code for 'READ' = Sum of reversed values $\times$ (Number of letters + 1) $= 80 \times (4+1) = 80 \times 5 = 400$.

This calculation matches the given code '400' for 'READ'. So, the rule based on reversed positional values and the number of letters is consistent for both examples.

Determining the Code Language Rule

Based on the analysis of 'BOOK' and 'READ', the rule used in this code language is:

Code = (Sum of Reversed Positional Values of Letters in the Word) $\times$ (Number of Letters in the Word + 1)

Where the Reversed Positional Value of a letter is calculated as $27 - $ its Standard Positional Value (A=1, B=2, ... Z=26).

Applying the Rule to Find the Code for ABLE

Now we apply the same rule to find the code for the word 'ABLE'.

First, find the number of letters in 'ABLE'. There are 4 letters.

Next, find the reversed positional values for each letter in 'ABLE':

• A: $27 - (\text{Standard value of A}) = 27 - 1 = 26$
• B: $27 - (\text{Standard value of B}) = 27 - 2 = 25$
• L: $27 - (\text{Standard value of L}) = 27 - 12 = 15$
• E: $27 - (\text{Standard value of E}) = 27 - 5 = 22$

Calculate the sum of these reversed positional values:

Sum of reversed values for 'ABLE' = $26 + 25 + 15 + 22 = 88$.

Finally, apply the rule to find the code for 'ABLE':

Code for 'ABLE' = Sum of reversed values $\times$ (Number of letters + 1)

Code for 'ABLE' $= 88 \times (4 + 1) = 88 \times 5$.

Performing the multiplication: $88 \times 5 = 440$.

Conclusion: Code for ABLE

Following the established pattern from the examples 'BOOK' (325) and 'READ' (400), the code for 'ABLE' is 440.

Revision Table: Letter Coding Fundamentals

Additional Information: Mastering Code Language Questions

Code language questions, like the one involving 'BOOK', 'READ', and 'ABLE', are designed to test your pattern recognition and logical deduction skills. Success in solving these problems comes from systematically exploring possible relationships between the input (the word) and the output (the code).

Here are some tips for tackling letter coding problems:

• Write down the standard (1-26) and reversed (26-1) positional values of the alphabet for quick reference.
• Look for simple patterns first: Is the code the sum of standard values? Is it related to the first or last letter?
• Consider reversed positional values if standard values don't reveal a clear pattern.
• Check if the number of letters in the word plays a role, perhaps as a multiplier, adder, or part of an exponent.
• Look for patterns involving vowels and consonants.
• Test any potential rule with all the given examples to ensure it is consistent.
• If the numbers are large, consider multiplication or squaring of values or sums. If they are small, consider division or subtraction.

By practicing different types of coding questions, you will become more adept at quickly identifying the underlying logic and applying it to find the correct code for the target word, such as finding the code for 'ABLE' in this case.