Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster. JAP: BSH :: NDZ: FVR ::LCX:?

Correct — A. Rule: every letter moves back 8 places, wrapping past A round to Z.

First pair: J(10) to B(2), A(1) to S (1 - 8 = -7, and -7 + 26 = 19), P(16) to H(8).
Second pair: N(14) to F(6), D(4) to V(22), Z(26) to R(18).

Apply it to LCX: L(12) - 8 = D(4), C(3) - 8 = U(21 after the wrap), X(24) - 8 = P(16).

That gives DUP, option (a).

Why the others are wrong

• (b)
  DVP — D and P are right, but the middle letter is C - 8 = U, not V. V is C - 7, a one-step slip in the wrap-around arithmetic: 3 - 8 = -5, then -5 + 26 = 21 = U.
• (c)
  EUP — U and P are right; the first letter must be L - 8 = D. E is L - 7 — the same off-by-one, applied to the leading letter instead of the middle one.
• (d)
  EVP — Both the first and the second letter are shifted by -7 instead of -8, so E and V each land one place late. Only P survives the error.

Letter-cluster analogies are positional arithmetic. Convert each letter to its place in the alphabet (A = 1 to Z = 26), read off the shift, convert back.

The whole difficulty is the wrap. Subtracting past A means adding 26: A(1) - 8 = -7, and -7 + 26 = 19 = S.

Do not look for meaning in the clusters. JAP and BSH are not words, and the intended rule is whichever shift works on all three letters of both worked pairs.

Key facts

• A back-shift of 8 is the same as a forward shift of 18, since 26 - 8 = 18.
• Wrapping backwards past A means adding 26 to the negative result.
• In LCX the position values are L = 12, C = 3, X = 24.

Common traps

• Shifting by 7 instead of 8 once the count crosses A.
• Applying the shift forwards on the wrapped letter and backwards on the rest.
• Reading only the first worked pair and never checking the rule against the second.

No directly related past PYQ was found.