Select the letter-cluster that can replace the question mark (?) in the following series.
AIW
Analyzing the Letter-Cluster Series Pattern
The question asks us to find the next letter-cluster in the given series: KQG, JTK, HXO, ECS, ?
To solve this, we need to identify the pattern between the consecutive letter-clusters. Let's examine the position of each letter in the alphabet (A=1, B=2, ..., Z=26).
Step-by-Step Pattern Analysis
We will analyze the pattern for each position (first, second, and third letter) independently.
First Letter Pattern
- KQG to JTK: K is the 11th letter, J is the 10th letter. The change is \(10 - 11 = -1\).
- JTK to HXO: J is the 10th letter, H is the 8th letter. The change is \(8 - 10 = -2\).
- HXO to ECS: H is the 8th letter, E is the 5th letter. The change is \(5 - 8 = -3\).
The pattern for the first letter is a decrease by 1, then 2, then 3. Following this pattern, the next decrease should be by 4.
Current first letter is E (5th letter). \(5 - 4 = 1\). The 1st letter is A.
So, the first letter of the next cluster is A.
Second Letter Pattern
- KQG to JTK: Q is the 17th letter, T is the 20th letter. The change is \(20 - 17 = +3\).
- JTK to HXO: T is the 20th letter, X is the 24th letter. The change is \(24 - 20 = +4\).
- HXO to ECS: X is the 24th letter, C is the 3rd letter. Moving from X (24), Y(25), Z(26), A(1), B(2), C(3). The change is \(+5\).
The pattern for the second letter is an increase by 3, then 4, then 5. Following this pattern, the next increase should be by 6.
Current second letter is C (3rd letter). \(3 + 6 = 9\). The 9th letter is I.
So, the second letter of the next cluster is I.
Third Letter Pattern
- KQG to JTK: G is the 7th letter, K is the 11th letter. The change is \(11 - 7 = +4\).
- JTK to HXO: K is the 11th letter, O is the 15th letter. The change is \(15 - 11 = +4\).
- HXO to ECS: O is the 15th letter, S is the 19th letter. The change is \(19 - 15 = +4\).
The pattern for the third letter is a consistent increase by 4.
Current third letter is S (19th letter). \(19 + 4 = 23\). The 23rd letter is W.
So, the third letter of the next cluster is W.
Determining the Next Letter-Cluster
Combining the letters found for each position:
- First letter: A
- Second letter: I
- Third letter: W
The next letter-cluster in the series is AIW.
Summary of Patterns
| Position | Letter Sequence | Pattern |
|---|---|---|
| First Letter | K, J, H, E, ? | -1, -2, -3, -4 |
| Second Letter | Q, T, X, C, ? | +3, +4, +5, +6 |
| Third Letter | G, K, O, S, ? | +4, +4, +4, +4 |
Conclusion
Based on the identified patterns for each letter position, the next letter-cluster after ECS is AIW.
Revision Table: Letter Series Analysis
| Cluster | Letter 1 | Letter 2 | Letter 3 |
|---|---|---|---|
| KQG | K (11) | Q (17) | G (7) |
| JTK | J (10) | T (20) | K (11) |
| HXO | H (8) | X (24) | O (15) |
| ECS | E (5) | C (3) | S (19) |
| Next (AIW) | A (1) | I (9) | W (23) |
| Pattern Step | -1, -2, -3, -4 | +3, +4, +5, +6 | +4, +4, +4, +4 |
Additional Information on Letter Sequence Patterns
Letter sequence questions are common in logical reasoning tests. They require you to identify the underlying rule or pattern governing the progression of letters or letter clusters. Common patterns include:
- Consistent addition or subtraction of a number from the letter's position in the alphabet.
- Sequential addition or subtraction where the number changes by a constant value (e.g., +2, +3, +4).
- Alternating patterns.
- Patterns based on vowels or consonants.
- Skipping a fixed number of letters.
Solving these types of questions often involves writing down the letter positions and calculating the difference or relationship between consecutive terms.
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