In a certain code language, the word BROTHER is coded as GWTYMJW using a uniform alphabetical shift. Using the same coding rule, how is the word SCHOOL coded in that language?

Introduction / Context:
This question uses a Caesar cipher style of coding, where every letter is shifted forward by the same fixed number of positions in the alphabet. We know that BROTHER is coded as GWTYMJW and must apply the same shift to encode SCHOOL.

Given Data / Assumptions:

• BROTHER → GWTYMJW.
• We need to encode SCHOOL.
• The shift is uniform for all letters.

Concept / Approach:
We compare each letter in BROTHER with its coded form in GWTYMJW to deduce the fixed shift. Once found, we apply this shift to every letter in SCHOOL to find its code.

Step-by-Step Solution:
Step 1: Determine the shift from BROTHER to GWTYMJW. B (2) → G (7), R (18) → W (23), O (15) → T (20), T (20) → Y (25), H (8) → M (13), E (5) → J (10), R (18) → W (23). In each case, new position − old position = 5. Step 2: So the code is a Caesar shift of +5 positions. Step 3: Apply the +5 shift to SCHOOL. S (19) + 5 = 24 → X. C (3) + 5 = 8 → H. H (8) + 5 = 13 → M. O (15) + 5 = 20 → T. O (15) + 5 = 20 → T. L (12) + 5 = 17 → Q. Step 4: Thus SCHOOL is encoded as XHMTTQ.

Verification / Alternative check:
We can test the shift on another letter pair, like H (8) in BROTHER becoming M (13) in GWTYMJW. The difference 13 − 8 = 5 confirms the same +5 pattern, so the rule is uniform.

Why Other Options Are Wrong:
Options that differ in even one letter violate the +5 shift rule. For instance, any code that ends with P instead of Q would reflect a +4 shift for L instead of +5, which is inconsistent with BROTHER → GWTYMJW.

Common Pitfalls:
Learners may miscount the shift by one position or mix up forward and backward direction. Writing down the alphabet with position numbers helps ensure the shift is applied correctly.

Final Answer:
With a Caesar shift of +5, SCHOOL is coded as XHMTTQ in that language.