In a certain code language, the word "PRICE" is written as "GEKTR". Using the same coding pattern, how is the word "VALUE" written in that code language?

Introduction / Context:
This question is from the coding decoding topic, where one English word is converted into a coded form using a hidden rule. You are given the mapping PRICE → GEKTR and asked to apply the same logic to a new word, VALUE. To succeed, you must understand how letters are transformed, including any reversal and shifting in the alphabet.

Given Data / Assumptions:

• PRICE is written as GEKTR in the code language.
• The same rule must be applied to VALUE.
• Only capital English letters are involved.
• Each letter of the original word maps to exactly one coded letter.

Concept / Approach:
We first compare PRICE and GEKTR letter by letter to detect any pattern. A direct position wise comparison is confusing, so an effective trick is to check whether the original word was reversed before encoding. If we reverse PRICE, we get ECIRP. Comparing ECIRP with GEKTR may reveal a consistent shift in alphabetical positions.

Step-by-Step Solution:
Step 1: Reverse PRICE to get ECIRP.Step 2: Compare letters: E → G, C → E, I → K, R → T, P → R.Step 3: Check shifts in the alphabet: E(5) to G(7) is +2, C(3) to E(5) is +2, I(9) to K(11) is +2, R(18) to T(20) is +2, P(16) to R(18) is also +2.Step 4: So the rule is: reverse the word, then shift every letter two positions forward in the alphabet.Step 5: Apply this to VALUE: reverse VALUE to get EULAV.Step 6: Shift each letter +2: E → G, U → W, L → N, A → C, V → X.Step 7: The coded form of VALUE is therefore GWNCX.

Verification / Alternative check:
If we tried only a plain shift without reversing, the mapping from PRICE to GEKTR would break at some position. Similarly, reversing without shifting would give ECIRP instead of GEKTR. Reversing followed by a +2 shift matches every single letter for the given example and therefore is the correct coding rule to apply to VALUE.

Why Other Options Are Wrong:

• FWNCX and FNWDY change some letters correctly but not all, indicating an incorrect or incomplete shift.
• DWNCY does not follow the precise +2 shift from the reversed word.
• GWNXY alters the final letter incorrectly and does not match the derived pattern.

Common Pitfalls:
Many students look only for direct shifts and ignore the possibility that the word might be reversed. Another error is miscounting positions when shifting letters in the alphabet. Always check the transformation on every letter, not just the first and last, to be confident in the rule you deduce.

Final Answer:
Using the rule "reverse the word and then shift each letter two places forward", VALUE is coded as GWNCX.