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. CAST ∶ DCVX ∶∶ BUSH ∶ CWVL ∶∶ ARMY ∶ ?
BTPC
Understanding Letter-Cluster Analogy Problems
This question asks us to find a relationship between pairs of letter-clusters. We need to figure out how the second letter-cluster in the first pair is formed from the first letter-cluster, and confirm that the same rule applies to the second pair. Once the rule is identified, we will apply it to the fifth letter-cluster to find the missing sixth one.
Analyzing the Relationship: CAST ∶ DCVX
Let's look at the letters in the first pair, CAST and DCVX, position by position. We can determine the position of each letter in the English alphabet (A=1, B=2, ..., Z=26).
| Position | 1st Letter | 2nd Letter | 3rd Letter | 4th Letter |
|---|---|---|---|---|
| CAST | C (3) | A (1) | S (19) | T (20) |
| DCVX | D (4) | C (3) | V (22) | X (24) |
| Change in Position | \$4 - 3 = +1\$ | \$3 - 1 = +2\$ | \$22 - 19 = +3\$ | \$24 - 20 = +4\$ |
From this analysis, it appears that the rule for the first pair is to add 1 to the position of the first letter, add 2 to the position of the second letter, add 3 to the third, and add 4 to the fourth.
Analyzing the Relationship: BUSH ∶ CWVL
Now let's check if the same rule applies to the second pair, BUSH and CWVL.
| Position | 1st Letter | 2nd Letter | 3rd Letter | 4th Letter |
|---|---|---|---|---|
| BUSH | B (2) | U (21) | S (19) | H (8) |
| CWVL | C (3) | W (23) | V (22) | L (12) |
| Change in Position | \$3 - 2 = +1\$ | \$23 - 21 = +2\$ | \$22 - 19 = +3\$ | \$12 - 8 = +4\$ |
The pattern of adding +1, +2, +3, and +4 to the respective letter positions is consistent in both pairs.
Applying the Pattern to ARMY
We will now apply the identified rule (+1, +2, +3, +4) to the letter-cluster ARMY.
- First letter: A (position 1). Add 1: \$1 + 1 = 2\$. The 2nd letter is B.
- Second letter: R (position 18). Add 2: \$18 + 2 = 20\$. The 20th letter is T.
- Third letter: M (position 13). Add 3: \$13 + 3 = 16\$. The 16th letter is P.
- Fourth letter: Y (position 25). Add 4: \$25 + 4 = 29\$. Since there are only 26 letters, we wrap around from Z. Position 26 is Z, 27 is A, 28 is B, 29 is C. The 29th letter is C.
Identifying the Final Letter-Cluster
Applying the rule +1, +2, +3, +4 to the letters of ARMY (A, R, M, Y) gives us the new letters B, T, P, C. Therefore, the letter-cluster related to ARMY is BTPC.
Revision Table: Key Learnings in Letter Analogy
| Concept | Explanation | Importance |
|---|---|---|
| Letter Position | Assigning a numerical value (1-26) to each letter of the alphabet. | Fundamental for identifying patterns based on addition/subtraction. |
| Pattern Identification | Analyzing the change between corresponding letters in the given pairs. | Crucial step to determine the rule governing the relationship. |
| Applying the Rule | Using the identified pattern to transform the new letter-cluster. | Final step to solve the analogy. |
| Alphabet Wrap-around | When a position goes beyond 26, returning to A=27, B=28, etc. | Essential for calculations involving letters near the end of the alphabet. |
Additional Information: Tips for Solving Analogy Problems
- Write down the alphabet and its positions (A=1...Z=26) if needed.
- Examine the change for each corresponding letter carefully.
- Look for patterns involving adding or subtracting numbers, reversing order, or alternating rules.
- Test the discovered pattern on the second given pair to confirm its consistency.
- Apply the confirmed pattern systematically to the new term.
- Be mindful of wrap-around (cyclic nature) of the alphabet.
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