Select the letter-cluster from among the given options that can replace the question mark (?) in the following series: MCFI, NEKP, OGPW, PIUD, ?

Correct — C.
Rule: +1, +2, +5, +7, one step for each of the four positions.

First: M, N, O, P → Q.
Second: C, E, G, I → I(9) + 2 = K(11).
Third: F, K, P, U → U(21) + 5 = Z(26).
Fourth: I, P, W, D → D(4) + 7 = K(11).

That gives Q K Z K → option (c).

Why the others are wrong

• (a)
  N K Y D — N K Y D fails at once: the first letters climb M, N, O, P, so the next is Q, not N. Its Y and D also miss Z and K.
• (b)
  Q L Y L — Q L Y L has the right first letter only. It steps the other columns +3, +4 and +8, where the given terms step +2, +5 and +7.
• (d)
  Q K Z L — Q K Z L is right in three columns and misses the fourth: D(4) + 7 is K(11), while L would need +8.

A four-letter cluster is four series running side by side. Convert to positions and read each column down the terms, never across one cluster.

The fourth column is where this one bites. I(9), P(16), W(23) climb by 7, and the next step wraps: W + 7 = 30, and 30 − 26 = D(4). Miss that wrap and PIUD looks like a break in the pattern. From D, one more +7 gives K.

Key facts

• Counting past Z restarts at A, so W(23) + 7 = 30 − 26 = D(4).
• F, K, P, U, Z is a +5 run.
• I, P, W, D, K is a +7 run with a wrap after W.

Common traps

• Reading the D of PIUD as a break instead of the wrap W + 7
• Stopping after three columns when options (c) and (d) differ only in the fourth

No directly related past PYQ was found.