Which of the following letter-clusters will replace the question mark (?) in the given series to make it logically complete? ICT, FES, CGR, ZIQ, ?

Correct — C. Split each cluster into three columns and number the alphabet A=1 to Z=26. Each column runs its own series.

Rule: first letter −3, second letter +2, third letter −1.

First column: I(9), F(6), C(3), Z(26) — three back each time, and 3 − 3 wraps round to Z(26). Z − 3 = W(23)

Second column: C(3), E(5), G(7), I(9) — two forward each time. I + 2 = K(11)

Third column: T(20), S(19), R(18), Q(17) — one back each time. Q − 1 = P(16)

W, K and P together give WKP, option (c).

Why the others are wrong

• (a)
  WJP — The first and third letters are right, but J(10) is only one place past I. The middle column climbs +2 every step — C, E, G, I — so the middle letter has to be K.
• (b)
  XKP — The middle and last letters are right and the first is not. Three places back from Z(26) is W(23), while X(24) is only two places back.
• (d)
  XLO — Every column is off by one: X is 2 back where the rule is 3, L is 3 forward where the rule is 2, and O is 2 back where the rule is 1.

A letter-cluster series is not a word puzzle. Each position holds its own independent series, so a three-letter cluster is three series printed side by side.

Write the alphabet positions under every letter first. Once the numbers are down, each column is ordinary arithmetic — here −3, +2 and −1.

The only complication is the wrap. When a column runs below A you add 26 before subtracting again, which is why the third cluster's C becomes Z rather than nothing at all.

Key facts

• Letter-cluster series are read column by column, never as words.
• A=1 through Z=26, and a step that falls below A wraps round by adding 26.
• In this series the three columns move −3, +2 and −1, and each keeps its step throughout.

Common traps

• Checking one column, then taking the first option that matches it.
• Missing the wrap below A, which makes the third term look like a break in the rule.
• Trying to read ICT, FES and CGR as abbreviations of something.

No directly related past PYQ was found.