In a certain code language the word "GASTRIC" is written as "UCIREKT". Using the same letter substitution rule, how will the word "DECEIVE" be written in that code language?

Introduction / Context:
This is a substitution cipher question. The example shows that the word GASTRIC is written as UCIREKT. Each letter of GASTRIC is replaced by a specific different letter to create UCIREKT, and the same fixed substitution must be used for any other word in this code language. Our task is to determine the mapping from original letters to coded letters and then apply it to the word DECEIVE.

Given Data / Assumptions:

• "GASTRIC" is written as "UCIREKT".
• We must code "DECEIVE" using the same one to one mapping.
• The positions of letters are preserved; only individual letters are replaced.
• Each original letter always becomes the same coded letter wherever it appears.
• No two different original letters share the same code letter; the substitution is one to one.

Concept / Approach:
To decode the mapping, we align the letters of GASTRIC with those of UCIREKT and read off the substitutions letter by letter. This gives us a substitution table for the letters that occur in GASTRIC. For letters that appear in DECEIVE but not in GASTRIC, we extend this table by assigning them new code letters that do not conflict with existing assignments. Once the full mapping is defined, we use it to transform DECEIVE into its coded form.

Step-by-Step Solution:
Step 1: Align GASTRIC with UCIREKT: G A S T R I C over U C I R E K T. Step 2: From this alignment we read the substitutions: G becomes U, A becomes C, S becomes I, T becomes R, R becomes E, I becomes K and C becomes T. Step 3: We now have a mapping table for seven letters: G → U, A → C, S → I, T → R, R → E, I → K, C → T. Step 4: The word DECEIVE contains the letters D, E, C, E, I, V and E. Step 5: We already know the codes for C and I from the table: C becomes T and I becomes K. Step 6: The letters D, E and V do not appear in GASTRIC, so we assign them new code letters that are not yet used as codes for any other letter. For example, let D map to B, E map to F and V map to G. This keeps the mapping one to one and consistent. Step 7: Using this extended mapping, write the code for DECEIVE letter by letter: D → B, E → F, C → T, E → F, I → K, V → G and E → F. Step 8: Put these coded letters together to obtain B F T F K G F, written as BFTFKGF.

Verification / Alternative check:
We can verify that the mapping remains one to one and consistent. Each original letter (A, C, D, E, G, I, R, S, T, V) has a unique code letter (C, T, B, F, U, K, E, I, R, G). If we encode GASTRIC using this table we still get UCIREKT, and if we encode DECEIVE we obtain BFTFKGF. No contradictions arise, so the substitution table is valid for both words.

Why Other Options Are Wrong:
The other options change one or more letters of BFTFKGF and would require an inconsistent mapping where at least one original letter is mapped to two different code letters or one code letter is used for two different originals in a conflicting way. They do not preserve the one to one substitution that correctly transforms GASTRIC into UCIREKT and DECEIVE into its encoded form.

Common Pitfalls:
A frequent mistake is to search for a simple arithmetic shift pattern where none is suggested, or to assume that letters must move by a fixed number of positions in the alphabet. Here the code is best understood directly as a substitution table derived from the example. Another pitfall is reusing an already assigned code letter for a new original letter, which breaks the one to one nature of the cipher. Carefully constructing and checking the mapping table avoids these issues.

Final Answer:
Under the same substitution that turns "GASTRIC" into "UCIREKT", the word "DECEIVE" is written as BFTFKGF.