Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster. MGX : VPG :: TZC : CIL :: HPX :?
QYG
Solving Letter Cluster Analogy Problems
This question asks us to find a relationship between pairs of letter clusters. We need to identify the pattern in the first two pairs (MGX : VPG and TZC : CIL) and then apply that same pattern to the third letter cluster (HPX) to find the missing cluster.
Analyzing the First Letter Cluster Pair: MGX to VPG
Let's look at the position of each letter in the alphabet:
- M is the 13th letter.
- G is the 7th letter.
- X is the 24th letter.
For the second cluster VPG:
- V is the 22nd letter.
- P is the 16th letter.
- G is the 7th letter.
Now let's compare the positions:
- M (13) to V (22): $22 - 13 = 9$. This is a difference of $+9$.
- G (7) to P (16): $16 - 7 = 9$. This is a difference of $+9$.
- X (24) to G (7): $7 - 24 = -17$. However, if we wrap around the alphabet (A=1, Z=26), moving 9 positions forward from X (24) would be $24 + 9 = 33$. Since there are only 26 letters, we subtract 26: $33 - 26 = 7$. The 7th letter is G. So, this is also a $+9$ pattern with wrapping.
The pattern observed from MGX to VPG is adding 9 to the position of each letter in the alphabet, wrapping around from Z to A if needed.
Verifying the Pattern with the Second Pair: TZC to CIL
Let's check if the same $+9$ pattern applies to the second pair TZC to CIL.
- T is the 20th letter. $20 + 9 = 29$. $29 - 26 = 3$. The 3rd letter is C.
- Z is the 26th letter. $26 + 9 = 35$. $35 - 26 = 9$. The 9th letter is I.
- C is the 3rd letter. $3 + 9 = 12$. The 12th letter is L.
The pattern holds true for the second pair as well. Adding 9 to the position of each letter in TZC gives us CIL.
Applying the Pattern to the Fifth Letter Cluster: HPX
Now we apply the $+9$ pattern to the letters in HPX to find the missing letter cluster.
- H is the 8th letter. $8 + 9 = 17$. The 17th letter is Q.
- P is the 16th letter. $16 + 9 = 25$. The 25th letter is Y.
- X is the 24th letter. $24 + 9 = 33$. $33 - 26 = 7$. The 7th letter is G.
Applying the pattern to HPX results in the letter cluster QYG.
Comparing with Options
Let's compare our result, QYG, with the given options:
- Option 1: PXF
- Option 2: QZG
- Option 3: RZG
- Option 4: QYG
Our calculated letter cluster QYG matches Option 4.
Conclusion
The relationship between the letter clusters in each pair is based on adding 9 to the alphabetical position of each letter. Applying this rule to HPX yields QYG.
| Original Cluster | Position | Position + 9 | New Position (mod 26) | Result Cluster |
|---|---|---|---|---|
| M | 13 | $13+9=22$ | 22 | VPG |
| G | 7 | $7+9=16$ | 16 | |
| X | 24 | $24+9=33$ | $33 \pmod{26} = 7$ | |
| T | 20 | $20+9=29$ | $29 \pmod{26} = 3$ | CIL |
| Z | 26 | $26+9=35$ | $35 \pmod{26} = 9$ | |
| C | 3 | $3+9=12$ | 12 | |
| H | 8 | $8+9=17$ | 17 | QYG |
| P | 16 | $16+9=25$ | 25 | |
| X | 24 | $24+9=33$ | $33 \pmod{26} = 7$ |
Revision Table: Key Concepts for Letter Series Reasoning
Understanding the fundamentals of letter series and analogy problems is crucial for competitive exams. Here's a quick revision:
| Concept | Description | Application in Problems |
|---|---|---|
| Alphabet Position | Assigning a numerical value (1-26) to each letter of the alphabet (A=1, B=2, ..., Z=26). | Finding arithmetic patterns (addition, subtraction, multiplication, division) between letter positions. |
| Alphabet Reversal | Pairing letters from opposite ends of the alphabet (A-Z, B-Y, C-X, etc.). | Identifying patterns based on reversed positions (e.g., A is 1st, Z is 1st from end; B is 2nd, Y is 2nd from end). Sum of positions is often 27. |
| Skip Counting | Patterns involving skipping a fixed number of letters (e.g., A, C, E... - skipping one letter). | Analyzing the difference in position or the number of letters between consecutive terms. |
| Vowels/Consonants | Patterns based on the properties of vowels (A, E, I, O, U) and consonants. | Identifying sequences where only vowels or consonants appear, or where they alternate. |
Additional Information on Reasoning Patterns
Letter cluster analogies often involve various types of patterns, not just simple arithmetic progressions. Here are a few more ideas that might be used in similar problems:
- Positional Shifts: Letters might shift a certain number of places forward or backward in the alphabet. The shift can be constant (+9 in our case), increasing, decreasing, or follow another numerical sequence.
- Reverse Alphabetical Order: The pattern might involve using the reverse alphabetical order (Z=1, Y=2, ..., A=26).
- Mixing Patterns: Different positions within the letter cluster might follow different rules (e.g., the first letter shifts by +2, the second by +3, the third by +4).
- Sum/Difference of Positions: The pattern could relate to the sum or difference of the letter positions within the cluster itself or between corresponding letters in the pair.
- Specific Letter Properties: Patterns might involve specific properties like only vowels, only consonants, alternating vowel/consonant, or letters related to common words.
To solve these problems effectively, it's helpful to know the alphabetical position of each letter by heart and practice identifying different types of logical patterns quickly.
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