Which letter-cluster will replace the question mark (?) to complete the given series? BKUZ, ENWB, ?, KTAF, NWCH

Correct — B. Read the four letter positions as four independent series, and keep counting past Z — A as 27, B as 28, C as 29.

Rule: positions 1 and 2 step +3. Positions 3 and 4 step +2.

Position 1: B(2), E(5), ?, K(11), N(14), so ? = H(8).
Position 2: K(11), N(14), ?, T(20), W(23), so ? = Q(17).
Position 3: U(21), W(23), ?, A(27), C(29), so ? = Y(25).
Position 4: Z(26), B(28), ?, F(32), H(34), so ? = D(30).

Reading the four answers down gives HQYD, option (b).

Why the others are wrong

• (a)
  HRYE — HRYE is wrong in two places. R is N + 4 in position 2, where the step is +3, and E is B + 3 in position 4, where the step is +2.
• (c)
  HRYD — HRYD is right everywhere except position 2. That series runs K, N, ?, T, W, and R is N + 4, while a +3 step gives Q — and Q + 3 = T, matching the next term.
• (d)
  HRZD — HRZD misses two positions: R is N + 4 in position 2, and Z is W + 3 in position 3, where the step is +2 and W + 2 = Y.

A four-letter cluster series is four alphabet series printed on top of each other. Convert each position to numbers first, because a step is far easier to see in 2, 5, 8, 11, 14 than in B, E, H, K, N.

Two shortcuts make it quick. Use the terms on either side of the gap: with a constant step the missing term sits halfway, so between E(5) and K(11) it is 8, and between W(23) and A(27) it is 25.

And carry on counting past Z rather than resetting. A is 27, B is 28, C is 29, and the arithmetic then runs without special cases.

Key facts

• Position 1 runs B, E, H, K, N, a +3 step.
• Position 2 runs K, N, Q, T, W, also +3.
• Position 3 runs U, W, Y, A, C, a +2 step that wraps past Z.
• Position 4 runs Z, B, D, F, H, also +2.

Common traps

• Counting inclusively, so B to E reads as +4 instead of +3.
• Resetting to 1 at A and losing the step in positions 3 and 4.
• Choosing HRYD, which differs from the answer by a single letter.

No directly related past PYQ was found.