In a certain code language, the word "MAKER" is written as "PDNHU". Using the same letter shifting rule, how is the word "TOOLS" written in that language?

Introduction / Context:
This question presents a simple Caesar cipher applied to the word MAKER. The coded form PDNHU suggests that each letter has been shifted forward by the same number of positions in the alphabet. Once we identify the size and direction of this shift, we can apply it to each letter of TOOLS to obtain its coded form.

Given Data / Assumptions:

• "MAKER" is written as "PDNHU".
• We must code the word "TOOLS" in the same way.
• The order of letters is preserved, and each letter is shifted by a fixed number of positions.
• Alphabet positions are A = 1 up to Z = 26 and wrap around if needed.

Concept / Approach:
To discover the rule, compare each letter of MAKER with the corresponding letter of PDNHU. If each mapping is a shift of plus three positions, then the code is a straightforward forward shift by three. Once this is confirmed, the same shift will be applied to each letter of TOOLS to get the encoded word.

Step-by-Step Solution:
Step 1: Compare M with P. M is the thirteenth letter and P is the sixteenth, so this is a shift forward of three positions. Step 2: A goes to D (1 to 4), K goes to N (11 to 14), E goes to H (5 to 8) and R goes to U (18 to 21). Every letter has moved forward by three positions. Step 3: Conclude that the rule is: coded letter = original letter shifted forward by three positions in the alphabet. Step 4: Apply this rule to each letter of TOOLS. T is the twentieth letter; adding three gives W, the twenty third letter. Step 5: O is the fifteenth letter; adding three gives R, the eighteenth letter. Since there are two Os, both become R. Step 6: L is the twelfth letter; adding three gives O, the fifteenth letter. Step 7: S is the nineteenth letter; adding three gives V, the twenty second letter. Step 8: Put the encoded letters together in order: W, R, R, O, V, written as WRROV.

Verification / Alternative check:
We can double check by shifting each letter of WRROV backward by three positions. W back three is T, R back three is O, again R back three is O, O back three is L and V back three is S. This returns us to TOOLS, confirming that the same shift by three has been applied consistently and correctly.

Why Other Options Are Wrong:
The options VTRPM, MLQGP and PTNLR either use letters that do not correspond to a plus three shift from the letters of TOOLS or change the order of the letters in a way that the established rule does not support. Only WRROV fits the exact shift and preserves letter order.

Common Pitfalls:
A common error is to forget that all letters must be shifted by the same amount or to miscount positions for letters near the end of the alphabet. Another mistake is to assume different shifts for different letters, which is not indicated here. Checking every letter pair in the example before applying the rule helps prevent misinterpretation.

Final Answer:
Applying the same plus three shift that encodes MAKER as PDNHU, the word "TOOLS" is written as WRROV.