In a certain digit code, GUIDE is written as 49132 and BEAM is written as 8257. Using the same digit code, how will the word IMAGE be written?

Introduction / Context:
This digit coding problem gives the codes for GUIDE and BEAM and asks you to encode the new word IMAGE. By comparing the letters and digits, we can build a mapping from letters to digits and then apply it. Since IMAGE uses only letters from GUIDE and BEAM, the mapping is complete once extracted. This type of question is frequently used to check your attention to detail and your ability to apply a derived code to a new word accurately.

Given Data / Assumptions:

• GUIDE → 49132.
• BEAM → 8257.
• Each letter has a single fixed digit assigned.
• Target word: IMAGE.
• There is no rearrangement of letters, only substitution with digits.

Concept / Approach:
We first map each letter in GUIDE to its respective digit and then refine or extend the mapping using BEAM. After building the mapping table, we encode IMAGE by replacing I, M, A, G, and E with their corresponding digits. This is simple substitution coding where consistency across words is the key.

Step-by-Step Solution:
Step 1: From GUIDE → 4 9 1 3 2, map G → 4, U → 9, I → 1, D → 3, E → 2. Step 2: From BEAM → 8 2 5 7, map B → 8, E → 2 (consistent with Step 1), A → 5, M → 7. Step 3: Now determine the digits for the letters in IMAGE: I, M, A, G, E. Step 4: Substitute: I → 1 M → 7 A → 5 G → 4 E → 2 Step 5: Combine digits in order: 1 7 5 4 2 → 17542.

Verification / Alternative check:
Verify that GUIDE and BEAM still match their codes using this mapping. GUIDE becomes 4 9 1 3 2 and BEAM becomes 8 2 5 7 exactly, showing that the mapping G → 4, U → 9, I → 1, D → 3, E → 2, B → 8, A → 5, M → 7 is consistent. Decoding 17542 using this mapping gives IMAGE, which confirms that 17542 is the correct code.

Why Other Options Are Wrong:
Options B, C, D, and E all differ in at least one digit from the required mapping for IMAGE. For example, any option that does not begin with 1 would not correctly encode I, and any that does not end in 2 would not match E. Similarly, the positions for digits corresponding to M, A, and G must be 7, 5, and 4, respectively; any deviation breaks the mapping derived from the original words. Only Option A perfectly matches all digit assignments in the correct order.

Common Pitfalls:
Sometimes candidates rush and misread digits or confuse letters that appear in both words. Another common mistake is to forget to check consistency where letters repeat, such as E in both GUIDE and BEAM. Building a neat mapping table and carefully encoding the target word avoids such errors.

Final Answer:
Therefore, in the given digit code, IMAGE is written as 17542.