Select the letter-cluster from among the given options that can replace the question mark (?) in the following series. ACE EIM IOU MUC ?

Correct — C.
Rule: each position has its own step: +4, +6, +8, wrapping past Z.

First letters: A, E, I, M (+4) → Q.
Second letters: C, I, O, U (+6) → 21 + 6 = 27 → A.
Third letters: E, M, U, C (+8) → 3 + 8 = 11 → K.

That gives QAK → option (c).

Why the others are wrong

• (a)
  QSA — QSA starts with the right Q, but the second letters step by 6, C, I, O, U, so the next is U + 6 = A, not S. The third letter must be K.
• (b)
  UHG — UHG fails at the first letter. The first letters climb A, E, I, M in fours, so the next is Q, not U.
• (d)
  CGD — CGD fails at the first letter: after M comes Q, not C. Its last letter is wrong too, since C + 8 = K.

Convert letters to positions (A = 1 … Z = 26) and read down each position. Here the three positions climb at different rates: +4, +6 and +8.

The same fact shows inside the clusters: ACE has gaps of 2, EIM of 4, IOU of 6, MUC of 8. So the fifth cluster needs gaps of 10: Q, then 27 → A, then 37 → K.

Key facts

• Inside the clusters the gaps are 2, 4, 6 and 8, so the fifth cluster's gaps are 10.
• The first letters A, E, I, M, Q are positions 1, 5, 9, 13, 17.
• Subtract 26 from any total above 26 to find the letter: 27 → A, 29 → C, 37 → K.

Common traps

• Stopping at 27 or 37 and hunting for a letter beyond Z instead of subtracting 26
• Applying the first position's +4 to every position

No directly related past PYQ was found.