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. CIVILIAN : AGREFCSF :: DOCTRINE : BMYPLCFW :: EQUATION : ?
COQWNCGF
Understanding Letter Cluster Analogy Patterns
This type of question asks us to find a relationship between two letter clusters and apply the same relationship to a new cluster to find the missing one. We are given two pairs that follow the same rule: CIVILIAN is related to AGREFCSF, and DOCTRINE is related to BMYPLCFW. We need to find the letter cluster related to EQUATION using this same rule.
Analyzing the First Letter Cluster Pair: CIVILIAN and AGREFCSF
Let's look at how each letter in CIVILIAN changes to become the corresponding letter in AGREFCSF. We can use the alphabetical position of each letter (A=1, B=2, ..., Z=26).
| Position | CIVILIAN | Position Value | AGREFCSF | Position Value | Difference | Pattern |
|---|---|---|---|---|---|---|
| 1 | C | 3 | A | 1 | \(1 - 3 = -2\) | \(-2\) |
| 2 | I | 9 | G | 7 | \(7 - 9 = -2\) | |
| 3 | V | 22 | R | 18 | \(18 - 22 = -4\) | \(-4\) |
| 4 | I | 9 | E | 5 | \(5 - 9 = -4\) | |
| 5 | L | 12 | F | 6 | \(6 - 12 = -6\) | \(-6\) |
| 6 | I | 9 | C | 3 | \(3 - 9 = -6\) | |
| 7 | A | 1 | S | 19 | \(19 - 1 = +18\) or \(1 - 8 = -7 \equiv 19 \pmod{26}\) | \(-8\) |
| 8 | N | 14 | F | 6 | \(6 - 14 = -8\) |
Looking at the differences, there seems to be a pattern based on the letter's position in the word. The shifts are -2, -2, -4, -4, -6, -6, -8, -8 for the 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, and 8th letters respectively. When the difference is negative and wraps around the alphabet (like 1 - 8 = -7), we add 26 to find the position (e.g., -7 + 26 = 19, which is S).
Verifying the Pattern with the Second Letter Cluster Pair: DOCTRINE and BMYPLCFW
Let's apply the same shift pattern (-2, -2, -4, -4, -6, -6, -8, -8) to DOCTRINE and see if we get BMYPLCFW.
| Position | DOCTRINE | Position Value | Shift | New Position Value | New Letter | BMYPLCFW |
|---|---|---|---|---|---|---|
| 1 | D | 4 | -2 | \(4 - 2 = 2\) | B | B |
| 2 | O | 15 | -2 | \(15 - 2 = 13\) | M | M |
| 3 | C | 3 | -4 | \(3 - 4 = -1 \equiv 25 \pmod{26}\) | Y | Y |
| 4 | T | 20 | -4 | \(20 - 4 = 16\) | P | P |
| 5 | R | 18 | -6 | \(18 - 6 = 12\) | L | L |
| 6 | I | 9 | -6 | \(9 - 6 = 3\) | C | C |
| 7 | N | 14 | -8 | \(14 - 8 = 6\) | F | F |
| 8 | E | 5 | -8 | \(5 - 8 = -3 \equiv 23 \pmod{26}\) | W | W |
The pattern successfully transforms DOCTRINE into BMYPLCFW. So, the identified positional shift pattern is correct.
Applying the Pattern to EQUATION
Now we apply the same positional shift pattern (-2, -2, -4, -4, -6, -6, -8, -8) to the letter cluster EQUATION.
| Position | EQUATION | Position Value | Shift | New Position Value | New Letter |
|---|---|---|---|---|---|
| 1 | E | 5 | -2 | \(5 - 2 = 3\) | C |
| 2 | Q | 17 | -2 | \(17 - 2 = 15\) | O |
| 3 | U | 21 | -4 | \(21 - 4 = 17\) | Q |
| 4 | A | 1 | -4 | \(1 - 4 = -3 \equiv 23 \pmod{26}\) | W |
| 5 | T | 20 | -6 | \(20 - 6 = 14\) | N |
| 6 | I | 9 | -6 | \(9 - 6 = 3\) | C |
| 7 | O | 15 | -8 | \(15 - 8 = 7\) | G |
| 8 | N | 14 | -8 | \(14 - 8 = 6\) | F |
Applying the pattern to EQUATION results in the letter cluster COQWNCGF.
Comparing with Options
Let's check the generated letter cluster COQWNCGF against the given options:
- Option 1: NUGFSDAX
- Option 2: BURDSTER
- Option 3: VUGHLOPA
- Option 4: COQWNCGF
The calculated result, COQWNCGF, matches Option 4.
Letter Cluster Analogy Revision Table
| Concept | Description | Example (from this problem) |
|---|---|---|
| Letter Cluster Analogy | Finding a pattern between two groups of letters and applying it to a new group. | CIVILIAN:AGREFCSF as DOCTRINE:BMYPLCFW |
| Positional Shift | The shift in the letter's alphabetical position depends on its place in the word. | 1st letter shifts by -2, 3rd by -4, 5th by -6, etc. |
| Alphabetical Position | Assigning a number to each letter (A=1, B=2, ...). | C=3, I=9, V=22, etc. |
| Modular Arithmetic (for wrap-around) | When a shift goes below 'A' (1), wrapping around from 'Z' (26) by adding 26. | \(3 - 4 = -1\), which is \(25\) (Y) after adding 26. |
Additional Information on Letter Series and Analogy
Letter series and analogy questions are common in reasoning tests. They require identifying the rule that connects the terms in the series or the pair of terms in the analogy. Common patterns include:
- Alphabetical Position Shifts: Adding or subtracting a fixed number to the position value of each letter, or shifts that change based on position (as in this question), or shifts based on the letter itself (e.g., vowel vs consonant).
- Reverse Order: Writing the letters of the word in reverse order.
- Skipping Letters: Following a pattern of skipping a certain number of letters in the alphabet.
- Consonant/Vowel Manipulation: Rules that apply specifically to consonants or vowels within the word.
- Combination of Patterns: Often, more than one rule is combined, making the pattern more complex to find.
To solve these problems effectively, it's helpful to:
- Write down the alphabetical positions of letters.
- Look for differences or relationships between corresponding letters.
- Check if the pattern is consistent across all given pairs.
- Apply the pattern systematically to find the missing term.
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