In a certain code language, the word "DELETE" is written as "#@^@%@" and the word "GRAM" is written as "!?*&". Using the same symbol code, how is the word "TELEGRAM" written in that code language?

Introduction:
This question involves a symbolic coding system where letters are replaced by special characters such as #, @, ^, %, !, ?, *, and &. We are given the coded forms of two words, "DELETE" and "GRAM", and asked to determine the code for "TELEGRAM". The objective is to deduce a consistent mapping from letters to symbols and then apply that mapping to the new word.

Given Data / Assumptions:
The word DELETE is written as #@^@%@. The word GRAM is written as !?*&. We assume that each letter corresponds to exactly one symbol and that the mapping is consistent across both words. The target word TELEGRAM is composed of letters T, E, L, E, G, R, A, M, all of which appear in DELETE or GRAM.

Concept / Approach:
We align the letters in each given word with their corresponding symbols in the same positions. This gives the mapping for D, E, L, T and G, R, A, M. Once we have the symbol for each letter, we construct the code for TELEGRAM by substituting letters with symbols in order.

Step-by-Step Solution:
Step 1: Analyze DELETE → #@^@%@. The letters D, E, L, E, T, E correspond to symbols #, @, ^, @, %, @.Step 2: From this, we deduce D = #, E = @, L = ^, and T = %.Step 3: Now analyze GRAM → !?*&. The letters G, R, A, M correspond to symbols !, ?, *, & respectively.Step 4: From this, we deduce G = !, R = ?, A = *, and M = &.Step 5: Collecting all mappings, we have D = #, E = @, L = ^, T = %, G = !, R = ?, A = *, and M = &.Step 6: The word TELEGRAM has letters T, E, L, E, G, R, A, M in that sequence.Step 7: Substitute each letter: T = %, E = @, L = ^, E = @, G = !, R = ?, A = *, M = &.Step 8: Concatenating these symbols, we get %@^@!?*&.Step 9: Therefore, TELEGRAM is written as %@^@!?*& in the given code language.

Verification / Alternative check:
We can verify our mappings by reapplying them to DELETE and GRAM. For DELETE, D = #, E = @, L = ^, T = %, so the sequence #@^@%@ matches exactly. For GRAM, G = !, R = ?, A = *, M = &, giving !?*& as required. This confirms that our mapping is correct.

Why Other Options Are Wrong:
Options that change any symbol position, such as replacing ! with ^ or moving @ into different positions, would contradict the fixed letter to symbol relationships already established. For instance, option a uses ^ where ! should appear, and option c introduces * in place of ^, both inconsistent with the mapping. Option b and option e similarly misplace symbols in a way that does not correspond to TELEGRAM letter by letter.

Common Pitfalls:
One typical mistake is to overlook that letters repeat, like E in DELETE, and thus to assign different symbols to the same letter. Another is to misalign positions when copying symbols from the mapping table to the target word. Careful, systematic substitution avoids these issues.

Final Answer:
The word "TELEGRAM" is written as %@^@!?*& in the given code language.