Understanding Letter-Cluster Analogies

This question asks us to find the relationship between two letter-clusters and apply that same relationship to a third letter-cluster to find the missing one. The given analogy is ROBY : TJDT :: GAIN : ?

Analyzing the First Letter-Cluster Pair: ROBY to TJDT

Let's examine how each letter in the first cluster 'ROBY' transforms into the corresponding letter in the second cluster 'TJDT'. We can look at the alphabetical positions of the letters.

• The first letter R is the 18th letter of the alphabet. The first letter T is the 20th letter. The change is $20 - 18 = +2$. R $\xrightarrow{+2}$ T.
• The second letter O is the 15th letter of the alphabet. The second letter J is the 10th letter. The change is $10 - 15 = -5$. O $\xrightarrow{-5}$ J.
• The third letter B is the 2nd letter of the alphabet. The third letter D is the 4th letter. The change is $4 - 2 = +2$. B $\xrightarrow{+2}$ D.
• The fourth letter Y is the 25th letter of the alphabet. The fourth letter T is the 20th letter. The change is $20 - 25 = -5$. Y $\xrightarrow{-5}$ T.

The pattern of transformation from ROBY to TJDT is consistently applying the changes +2, -5, +2, -5 to the alphabetical positions of the letters.

Applying the Pattern to the Third Letter-Cluster: GAIN

Now, we apply the same +2, -5, +2, -5 pattern to the letter-cluster 'GAIN' to find the missing cluster.

• For the first letter G (7th position): Apply +2. $7 + 2 = 9$. The 9th letter is I. G $\xrightarrow{+2}$ I.
• For the second letter A (1st position): Apply -5. $1 - 5 = -4$. When subtracting from A (position 1), we wrap around the alphabet from Z (position 26). $1 - 5 = -4$. To find the letter, we can think of it as $26 + (-4) = 22$. The 22nd letter is V. A $\xrightarrow{-5}$ V.
• For the third letter I (9th position): Apply +2. $9 + 2 = 11$. The 11th letter is K. I $\xrightarrow{+2}$ K.
• For the fourth letter N (14th position): Apply -5. $14 - 5 = 9$. The 9th letter is I. N $\xrightarrow{-5}$ I.

Applying the pattern +2, -5, +2, -5 to GAIN results in the letter-cluster IVKI.

Checking the Options

Let's compare our resulting letter-cluster with the given options:

1. IVKI
2. IUKJ
3. IUKI
4. IVKJ

Our derived letter-cluster IVKI matches option 1.

Revision Table: Letter Positions

Here is a quick reference for the alphabetical positions used in the analysis:

Additional Information: Solving Letter Analogies

Letter analogy questions test your ability to find patterns in how letters or groups of letters change. Common patterns include:

• Positional Shift: Adding or subtracting a fixed number to the letter's position in the alphabet (like the +2, -5 pattern here).
• Reverse Alphabetical Order: Using the alphabet in reverse (Z=1, Y=2, etc.).
• Skipping Letters: The pattern might involve skipping a certain number of letters between corresponding letters.
• Consonants/Vowels: The pattern might relate to whether a letter is a consonant or a vowel.
• Combination of Patterns: Sometimes, different rules apply to different positions within the cluster, as seen in the alternating +2, -5 pattern in this problem.

To solve these problems, it's helpful to write down the alphabet and its positions (1 to 26) or visualize them clearly. Analyze the first pair carefully, looking for consistent rules applied letter by letter. Once the rule is found, apply it consistently to the third term to find the fourth.