Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster. ALW: NYJ :: CNY :PAL :: DEP:?

Correct — B. Every letter moves the same distance, and the count wraps round from Z back to A.

Rule: add 13 to each letter, subtracting 26 whenever the count passes Z.

ALW to NYJ: A+13=N, L+13=Y, W is 23 and 23+13=36, so 36−26=10=J.
CNY to PAL: C+13=P, N+13=27, so 27−26=1=A, and Y+13=38, so 38−26=12=L.

DEP: D+13=Q, E+13=R, P is 16 and 16+13=29, so 29−26=3=C.
That is QRC — option (b).

Why the others are wrong

• (a)
  QRD — QRD has the first two letters right and ends in D. P is the 16th letter and 16 + 13 = 29, which wraps to 3, the letter C, not to 4.
• (c)
  SRC — SRC moves D by +15 to reach S. The first worked pair fixes the step at +13, since A to N is thirteen places.
• (d)
  SRD — SRD misses at both ends: S is D+15 and D is P+14, while every letter in the two worked pairs moves exactly +13.

Adding 13 moves a letter halfway round a 26-letter alphabet, so it pairs each letter with the one directly opposite it: A with N, B with O, and so on all the way round.

That makes the rule its own inverse — apply it again and the original letter comes back — so it does not matter which end of a pair you start from. The real work is the wrap: once the count passes 26, subtract 26 and carry on.

Key facts

• Adding 13 twice returns the original letter, so the mapping is symmetric.
• W is the 23rd letter and 23 + 13 = 36, which wraps to 36 − 26 = 10, the letter J.
• Both given pairs use the same +13 step, which is what confirms the rule.

Common traps

• Forgetting to subtract 26 once the count runs past Z.
• Subtracting 26 but losing a place in the process, which lands one letter off.
• Deriving the rule from one pair only when a second worked pair is printed.

No directly related past PYQ was found.