Understanding the Coding Pattern

This question asks us to decipher a specific coding pattern used to convert words into numbers. We are given an example: the word DOG is coded as 4157. We need to use this example to figure out the rule and then apply it to find the code for the word MAT.

Analysing the Example: DOG to 4157

Let's look at the letters in the word DOG and their positions in the English alphabet:

• The letter D is the 4th letter of the alphabet.
• The letter O is the 15th letter of the alphabet.
• The letter G is the 7th letter of the alphabet.

Now let's compare these positions with the given code, 4157.

We can see the following correlation:

• The first letter D corresponds to the number 4, which is its alphabet position.
• The last letter G corresponds to the number 7, which is its alphabet position.
• The middle letter O corresponds to the number 15, which is its alphabet position.

It appears the code is formed by simply concatenating the numerical positions of the letters in the word, in order from left to right.

Let's verify this pattern:

$\text{D} \rightarrow 4^{\text{th}} \text{ letter} \rightarrow 4$
$\text{O} \rightarrow 15^{\text{th}} \text{ letter} \rightarrow 15$
$\text{G} \rightarrow 7^{\text{th}} \text{ letter} \rightarrow 7$

Concatenating these numbers ($4$, $15$, $7$) gives us $4157$. This matches the given code for DOG, confirming our pattern.

Applying the Pattern to MAT

Now we apply the same rule to the word MAT. We need to find the alphabet position for each letter in MAT:

• The letter M is the 13th letter of the alphabet.
• The letter A is the 1st letter of the alphabet.
• The letter T is the 20th letter of the alphabet.

According to the pattern, we concatenate these numerical positions in order:

$\text{M} \rightarrow 13^{\text{th}} \text{ letter} \rightarrow 13$
$\text{A} \rightarrow 1^{\text{st}} \text{ letter} \rightarrow 1$
$\text{T} \rightarrow 20^{\text{th}} \text{ letter} \rightarrow 20$

Concatenating these numbers ($13$, $1$, $20$) gives us $13120$.

Comparing with Options

Let's compare our calculated code for MAT with the given options:

• Option 1: 12120
• Option 2: 13012
• Option 3: 13120
• Option 4: 14120

Our calculated code, 13120, matches Option 3.

Conclusion

The coding pattern used is to represent each letter by its position in the English alphabet and then concatenate these numbers to form the code for the word. Following this pattern, the word MAT is coded as 13120.

Revision Table: Coding and Decoding

Understanding letter-to-number codes is important for logical reasoning tests. The key is to identify the rule applied in the given example.

• Identify the rule: Look at the relationship between the letters of the word and the numbers in the code. Is it based on position, reverse position, sum of positions, etc.?
• Test the rule: Apply the potential rule to the given example (DOG to 4157) to see if it matches.
• Apply the rule: Once the rule is confirmed, apply it to the new word (MAT).
• Verify the answer: Check if the result matches any of the options provided.

Additional Information: Types of Letter Coding

Coding-decoding questions can involve various patterns. Some common types include:

• Alphabet Position: Using the serial number of letters (A=1, B=2, ..., Z=26). This is the pattern used in this question.
• Reverse Alphabet Position: Using the position from the end (A=26, B=25, ..., Z=1).
• Letter Shifting: Shifting letters by a fixed number of positions (e.g., A becomes C, B becomes D - shifting by +2).
• Opposite Letters: Using letters that are opposite in the alphabet (A opposite Z, B opposite Y, etc.).
• Mixed Patterns: Combinations of the above or other unique logical rules.

Practicing different types helps in quickly identifying the pattern during exams.