Select the letter-cluster from among the given options that can replace the question mark (?) in the following series. A E I,E I M,I M Q,M Q U, ?

Correct — A.
Rule: +4 at every position, read down the series.

First letters: A, E, I, M → Q.
Second letters: E, I, M, Q → U.
Third letters: I, M, Q, U → Y.

That gives QUY → option (a).

Why the others are wrong

• (b)
  QKS — QKS has the right first letter but breaks at the second. The second letters run E, I, M, Q in fours, so the next one is U, not K.
• (c)
  LMX — LMX fails at the first letter. The first letters climb A, E, I, M, and M + 4 is Q, not L.
• (d)
  KJS — KJS fails at the first letter too: after M comes Q. Its K and J also run backwards, where every given cluster climbs in fours.

A letter-cluster series is three number series side by side. Turn letters into positions (A = 1 … Z = 26) and read one position at a time down the terms.

Here every position climbs by 4, and the letters inside each cluster are also 4 apart: A, E, I is 1, 5, 9. So each cluster repeats the last two letters of the one before, and the answer must begin QU.

Key facts

• A, E, I, M, Q, U, Y are positions 1, 5, 9, 13, 17, 21, 25, each 4 after the last.
• When the gap inside a cluster equals the step between clusters, each cluster shares two letters with the next.
• No step in this series runs past Z: the last letter needed is Y, the 25th.

Common traps

• Reading across a cluster instead of down each position
• Choosing QKS because its first letter is right, without checking the second

No directly related past PYQ was found.