In a certain code language, the word "BORROW" is written as "769965" and the word "BOMB" is written as "7647". Using the same code, how is the word "WOMB" written in that language?

Introduction:
This coding and decoding question involves mapping letters of words to digits. We are told how "BORROW" and "BOMB" are written in a numeric code and asked to determine the code for "WOMB". Such questions require building a consistent letter to digit mapping by carefully aligning letters with their corresponding digits in the examples.

Given Data / Assumptions:
The word BORROW is written as 769965. The word BOMB is written as 7647. We assume each letter corresponds to exactly one digit and that the code is consistent between both examples. The target word WOMB includes only letters that appear in the given examples, namely W, O, M, and B.

Concept / Approach:
The approach is to determine the digit associated with each letter by comparing positions in the coded words. Once we know the codes for B, O, M, and W, we can directly encode the word WOMB by substituting digits for each letter in order.

Step-by-Step Solution:
Step 1: Consider BORROW coded as 769965. The letters in order are B, O, R, R, O, W, and the digits are 7, 6, 9, 9, 6, 5.Step 2: From this, we can deduce: B = 7, O = 6, R = 9, and W = 5.Step 3: Now look at BOMB coded as 7647. The letters are B, O, M, B, and the digits are 7, 6, 4, 7.Step 4: This confirms B = 7 and O = 6 again, and gives M = 4.Step 5: We now have the mappings: B = 7, O = 6, M = 4, W = 5.Step 6: The word WOMB has letters W, O, M, B in that order.Step 7: Substitute the digits: W = 5, O = 6, M = 4, B = 7 which gives 5 6 4 7.Step 8: Therefore, "WOMB" is written as 5647 in the code language.

Verification / Alternative check:
By reapplying the mappings to the original words, BORROW becomes 7 6 9 9 6 5, and BOMB becomes 7 6 4 7, which match the given codes exactly. This double check confirms that our mapping table is correct and that the encoding of WOMB is consistent.

Why Other Options Are Wrong:
The option 5467 would assign 4 to O instead of M, contradicting O = 6. The option 5677 cannot be formed from the consistent mappings because W and B cannot both map to 7. The option 5776 assigns 7 to W and 6 to B, both of which contradict the established mapping. The option 5967 introduces 9, which belongs to R, a letter not present in WOMB.

Common Pitfalls:
A frequent mistake is to copy the digits in the wrong order or to assume that the numeric positions in the code directly follow alphabetical order, which is not the case. Another error is forgetting to verify the mapping with both given coded words, which can allow an inconsistent assignment to slip through unnoticed.

Final Answer:
The word "WOMB" is written as 5647 in the given code language.