Select the combination of letters that when sequentially placed in the blanks of the given series will complete the series. E_GHEI_GELK_ _OME

Correct — C. Split the string into four blocks of four letters: E_GH / EI_G / ELK_ / _OME.

Rule: read the blocks column-wise, not straight through.

Column 1 is a constant E.
Column 2 runs F, I, L, O (+3 each step).
Column 3 runs G, I, K, M (+2 each step).
Column 4 runs H, G, F, E (-1 each step).

The gaps fall at column 2 of block 1, column 3 of block 2, column 4 of block 3 and column 1 of block 4, so they take F, I, F, E — option (c).

Why the others are wrong

• (a)
  IFGE — Puts I in the first gap. Column 2 would then read I, I, L, O, which climbs by 0 and then by 3 — the column has to climb by 3 every time, so it must open at F.
• (b)
  IGFE — Opens with the same wrong I, and its second letter G lands in column 3, where the run G, ?, K, M needs the +2 term I.
• (d)
  FGEI — Its first letter F is right, but the last gap gets I — and column 1 is a plain E in every block, which is what the fourth block already shows you.

SSC writes this as a missing-letter series, but the series is really a small grid. The string is a fixed number of equal blocks, and each position inside a block runs its own arithmetic progression down the blocks.

Reading straight through gives you nothing, because four different rules are interleaved. Cutting the string into blocks of equal length puts the four progressions into columns where each is obvious.

Block length is fixed by the string length: sixteen positions, four of them blank, gives four blocks of four.

Key facts

• The completed string is EFGH / EIIG / ELKF / EOME.
• Column 2 runs F, I, L, O, a +3 progression.
• Column 3 runs G, I, K, M, a +2 progression.
• Column 4 runs H, G, F, E, a -1 progression.

Common traps

• Reading the string left to right and hunting for one rule that never exists.
• Choosing a block length that does not divide the string evenly.
• Filling the gaps in the wrong order — the answer string is read gap by gap, left to right.

No directly related past PYQ was found.