Which of the following terms will replace the question mark (?) in the given series? EQBY, GPDX, ?, KNHV, MMJU

Correct — D.

Rule: read the four letters as four independent series — positions 1 and 3 move +2, positions 2 and 4 move −1.

Position 1: E, G, ?, K, M. As numbers 5, 7, so +2 gives I at 9, then 11 and 13. Checks out.

Position 2: Q, P, ?, N, M. As numbers 17, 16, so −1 gives O at 15, then 14 and 13. Checks out.

Position 3: B, D, ?, H, J. As numbers 2, 4, so +2 gives F at 6, then 8 and 10. Checks out.

Position 4: Y, X, ?, V, U. As numbers 25, 24, so −1 gives W at 23, then 22 and 21. Checks out.

I, O, F, W together give IOFW → option (d).

Why the others are wrong

• (a)
  IPFW — The second position has not moved. IPFW keeps the P of the previous term, but that column steps back one letter every time — Q, P, O, N, M — so the missing letter is O.
• (b)
  HOFW — The first position steps by one instead of two. H is G plus 1, while the column runs E, G, I, K, M in steps of two, so the letter needed is I.
• (c)
  IOEW — The third position steps by one instead of two. E is D plus 1, while that column climbs B, D, F, H, J in steps of two, so the letter needed is F.

A letter-cluster series is four small series printed side by side. Trying to see one rule for the whole cluster is what makes these look hard.

Write each column as alphabet positions and the pattern becomes ordinary arithmetic. Steps in opposite directions, as here, are common and are invisible until you do that.

Confirm each column against every term you have been given, not just the first pair. A step that fits two terms and fails the fourth is the usual sign that you have mis-read a letter.

Key facts

• Alphabet positions used here: E is 5, G is 7, I is 9, K is 11, M is 13.
• Columns 1 and 3 both advance by +2 while columns 2 and 4 both retreat by −1.
• Turning letters into their positions converts a letter series into an arithmetic one.

Common traps

• Looking for one rule across the whole cluster instead of four column rules.
• Fixing the step from the first pair only and never testing it against the last two terms.
• Slipping a place near the end of the alphabet, where W, X and Y are easy to confuse.

No directly related past PYQ was found.