In a certain code language, the word "MOTHER" is written as "NPUGDQ". Using the same letter shifting rule, how is the word "ORANGE" written in that code language?

Introduction / Context:
This is another letter shifting code question. The word MOTHER becomes NPUGDQ in the code language. Our goal is to discover the rule used to shift each letter of MOTHER and then apply the same rule to the word ORANGE. This tests the ability to recognise position wise transformations and to apply them consistently to a different six letter word.

Given Data / Assumptions:

• MOTHER is coded as NPUGDQ.
• Target word: ORANGE.
• Both words contain six letters.
• Each position in the original word is shifted by a fixed amount forward or backward in the alphabet to obtain the corresponding coded letter.

Concept / Approach:
We compare MOTHER and NPUGDQ letter by letter. M → N, O → P, T → U, H → G, E → D, R → Q. The first three letters are each shifted forward by one place: M to N, O to P, T to U. The last three letters are each shifted backward by one place: H to G, E to D, R to Q. So the rule is: for a six letter word, add 1 to the first three letters and subtract 1 from the last three letters. We then apply this rule directly to O R A N G E.

Step-by-Step Solution:
Step 1: Confirm the pattern using MOTHER: M (13) → N (14): +1. O (15) → P (16): +1. T (20) → U (21): +1. H (8) → G (7): -1. E (5) → D (4): -1. R (18) → Q (17): -1. Step 2: Now apply the same pattern to ORANGE: letters O, R, A, N, G, E. Step 3: First three letters +1: O (15) +1 → P (16). R (18) +1 → S (19). A (1) +1 → B (2). Step 4: Last three letters -1: N (14) -1 → M (13). G (7) -1 → F (6). E (5) -1 → D (4). Step 5: Combine all six coded letters to obtain P S B M F D.

Verification / Alternative check:
To verify, we can again check the original MOTHER example: the first three letters are all shifted up by one and the last three down by one. This pattern is consistent and simple. Applying it to ORANGE gives PSBMFD, which is present as option B. Recalculating the shifts for each letter confirms that no mistakes were made in counting alphabet positions, and none of the other options follow this exact split pattern of +1 then -1.

Why Other Options Are Wrong:
Option A (PSBMDF) swaps the positions of the last two letters compared to the correct PSBMFD. Option C and option D change one or more letters in ways that break the +1 then -1 pattern. Option E introduces additional changes that do not match the transformation shown by MOTHER → NPUGDQ. Since the coding rule is clearly defined by that original pair, only PSBMFD respects the same position wise shifts for ORANGE.

Common Pitfalls:
Common mistakes include assuming all letters are shifted in the same direction or miscounting forward and backward moves in the alphabet. Another pitfall is failing to notice that the first half and second half of the word follow different shift directions. Writing down the alphabet and marking the movement for each letter step by step prevents these errors. Always verify your rule on the given example before applying it elsewhere.

Final Answer:
Using the same rule that converts MOTHER to NPUGDQ, the word ORANGE is written as PSBMFD in the code language.