If INSURANCE is coded as ECNARUSNI, how will HINDRANCE be coded?
2010
If INSURANCE is coded as ECNARUSNI, how will HINDRANCE be coded?
Answer: D. ECNARDNIH — ConceptLetter-coding questions give a word together with its code and ask for the code of a second word. In the positional family of such rules no letter is…
- A.
CADNIHWCE
- B.
HANODEINR
- C.
AENIRHDCN
- D.
ECNARDNIH
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Correct answer: D
Concept
Letter-coding questions give a word together with its code and ask for the code of a second word. In the positional family of such rules no letter is replaced by another; the letters are only moved, the letter standing at position i being written at a new position fixed by the rule. Other families instead shift each letter along the alphabet or substitute symbols. The simplest positional rule is complete reversal: in a word of n letters, the letter at position i is written at position n + 1 - i, so the last letter comes first and the first letter comes last.
Reading the rule from the given pair
INSURANCE has nine letters. Writing them from the last letter to the first gives E, C, N, A, R, U, S, N, I, which is exactly the given code ECNARUSNI. So the coding scheme here is plain reversal, with no letter shift and no substitution.
Word | Letters read from last to first | Code |
|---|---|---|
INSURANCE | E, C, N, A, R, U, S, N, I | ECNARUSNI |
HINDRANCE | E, C, N, A, R, D, N, I, H | ECNARDNIH |
Applying the rule to HINDRANCE
Number the letters of HINDRANCE: H(1), I(2), N(3), D(4), R(5), A(6), N(7), C(8), E(9).
The rule sends the letter at position i to position 10 - i, so the code opens with the ninth letter E, followed by the eighth letter C.
Continuing inwards from the end: N (position 7), A (6), R (5), D (4).
The remaining letters follow in the same descending order: N (3), I (2), and finally H (1).
Collecting them in that order gives E, C, N, A, R, D, N, I, H, that is ECNARDNIH.
Cross-check and contrast
Reversal is self-inverse: reading ECNARDNIH backwards returns HINDRANCE, just as reading ECNARUSNI backwards returns INSURANCE. That two-way check confirms the derivation. The remaining strings fail a check that can be made before any reversal is attempted:
CADNIHWCE is made of A, C, C, D, E, H, I, N, W, a set carrying a W and a second C, so it cannot be a rearrangement of HINDRANCE at all.
HANODEINR is made of A, D, E, H, I, N, N, O, R, a set carrying an O in place of a C, so it too comes from different letters.
AENIRHDCN does use the nine letters of HINDRANCE, but in the order A-E-N-I-R-H-D-C-N; reversing HINDRANCE produces E first, not A.