Understanding the Coding Pattern

This question asks us to identify a coding pattern based on two examples and apply it to a new word. The examples link letter sequences ('QKV', 'SHY') to numerical codes ('14819', '16522'). We need to find the code for 'MDS' following the same logic.

Decoding 'QKV' to '14819'

First, let's determine the standard alphabetical position for each letter in 'QKV':

• Q is the 17^th letter of the alphabet.
• K is the 11^th letter of the alphabet.
• V is the 22^nd letter of the alphabet.

If we represent these positions numerically, we get 17, 11, 22.

Now, let's compare this sequence (17, 11, 22) with the given code '14819'. A simple concatenation doesn't work. Let's explore a possible mathematical transformation. A common technique in these problems is subtracting a constant value.

Let's try subtracting 3 from each alphabetical position:

• For Q: $17 - 3 = 14$
• For K: $11 - 3 = 8$
• For V: $22 - 3 = 19$

Concatenating these results (14, 8, 19) yields '14819'. This perfectly matches the code provided for 'QKV'.

Validating the Pattern with 'SHY' to '16522'

To ensure this pattern is correct, let's apply it to the second example, 'SHY' which is coded as '16522'.

Find the alphabetical positions for the letters in 'SHY':

• S is the 19^th letter.
• H is the 8^th letter.
• Y is the 25^th letter.

The sequence of positions is 19, 8, 25.

Applying the rule of subtracting 3 from each position:

• For S: $19 - 3 = 16$
• For H: $8 - 3 = 5$
• For Y: $25 - 3 = 22$

Concatenating these results (16, 5, 22) gives '16522'. This matches the code given for 'SHY', confirming the pattern: find the alphabetical position, subtract 3, and concatenate the results.

Coding 'MDS' Using the Identified Pattern

Finally, we apply this established pattern to find the code for 'MDS'.

First, list the alphabetical positions of the letters in 'MDS':

• M is the 13^th letter.
• D is the 4^th letter.
• S is the 19^th letter.

Next, subtract 3 from each of these positions:

• For M: $13 - 3 = 10$
• For D: $4 - 3 = 1$
• For S: $19 - 3 = 16$

The resulting numbers are 10, 1, and 16.

Concatenate these numbers in order to get the final code:

10 followed by 1 followed by 16 gives the code '10116'.

Conclusion on MDS Code

By identifying and applying the consistent pattern of subtracting 3 from the alphabetical position of each letter, the code for 'MDS' is determined to be '10116'.