Letter Analogy Pattern Identification

The question presents a letter analogy problem. We need to identify the relationship between the first pair of letter clusters (EYXJ : IGBR) and the second pair (CRFQ : GZJY) and apply the same logic to find the missing cluster related to ZIQM.

Analyzing the Relationship

Let's determine the pattern by comparing the positions of the letters in the alphabet (A=1, B=2, ..., Z=26).

1. First Pair Analysis (EYXJ : IGBR):
   • E (5) to I (9): +4 positions ( $5 + 4 = 9$ )
   • Y (25) to G (7): +8 positions ( $25 + 8 = 33$; $33 - 26 = 7$ )
   • X (24) to B (2): +4 positions ( $24 + 4 = 28$; $28 - 26 = 2$ )
   • J (10) to R (18): +8 positions ( $10 + 8 = 18$ )
   The pattern observed is +4, +8, +4, +8.
2. Second Pair Analysis (CRFQ : GZJY):
   • C (3) to G (7): +4 positions ( $3 + 4 = 7$ )
   • R (18) to Z (26): +8 positions ( $18 + 8 = 26$ )
   • F (6) to J (10): +4 positions ( $6 + 4 = 10$ )
   • Q (17) to Y (25): +8 positions ( $17 + 8 = 25$ )
   The pattern (+4, +8, +4, +8) is consistent.

Applying the Pattern to Find the Missing Cluster

Now, we apply the identified pattern (+4, +8, +4, +8) to the third cluster ZIQM:

• Z (26) + 4: $26 + 4 = 30$. Since there are 26 letters, $30 - 26 = 4$. The 4th letter is D.
• I (9) + 8: $9 + 8 = 17$. The 17th letter is Q.
• Q (17) + 4: $17 + 4 = 21$. The 21st letter is U.
• M (13) + 8: $13 + 8 = 21$. The 21st letter is U.

Therefore, the missing letter cluster is DQUU.