In the following question, select the related group of letters from the given alternatives: AMC is to COE as RAX is to which group?

Introduction / Context:
This question presents a letter coding analogy. The group AMC is related to COE according to a fixed shift in the alphabet, and you must find which option gives the correct related group for RAX under the same rule. Such questions check your skill in working with alphabet positions and uniform shifts across multiple letters.

Given Data / Assumptions:

• AMC is the original group of letters and COE is its coded form.
• RAX is the second original group, and its coded form is missing.
• The options are MKZ, TCZ, ECB, and FBT.
• Alphabet positions are taken as A = 1, B = 2, ..., Z = 26.
• We assume the same positional shift is applied to each letter of AMC to get COE, and then to each letter of RAX.

Concept / Approach:
We convert the letters of AMC and COE into numbers, compute the difference for each corresponding pair, and see whether the shift is constant. If all letters shift by the same number of positions, that constant shift is the coding rule. We then apply that to RAX to find the matching coded group. This kind of uniform shift is standard in alphabet coding problems and is often the simplest explanation.

Step-by-Step Solution:
Step 1: Write the positions of AMC. A is 1, M is 13, and C is 3. Step 2: Write the positions of COE. C is 3, O is 15, and E is 5. Step 3: Compute the shift for each letter. From A(1) to C(3) is +2, from M(13) to O(15) is +2, and from C(3) to E(5) is also +2. Step 4: Conclude that the coding rule is to add 2 to the position of each letter. Step 5: Now take RAX and find the positions. R is 18, A is 1, and X is 24. Step 6: Add 2 to each position. R(18) + 2 = 20, which is T. A(1) + 2 = 3, which is C. X(24) + 2 = 26, which is Z. Step 7: Combine these letters to get TCZ and compare with the options. TCZ matches option b.

Verification / Alternative check:
To verify, subtract 2 from each letter of TCZ and see if we return to RAX. T(20) minus 2 equals 18 (R), C(3) minus 2 equals 1 (A), and Z(26) minus 2 equals 24 (X). This confirms the rule is consistent both forward and backward. None of the other options, when reduced by 2 letters each, produces RAX, so they do not satisfy the same uniform shift rule.

Why Other Options Are Wrong:
MKZ, ECB, and FBT each require a different set of shifts from RAX and do not follow the constant plus two rule. For example, to get M from R requires a shift of minus 5, while to get K from A requires plus 10, which is inconsistent. Since a true letter coding analogy must apply the same transformation to all letters, these options cannot be correct.

Common Pitfalls:
Learners sometimes look for more complicated patterns such as alternating forward and backward shifts. While such patterns do occur in harder questions, the first thing to check in a simple three letter group coding is whether a single constant shift works across all letters. In this case, that straightforward test quickly reveals the +2 rule.

Final Answer:
Applying the same +2 alphabet shift that converts AMC to COE, the group RAX is coded as TCZ.