‘LISP’ is related to ‘ORHK’ in a certain way based on the English alphabetical order. In the same way, ‘WAND’ is related to ‘DZMW’. To which of the following is ‘BOTE’ related, following the same logic?

Correct — A. Rule: each letter is replaced by its opposite in the alphabet — A pairs with Z, B with Y, and so on, so the two positions always add to 27.

Check it on the pairs you are given.
L(12) to O(15) sums to 27, and I(9) to R(18) sums to 27.
W(23) to D(4) sums to 27, and A(1) to Z(26) sums to 27.

Now BOTE.
B(2) becomes Y(25) and O(15) becomes L(12).
T(20) becomes G(7) and E(5) becomes V(22).
That is YLGV — option (a).

Why the others are wrong

• (b)
  YKFU — The last three letters each sit one place short. K, F and U are the opposites of P, U and F, not of O, T and E, whose opposites are L, G and V.
• (c)
  YMHV — M and H sit one place past the true opposites. O pairs with L and T with G because 15 + 12 and 20 + 7 both make 27, while M and H would need sums of 28.
• (d)
  YKFW — No single pairing produces it. K and F fall short while W overshoots V, so for O, T and E the sums come to 26, 26 and 28 instead of a constant 27.

Opposite-letter coding rests on one fact: the alphabet has 26 letters, so the letter at position n is replaced by the letter at position 27 - n.

Learn the thirteen anchor pairs and you never have to count: A-Z, B-Y, C-X, D-W, E-V, F-U, G-T, H-S, I-R, J-Q, K-P, L-O, M-N.

The mapping is its own inverse, so the same table decodes a cluster as well as it codes one.

Key facts

• A letter at position n maps to position 27 - n, so each pair of positions sums to 27.
• The thirteen opposite pairs are A-Z, B-Y, C-X, D-W, E-V, F-U, G-T, H-S, I-R, J-Q, K-P, L-O and M-N.
• The mapping is self-inverse, so applying it twice returns the original letter.
• BOTE maps to YLGV: 2+25, 15+12, 20+7 and 5+22 all make 27.

Common traps

• Pairing A with Y instead of Z, which makes every image one letter short
• Counting backwards from Z under time pressure instead of subtracting from 27

No directly related past PYQ was found.