Understanding the Logic Puzzle

This problem asks us to identify a relationship between pairs of letter-number combinations and apply that same relationship to a new combination. We are given two examples of this relationship:

• DM 12 is related to HQ 17
• TS 19 is related to XW 24

We need to find which option KG 17 is related to following the exact same logic.

Analyzing the Pattern: Letters and Numbers

Let's break down the pattern into two parts: the change in the letters and the change in the numbers.

Letter Pattern Analysis

We look at the transformation of the letter pairs in the given examples:

Example 1: DM to HQ

• First letter: D to H. The alphabetical position of D is 4, and H is 8. The change is $\text{Position}(H) - \text{Position}(D) = 8 - 4 = 4$. The first letter moves 4 steps forward.
• Second letter: M to Q. The alphabetical position of M is 13, and Q is 17. The change is $\text{Position}(Q) - \text{Position}(M) = 17 - 13 = 4$. The second letter also moves 4 steps forward.

Example 2: TS to XW

• First letter: T to X. The alphabetical position of T is 20, and X is 24. The change is $\text{Position}(X) - \text{Position}(T) = 24 - 20 = 4$. The first letter moves 4 steps forward.
• Second letter: S to W. The alphabetical position of S is 19, and W is 23. The change is $\text{Position}(W) - \text{Position}(S) = 23 - 19 = 4$. The second letter also moves 4 steps forward.

The letter pattern is consistent: both letters in the pair move 4 positions forward in the English alphabet.

Number Pattern Analysis

Now, let's look at the transformation of the numbers associated with the pairs:

• DM 12 is related to HQ 17. The number changes from 12 to 17. The change is $17 - 12 = 5$. The number increases by 5.
• TS 19 is related to XW 24. The number changes from 19 to 24. The change is $24 - 19 = 5$. The number increases by 5.

The number pattern is consistent: the number increases by 5.

Applying the Pattern to KG 17

We need to apply the established patterns to KG 17 to find the related combination.

Applying the Letter Pattern to KG

• First letter: K. The alphabetical position of K is 11. Moving 4 steps forward: $11 + 4 = 15$. The letter at position 15 is O.
• Second letter: G. The alphabetical position of G is 7. Moving 4 steps forward: $7 + 4 = 11$. The letter at position 11 is K.

So, the letter pair related to KG is OK.

Applying the Number Pattern to 17

The number associated with KG is 17. The pattern shows the number increases by 5.

• Number: 17. Adding 5: $17 + 5 = 22$.

So, the number related to 17 is 22.

Determining the Related Combination

Combining the results for the letters and the number, KG 17 is related to OK 22.

Comparing with Options

Let's check the given options to find OK 22:

1. MK 20
2. OK 22
3. NK 22
4. NJ 21

Option 2, OK 22, matches the combination derived from applying the discovered logic pattern.

Revision Table: Pattern Summary

Additional Information: Logic Reasoning Patterns

Logic reasoning questions often involve identifying patterns in sequences of letters, numbers, or symbols. These patterns can be based on:

• Alphabetical Position: Moving a fixed number of steps forward or backward in the alphabet.
• Mathematical Operations: Adding, subtracting, multiplying, or dividing numbers by a fixed value or a value that changes according to a pattern.
• Combination of Patterns: As seen in this question, a pattern can involve transformations applied simultaneously to different parts of the given elements (like letters and numbers).
• Specific Sequences: Patterns might relate to prime numbers, square numbers, cube numbers, or positions in the alphabet that correspond to such sequences.

To solve such problems, it is crucial to systematically analyze the given examples, isolate the different components (letters, numbers, symbols), identify the rule governing the transformation of each component, and then apply these rules to the new element.