This question is a letter-cluster analogy problem. We need to find the relationship between the first two letter-clusters (PAG and NYE) and the third and fourth letter-clusters (TUB and RSZ). Once the pattern is identified, we apply it to the fifth letter-cluster (RICE) to find the missing one.

Analyzing the First Letter Analogy: PAG to NYE

Let's examine the relationship between each letter in the first cluster (PAG) and the corresponding letter in the second cluster (NYE).

• The first letter P changes to N. In the English alphabet, N is 2 letters before P (P $\rightarrow$ O $\rightarrow$ N). This is a shift of -2.
• The second letter A changes to Y. Going backwards from A, we pass Z to get to Y (A $\rightarrow$ Z $\rightarrow$ Y). This is also a shift of -2.
• The third letter G changes to E. In the English alphabet, E is 2 letters before G (G $\rightarrow$ F $\rightarrow$ E). This is a shift of -2.

So, the pattern observed in the first analogy is a consistent backward shift of 2 positions for each letter.

Analyzing the Second Letter Analogy: TUB to RSZ

Now, let's check if the same pattern applies to the third and fourth letter-clusters (TUB and RSZ).

• The first letter T changes to R. In the English alphabet, R is 2 letters before T (T $\rightarrow$ S $\rightarrow$ R). This is a shift of -2.
• The second letter U changes to S. In the English alphabet, S is 2 letters before U (U $\rightarrow$ T $\rightarrow$ S). This is a shift of -2.
• The third letter B changes to Z. Going backwards from B, we pass A to get to Z (B $\rightarrow$ A $\rightarrow$ Z). This is also a shift of -2.

The pattern of a -2 shift is confirmed for the second analogy as well.

Applying the Pattern to RICE

Since the pattern is consistent across the first two analogies, we will apply the same -2 shift to each letter in the fifth letter-cluster, RICE, to find the missing cluster.

• Apply -2 shift to R: R $\rightarrow$ Q $\rightarrow$ P. The new letter is P.
• Apply -2 shift to I: I $\rightarrow$ H $\rightarrow$ G. The new letter is G.
• Apply -2 shift to C: C $\rightarrow$ B $\rightarrow$ A. The new letter is A.
• Apply -2 shift to E: E $\rightarrow$ D $\rightarrow$ C. The new letter is C.

Combining the shifted letters, RICE becomes PGAC.

Therefore, the letter-cluster that is related to RICE in the same way as the others is PGAC.

Revision Table: Letter Analogy Patterns

Additional Information: Understanding Letter Analogies

Letter analogies test your ability to identify relationships between groups of letters. These relationships can be based on various patterns, such as:

• Position in the alphabet: A fixed shift forward or backward (like in this problem).
• Skipping letters: Jumping a fixed number of letters.
• Reversal: Reversing the order of letters.
• Vowel/Consonant patterns: Relationships based on whether letters are vowels or consonants.
• Combination of patterns: Sometimes multiple rules apply.

To solve letter analogy problems, it's helpful to write down the alphabetical series or assign numerical values to each letter (A=1, B=2, ..., Z=26) to easily calculate shifts. Practice with different types of patterns helps in quickly identifying the underlying rule.