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Difficulty: HardAnalogy and Classification

A logical relationship is established between two letter-groups through a compound alphabetical transformation. The transformation linking the word FORGE\text{FORGE} to the sequence GDWHQ\text{GDWHQ} relies on a specific structural rearrangement of the letters, followed immediately by a sequence of position-dependent alphabetic shifts. Assuming the exact same multi-step transformation rules are applied, which of the following sequences logically pairs with the word VAULT\text{VAULT}?

  1. A
    \text{XXZEE}
  2. B
    \text{VOZHG}
  3. \text{VIZTG}Answer
  4. D
    \text{UIZTE}

Answer

The correct sequence is \text{VIZTG}.
The established logical rule consists of two distinct phases. First, the input word is spelled backwards. Second, the letters are shifted alphabetically by an alternating sequence of addition and subtraction using consecutive prime numbers (+2, -3, +5, -7, +11). Applying this to VAULT\text{VAULT}: reversing the word yields TLUAV\text{TLUAV}. Applying the shifts: T\text{T} shifted forward by 2 is V\text{V}; L\text{L} shifted backward by 3 is I\text{I}; U\text{U} shifted forward by 5 is Z\text{Z}; A\text{A} shifted backward by 7 wraps around to T\text{T}; and V\text{V} shifted forward by 11 wraps around to G\text{G}. This produces the correct pairing VIZTG\text{VIZTG}.

Step-by-Step Solution

1
Analyze the structural rearrangement in the given example.
The word FORGE\text{FORGE} is reversed to form EGROF\text{EGROF}.
Direct position-to-position mapping between FORGE\text{FORGE} and GDWHQ\text{GDWHQ} yields no logical mathematical sequence, indicating a structural shift occurs first.
2
Determine the alphabetic shifts between the reversed word EGROF\text{EGROF} and the target sequence GDWHQ\text{GDWHQ}.
The shifts are: E→+2G\text{E} \xrightarrow{+2} \text{G}, G→−3D\text{G} \xrightarrow{-3} \text{D}, R→+5W\text{R} \xrightarrow{+5} \text{W}, O→−7H\text{O} \xrightarrow{-7} \text{H}, F→+11Q\text{F} \xrightarrow{+11} \text{Q}.
By calculating the numerical difference between the alphabet positions, a clear pattern emerges: the operations alternate between addition and subtraction (+, -, +, -, +), and the magnitudes follow the sequence of prime numbers (2, 3, 5, 7, 11).
3
Apply the identical structural rearrangement to the target word VAULT\text{VAULT}.
Reversing VAULT\text{VAULT} gives the sequence TLUAV\text{TLUAV}.
The analogy rule requires the exact same multi-step logic to be applied to the new input.
4
Apply the derived alternating prime number shift sequence to TLUAV\text{TLUAV}.
T(+2)=V\text{T} (+2) = \text{V}; L(−3)=I\text{L} (-3) = \text{I}; U(+5)=Z\text{U} (+5) = \text{Z}; A(−7)=T\text{A} (-7) = \text{T}; V(+11)=G\text{V} (+11) = \text{G}.
A\text{A} (position 1 or 27) minus 7 lands on T\text{T} (position 20). V\text{V} (position 22) plus 11 equals 33, wrapping around the 26-letter alphabet to land on G\text{G} (position 7).

Key Concept

Compound Letter Analogy involving structural reversal and alternating prime number alphabetic shifts.
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Topics

Analogy and Classification

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