In the following question, a group of letters is given. The letters of each…

Concept

Letter-analogy groups follow a positional rule: convert each letter to its alphabet position (A=1, B=2, ... Z=26), then look for a fixed pattern that links the three words of one group. Here the governing rule has two parts, the same for every valid group:

• The third word is the first word with every letter moved one step BACK in the alphabet (a uniform shift of -1 per letter).

• The letter-by-letter step that turns word-1 into word-2 is the exact mirror (reverse order) of the step that turns word-2 into word-3.

Application to the given group (GROB, EKUC, FQNA)

1. First to third: G(7), R(18), O(15), B(2). Subtract 1 from each: 6, 17, 14, 1, which spell F, Q, N, A = FQNA. So the third word is exactly the first word shifted back by one letter.

2. First to second step: G->E is -2, R->K is -7, O->U is +6, B->C is +1, giving the step sequence [-2, -7, +6, +1].

3. Second to third step: E->F is +1, K->Q is +6, U->N is -7, C->A is -2, giving [+1, +6, -7, -2] - the same four numbers in reverse order. The mirror condition holds.

Cross-check across the alternatives

Apply the SAME two tests to each alternative; only one passes both:

• (LAPT, WLDH, KZOS): L,A,P,T positions 12,1,16,20; subtracting 1 gives 11,26,15,19 = K,Z,O,S = KZOS, so the third word IS the first shifted back by one. Its word-1 to word-2 step is [+11,+11,-12,-12] and its word-2 to word-3 step is [-12,-12,+11,+11], the same numbers in reverse order. Both tests pass - this group obeys the rule.

• (CGND, GJJY, BFMD): subtracting 1 from CGND gives BFMC, not BFMD, so the third-word test already fails.

• (RFID, GECV, YHHC): subtracting 1 from RFID gives QEHC, not YHHC, so the third-word test fails outright.

• (NEFT, WBHJ, MDEA): subtracting 1 from NEFT gives MDES, not MDEA, so the third-word test fails on the last letter.

Only the group (LAPT, WLDH, KZOS) satisfies both the back-by-one third word and the mirrored step pattern, so it is the answer.