Select the option that represents the letters that when sequentially placed from left to right in the blanks below will complete the letter series. _ X _ F _ _ _ X T _ X _

Correct — B. Twelve places split into four blocks of three, and the printed letters already fix the block.

Rule: F X T, repeating across four blocks of three.

Places 2, 8 and 11 all carry X, and those are every third place counting from 2 — the middle slot of a three-slot block. Place 9 carries T, the slot right after X; place 4 carries F, the slot right before X.

So each block reads F X T, and the blanks at 1, 3, 5, 6, 7, 10 and 12 take F T X T F F T, giving F X T | F X T | F X T | F X T → option (b).

Why the others are wrong

• (a)
  XTTFXFX — Option (a) opens with X at place 1, but place 2 already prints X. A three-letter cycle of F, X and T puts no letter next to itself, so the row is dead at its first pair.
• (c)
  XFTTXFX — Option (c) puts F at place 3, immediately before the F printed at place 4. The repeating block contains one F, so FF cannot occur anywhere in the row.
• (d)
  FXXTFXT — Option (d) puts X at place 3, beside the X printed at place 2. Its first block would read F X X, which is not a cycle of three distinct letters at all.

A blank series of this kind is a cyclic block, not an arithmetic progression. A short string repeats until the row is full, and the printed letters are a partial view of that repetition.

Find the period before you test any option. Measure the gap between two identical printed letters: X sits at places 2, 8 and 11, so the gaps are 6 and 3 and the period is 3.

Once the period is known every place has a fixed role, and an option that breaks one role anywhere is out. You never have to build the whole row.

Key facts

• Only three letters appear anywhere in the row: F, X and T.
• X is printed at places 2, 8 and 11, and the gaps of 6 and 3 fix the period at 3.
• The completed row reads F X T F X T F X T F X T.
• Seven of the twelve places are blank, so the answer string must be seven letters long.

Common traps

• Filling blanks left to right from one option instead of finding the period first.
• Miscounting the underscores, so a seven-letter option is matched against six slots.
• Missing that places 5, 6 and 7 are three blanks in a row and treating them as two.

No directly related past PYQ was found.