Understanding Letter Analogy and Finding the Pattern

Letter analogy questions test your ability to identify the relationship between a pair of letter-clusters and apply that same relationship to another letter-cluster to find the missing one. In the given question, we have the analogy: KSZ : PHC :: TNK : ? We need to find the letter-cluster that replaces the question mark.

Let's analyze the relationship between the first pair of letter-clusters, KSZ and PHC. We can look at the positions of the letters in the English alphabet (A=1, B=2, ..., Z=26).

Let's examine the correspondence between the letters of KSZ and PHC by their positions:

• First letter: K (11) corresponds to P (16)
• Second letter: S (19) corresponds to H (8)
• Third letter: Z (26) corresponds to C (3)

Now let's look for a pattern in these correspondences.

Identifying the Relationship for KSZ to PHC

Let's consider different types of relationships, such as position shifts or reverse letters.

• For the first letter, K (11) to P (16): The shift is $+5$ positions ($\text{11} \xrightarrow{+5} \text{16}$).
• For the second letter, S (19) to H (8): The shift is $-11$ positions ($\text{19} \xrightarrow{-11} \text{8}$). However, let's think about reverse letters. Two letters are reverses of each other if their positions add up to 27. K is 11th, its reverse is P (16th), $11+16=27$. S is 19th, its reverse is H (8th), $19+8=27$. Z is 26th, its reverse is A (1st), $26+1=27$.

Looking at KSZ $\rightarrow$ PHC:

• K $\rightarrow$ P: P is the reverse of K.
• S $\rightarrow$ H: H is the reverse of S.
• Z $\rightarrow$ C: C is NOT the reverse of Z (reverse is A). Let's revisit the position shift here. Z is 26th, C is 3rd. To go from Z to C, we wrap around: Z $\rightarrow$ A $\rightarrow$ B $\rightarrow$ C. This is a shift of $+3$ positions ($\text{26} \xrightarrow{+3} \text{3 mod 26}$).

So, the pattern seems to be:

1. The first letter is replaced by its alphabetical reverse.
2. The second letter is replaced by its alphabetical reverse.
3. The third letter is replaced by a letter that is 3 positions ahead in the alphabet (wrapping around from Z to A).

Applying the Pattern to TNK

Now, let's apply this identified pattern to the letter-cluster TNK to find the missing letter-cluster.

We will apply the rule to each letter of TNK:

• First letter (T): Apply Rule 1 (reverse). The position of T is 20. Its reverse will have position $27 - 20 = 7$. The 7th letter of the alphabet is G. So, T $\rightarrow$ G.
• Second letter (N): Apply Rule 2 (reverse). The position of N is 14. Its reverse will have position $27 - 14 = 13$. The 13th letter of the alphabet is M. So, N $\rightarrow$ M.
• Third letter (K): Apply Rule 3 (+3 shift). The position of K is 11. We shift 3 positions ahead: $11 + 3 = 14$. The 14th letter of the alphabet is N. So, K $\rightarrow$ N.

Combining the resulting letters, we get GMN.

Comparing with Options

Let's check the options provided:

1. MGN
2. GNO
3. GMO
4. GMN

Our derived letter-cluster is GMN, which matches Option 4.

Conclusion

The relationship between KSZ and PHC follows the pattern where the first two letters are replaced by their alphabetical reverses, and the third letter is shifted 3 positions forward. Applying this same pattern to TNK results in GMN.

Revision Table: Letter Analogy Pattern

Additional Information on Letter Reasoning

Letter reasoning questions often involve patterns based on:

• Alphabetical Position: Adding or subtracting a fixed number from the letter's position.
• Position Shift Sequence: Applying a sequence of shifts (e.g., +1, +2, +3) to consecutive letters.
• Reverse Letters: Using the letter which is equidistant from the end of the alphabet as the original letter is from the beginning (sum of positions is 27).
• Skip Letters: Skipping a fixed number of letters between the corresponding letters.
• Vowel/Consonant Pattern: Rules that apply differently to vowels and consonants.
• Combination of Patterns: Using different rules for different letter positions within the cluster, as seen in this problem.

Solving these questions requires familiarity with the alphabet and practicing different types of pattern identification.