Solving the Letter Cluster Analogy: CA to GH, TK to ?

This question asks us to find the relationship between two letter clusters, CA and GH, and then apply the same relationship to the third letter cluster, TK, to find the fourth one. This type of problem tests our ability to identify patterns and apply them.

Analyzing the Relationship between CA and GH

Let's look at the position of each letter in the English alphabet:

• C is the 3rd letter.
• A is the 1st letter.
• G is the 7th letter.
• H is the 8th letter.

Now, let's see how the positions change from CA to GH:

• The first letter changes from C (3rd) to G (7th). The difference in position is \(7 - 3 = +4\).
• The second letter changes from A (1st) to H (8th). The difference in position is \(8 - 1 = +7\).

So, the pattern is: the first letter's position increases by 4, and the second letter's position increases by 7.

Applying the Pattern to TK

Now we will apply the same pattern to the letter cluster TK.

First, let's find the positions of the letters in TK:

• T is the 20th letter.
• K is the 11th letter.

Now, let's apply the shifts we found:

• For the first letter (T, 20th position), we add 4: \(20 + 4 = 24\). The 24th letter is X.
• For the second letter (K, 11th position), we add 7: \(11 + 7 = 18\). The 18th letter is R.

Combining the new letters, we get the cluster XR.

Verification with Options

Let's check if XR is among the given options:

1. XR
2. YR
3. YS
4. XS

Our derived letter cluster, XR, matches option 1.

Conclusion on Letter Cluster Analogy

Based on the analysis of the pattern between CA and GH, applying the same logic to TK results in the letter cluster XR. The relationship involves a fixed increase in the alphabetical position of each letter.

The shifts are:

• First letter shift: \(7 - 3 = +4\)
• Second letter shift: \(8 - 1 = +7\)

Applying these shifts to TK:

• T (20) \(\xrightarrow{+4}\) X (24)
• K (11) \(\xrightarrow{+7}\) R (18)

Thus, TK is related to XR in the same way CA is related to GH.

Revision Table: Letter Analogy Practice

Understanding letter positions is key to solving such analogy problems quickly.

Additional Information: Tips for Letter Reasoning

Letter-based reasoning questions, like letter cluster analogies, often involve patterns related to:

• Alphabetical position of letters (A=1, B=2, ..., Z=26).
• Skipping letters (e.g., skipping one letter, skipping two letters).
• Forward or backward movement in the alphabet.
• Vowel/consonant patterns.
• Reversal of letter order.
• Combinations of these patterns.

Practicing with different types of letter series and analogy problems helps in quickly identifying the underlying rule.