Understanding the Code Language

The problem describes a specific code language where words are represented by numerical codes. We are given two examples of words and their corresponding codes to help us understand the rules of this language:

• 'CAKE' is coded as '6874'
• 'EASY' is coded as '4882'

Our goal is to find the code for the word 'MAKE' using the pattern established by these examples.

Decoding the Given Words

Let's analyze the two examples to see if we can determine the numerical value assigned to each letter. We can look for letters that appear in both words.

From 'CAKE' → '6874':

• C corresponds to 6
• A corresponds to 8
• K corresponds to 7
• E corresponds to 4

From 'EASY' → '4882':

• E corresponds to 4 (This matches the code for E in 'CAKE')
• A corresponds to 8 (This matches the code for A in 'CAKE')
• S corresponds to 8
• Y corresponds to 2

Based on this analysis, we can establish the following letter-to-number mappings:

Notice that the letter 'A' and 'S' both share the code '8'. This is possible in certain coding schemes where the mapping is not strictly one-to-one for all letters. However, 'A', 'K', and 'E' seem to have consistent unique codes based on the examples provided.

Finding the Code for 'MAKE'

Now we need to find the code for the word 'MAKE'. The letters in 'MAKE' are M, A, K, and E.

Using the mappings we found:

• For A, the code is 8.
• For K, the code is 7.
• For E, the code is 4.

The only letter whose code is not directly provided in the examples is 'M'. However, we know the codes for A, K, and E are 8, 7, and 4 respectively. Therefore, the code for 'MAKE' must have the structure:

Code for M |   Code for A   |   Code for K   |   Code for E

Code for M   |   8               |   7               |   4

So, the code for 'MAKE' will be a 4-digit number starting with the code for M, followed by 874. We can look at the given options to determine the code for M.

Let's examine the options:

1. 5875
2. 5874
3. 5884
4. 5774

We are looking for a code that ends in 874 (the code for AKE).

• Option 1 ends in 875, which does not match 874.
• Option 2 ends in 874. The first digit is 5. This suggests the code for M is 5.
• Option 3 ends in 884, which does not match 874.
• Option 4 ends in 774, which does not match 874.

Option 2, '5874', is the only one that fits the structure [Code for M]874, implying that the code for 'M' is 5.

Thus, the code for 'MAKE' is 5874.

Final Answer Derivation

By analyzing the code language using the words 'CAKE' and 'EASY', we derived the codes for individual letters: A=8, K=7, E=4. Applying these to 'MAKE', we see the code must end in 874. Comparing this pattern to the provided options, only '5874' matches, indicating that 'M' is coded as 5.

So, 'MAKE' is written as '5874' in this code language.

Revision Table: Code Language Summary

Additional Information on Coding Language Problems

Coding and decoding problems often appear in reasoning and aptitude tests. These problems test your ability to identify patterns and apply logical rules. Common types of coding include:

• Letter Shifting: Each letter is replaced by a letter a fixed number of positions away in the alphabet (e.g., A becomes C, B becomes D, etc.).
• Direct Letter Coding: Each letter is assigned a specific code (number, symbol, or another letter) regardless of its position in the alphabet. The code may be based on alphabetical position (A=1, B=2, etc.) or an arbitrary mapping provided in the examples, as seen in this problem.
• Mixed Letter Coding: Letters are arranged in a different order, sometimes combined with letter shifting or direct coding.
• Word/Phrase Coding: Entire words or phrases are coded, often involving replacing words with other words based on a hidden rule or context.

In this specific problem, the coding is a form of direct letter coding based on an arbitrary mapping derived from the examples. The key is to carefully compare the given coded words to identify the individual letter codes. When a new word contains letters not seen before (like 'M' in this case), the options usually provide the missing code, allowing you to complete the pattern.