Understanding the Letter Triad Pattern

This question requires us to identify a specific pattern involving letter triads. We need to examine the relationship between the letters in the given examples (KF-MH-OQ and ID-KF-MO) and then apply this logic to find the matching option.

Analyzing the Example Triads

First, let's determine the numerical position of each letter in the English alphabet (where A=1, B=2, C=3, and so on).

Triad 1: KF-MH-OQ

• KF: K is the 11^th letter, F is the 6^th letter.
• MH: M is the 13^th letter, H is the 8^th letter.
• OQ: O is the 15^th letter, Q is the 17^th letter.

Pattern Analysis for Triad 1:

• First Letters: The sequence is K (11), M (13), O (15). The progression is $11 \xrightarrow{+2} 13 \xrightarrow{+2} 15$. Each first letter increases by 2.
• Second Letters: The sequence is F (6), H (8), Q (17). The progression is $6 \xrightarrow{+2} 8 \xrightarrow{+9} 17$. The second letter increases by 2, followed by an increase of 9.

Triad 2: ID-KF-MO

• ID: I is the 9^th letter, D is the 4^th letter.
• KF: K is the 11^th letter, F is the 6^th letter.
• MO: M is the 13^th letter, O is the 15^th letter.

Pattern Analysis for Triad 2:

• First Letters: The sequence is I (9), K (11), M (13). The progression is $9 \xrightarrow{+2} 11 \xrightarrow{+2} 13$. Each first letter increases by 2.
• Second Letters: The sequence is D (4), F (6), O (15). The progression is $4 \xrightarrow{+2} 6 \xrightarrow{+9} 15$. The second letter increases by 2, followed by an increase of 9.

Both example triads exhibit the same pattern: the first letter in each pair advances by 2 positions, and the second letter advances by 2 positions, then by 9 positions.

Evaluating the Options Against the Pattern

Let's examine each option to see if it matches the identified pattern (First letters: +2, +2; Second letters: +2, +9):

Option 1: GB-ID-KN

• G (7), B (2)
• I (9), D (4)
• K (11), N (14)
• First Letters: G (7) $7 \xrightarrow{+2} 9 \xrightarrow{+2} 11$ K (11). (Matches the +2, +2 pattern)
• Second Letters: B (2) $2 \xrightarrow{+2} 4 \xrightarrow{+10} 14$ N (14). (Does not match the +2, +9 pattern)

Option 2: GB-ID-KM

• G (7), B (2)
• I (9), D (4)
• K (11), M (13)
• First Letters: G (7) $7 \xrightarrow{+2} 9 \xrightarrow{+2} 11$ K (11). (Matches the +2, +2 pattern)
• Second Letters: B (2) $2 \xrightarrow{+2} 4 \xrightarrow{+9} 13$ M (13). (Matches the +2, +9 pattern)

Option 3: HB-IC-KN

• H (8), B (2)
• I (9), C (3)
• K (11), N (14)
• First Letters: H (8) $8 \xrightarrow{+1} 9 \xrightarrow{+2} 11$ K (11). (Does not match the +2, +2 pattern)

Option 4: HB-ID-KN

• H (8), B (2)
• I (9), D (4)
• K (11), N (14)
• First Letters: H (8) $8 \xrightarrow{+1} 9 \xrightarrow{+2} 11$ K (11). (Does not match the +2, +2 pattern)

Determining the Correct Triad

Option 2, GB-ID-KM, correctly adheres to the established pattern:

• First Letters Progression: $7 \to 9 \to 11$ (Increases by 2 each time)
• Second Letters Progression: $2 \to 4 \to 13$ (Increases by 2, then by 9)

This makes GB-ID-KM the triad that follows the same pattern as KF-MH-OQ and ID-KF-MO.