‘RUCK’ is related to ‘TWAI’ in a certain way based on the English alphabetical order. In the same way, ‘DPHM’ is related to ‘FRFK’. To which of the following is ‘KNOM’ related, following the same logic?

Correct — B. Work in alphabet positions and check the rule against both worked pairs.

Rule: letters 1 and 2 rise by 2, letters 3 and 4 fall by 2.

RUCK: R(18)+2 = T, U(21)+2 = W, C(3)−2 = A, K(11)−2 = I = TWAI
DPHM: D(4)+2 = F, P(16)+2 = R, H(8)−2 = F, M(13)−2 = K = FRFK

Apply it to KNOM:
K(11)+2 = M, N(14)+2 = P, O(15)−2 = M, M(13)−2 = K

That gives MPMK -> option (b).

Why the others are wrong

• (a)
  IPMJ — IPMJ takes the first letter down instead of up — I is K − 2 — and then ends on J, which is M − 3. Only its middle two letters follow the rule.
• (c)
  IQNK — IQNK opens downward with I = K − 2 and then moves N by 3 and O by 1. Its final K is right, which is exactly what makes it tempting.
• (d)
  MQNJ — MQNJ opens correctly with M and then shifts by 3, 1 and 3 — Q is N + 3, N is O − 1, J is M − 3. Every step in this rule is exactly 2.

A letter-pair analogy is solved on the number line, not by eye. Write the alphabet position under every letter of both worked examples before you touch the target group.

The shift here is not uniform. Letters 1 and 2 rise by 2 while letters 3 and 4 fall by 2, and a shift that changes with position is what makes this harder than a plain +2 code.

Two worked pairs are given for a reason. A single pair can often be explained by more than one rule, and testing the second pair is what pins the rule down.

Key facts

• RUCK becomes TWAI under +2, +2, −2, −2.
• DPHM becomes FRFK under the same +2, +2, −2, −2.
• KNOM under that rule becomes MPMK.
• Every shift in this item is exactly two places, only the direction changes.

Common traps

• Applying +2 to all four letters, which gives MPQO.
• Applying the two directions to the wrong halves, which gives ILQO.
• Verifying the rule on RUCK alone and never checking DPHM.

No directly related past PYQ was found.