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. HEROES : LBVLBW :: INVEST : FRZBWX :: KIDNAP : ?
OFHRXT
Solving Letter-Cluster Analogy Problems
This question asks us to identify the relationship between letter-clusters and apply that same relationship to a new cluster. We are given two pairs of related letter-clusters: HEROES is related to LBVLBW, and INVEST is related to FRZBWX. We need to find the cluster related to KIDNAP in the same way.
Let's analyze the relationship by looking at the alphabetical position of each letter in the original word and the resulting cluster.
We can assign a numerical value to each letter based on its position in the English alphabet (A=1, B=2, ..., Z=26).
Analyzing the First Letter-Cluster Pair: HEROES and LBVLBW
Let's compare the letters in HEROES and LBVLBW:
| Position | HEROES | Alphabetical Position | LBVLBW | Alphabetical Position | Difference/Shift | Type |
|---|---|---|---|---|---|---|
| 1 | H | 8 | L | 12 | $+12 - 8 = +4$ | Consonant |
| 2 | E | 5 | B | 2 | $+2 - 5 = -3$ | Vowel |
| 3 | R | 18 | V | 22 | $+22 - 18 = +4$ | Consonant |
| 4 | O | 15 | L | 12 | $+12 - 15 = -3$ | Vowel |
| 5 | E | 5 | B | 2 | $+2 - 5 = -3$ | Vowel |
| 6 | S | 19 | W | 23 | $+23 - 19 = +4$ | Consonant |
Looking at the differences, we see a pattern based on whether the letter is a consonant or a vowel (A, E, I, O, U).
- If the letter in HEROES is a consonant (H, R, S), the shift is $+4$.
- If the letter in HEROES is a vowel (E, O, E), the shift is $-3$.
Analyzing the Second Letter-Cluster Pair: INVEST and FRZBWX
Let's check if the same rule applies to the second pair:
| Position | INVEST | Alphabetical Position | FRZBWX | Alphabetical Position | Difference/Shift | Type |
|---|---|---|---|---|---|---|
| 1 | I | 9 | F | 6 | $+6 - 9 = -3$ | Vowel |
| 2 | N | 14 | R | 18 | $+18 - 14 = +4$ | Consonant |
| 3 | V | 22 | Z | 26 | $+26 - 22 = +4$ | Consonant |
| 4 | E | 5 | B | 2 | $+2 - 5 = -3$ | Vowel |
| 5 | S | 19 | W | 23 | $+23 - 19 = +4$ | Consonant |
| 6 | T | 20 | X | 24 | $+24 - 20 = +4$ | Consonant |
The pattern holds true for the second pair as well:
- If the letter in INVEST is a vowel (I, E), the shift is $-3$.
- If the letter in INVEST is a consonant (N, V, S, T), the shift is $+4$.
The established rule is: Consonants shift $+4$ positions forward, and Vowels shift $-3$ positions backward.
Applying the Rule to the Fifth Letter-Cluster: KIDNAP
Now, let's apply this rule to KIDNAP to find the related letter-cluster.
| Position | KIDNAP | Alphabetical Position | Type | Shift | Calculation | New Position | Resulting Letter |
|---|---|---|---|---|---|---|---|
| 1 | K | 11 | Consonant | $+4$ | $11 + 4 = 15$ | 15 | O |
| 2 | I | 9 | Vowel | $-3$ | $9 - 3 = 6$ | 6 | F |
| 3 | D | 4 | Consonant | $+4$ | $4 + 4 = 8$ | 8 | H |
| 4 | N | 14 | Consonant | $+4$ | $14 + 4 = 18$ | 18 | R |
| 5 | A | 1 | Vowel | $-3$ | $1 - 3 = -2$ (wrap around $26 - 2$) | 24 | X |
| 6 | P | 16 | Consonant | $+4$ | $16 + 4 = 20$ | 20 | T |
The resulting letter-cluster for KIDNAP is OFHRXT.
Conclusion
Based on the pattern where consonants shift $+4$ and vowels shift $-3$, the letter-cluster related to KIDNAP is OFHRXT. This matches option 4.
Revision Table: Letter-Cluster Analogy
Understanding the type of transformation (shift, reversal, substitution) and the basis of the rule (position, vowel/consonant, numeric value) is key to solving letter-cluster analogy problems.
| Original Letter | Type | Rule Applied | Resulting Letter |
|---|---|---|---|
| K | Consonant | $+4$ shift | O |
| I | Vowel | $-3$ shift | F |
| D | Consonant | $+4$ shift | H |
| N | Consonant | $+4$ shift | R |
| A | Vowel | $-3$ shift (with wrap-around) | X |
| P | Consonant | $+4$ shift | T |
Additional Information: Alphabetical Reasoning Concepts
Letter-based reasoning questions often involve:
- Alphabetical Position: Using A=1, B=2, etc.
- Letter Shifting: Moving a certain number of positions forward or backward in the alphabet. This can include wrapping around from Z to A or A to Z.
- Vowel/Consonant Rules: Applying different rules based on whether a letter is a vowel or a consonant.
- Reverse Alphabetical Order: Using Z=1, Y=2, etc.
- Skipping Letters: Rules based on skipping a fixed number of letters.
- Combination of Rules: Sometimes multiple rules are combined or applied alternately.
Practice with different types of letter patterns helps in quickly identifying the underlying logic during exams.
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