In a certain coding scheme, each word is assigned a value based on the letters it contains. If A = 26 and the word X-RAY has the coded value 40, then what is the coded value of the word WHAT?

Introduction / Context:
This question defines a letter based numerical code with two examples. We are told that A has a code value of 26 and that X-RAY has a total code of 40. Using this information, we must deduce the coding rule and then find the code for WHAT. This problem tests understanding of alphabetical positions and a simple transformation involving reversing the order of the alphabet to assign numeric values to letters.

Given Data / Assumptions:

• Single letter A has code 26.
• Word X-RAY has code 40.
• Hyphens in words like X-RAY are not letters and do not get codes.
• The same coding rule is used consistently for all letters.
• We must find the code value for the word WHAT.

Concept / Approach:
In the standard alphabet, A has position 1, B has 2 and Z has 26. Here, however, A is assigned the value 26. This suggests that letter values are counted from the end of the alphabet: A gets 26, B gets 25, C gets 24 and so on down to Z which would get 1. Thus, each letter's code value is 27 minus its normal alphabetical position. For X-RAY, we sum the reversed positions of X, R, A and Y and check whether this equals 40. If it does, we apply the same reversed position rule to W, H, A and T in WHAT.

Step-by-Step Solution:
Step 1: Confirm the reversed alphabet rule using A. In normal order, A is 1st, so reversed value is 27 - 1 = 26, matching the given A = 26. Step 2: Compute reversed values for X-RAY. Normal positions: X = 24, R = 18, A = 1, Y = 25. Step 3: Reversed values are: X → 27 - 24 = 3, R → 27 - 18 = 9, A → 27 - 1 = 26, Y → 27 - 25 = 2. Step 4: Sum these values: 3 + 9 + 26 + 2 = 40, which matches the given code for X-RAY. Step 5: Now apply the same rule to WHAT: letters W, H, A and T. Step 6: Normal positions: W = 23, H = 8, A = 1, T = 20. Step 7: Reversed values: W → 27 - 23 = 4, H → 27 - 8 = 19, A → 27 - 1 = 26, T → 27 - 20 = 7. Step 8: Add these: 4 + 19 + 26 + 7. Step 9: 4 + 19 = 23, then 23 + 26 = 49, and 49 + 7 = 56.

Verification / Alternative check:
We can verify by checking that the pattern works on both A and X-RAY without any inconsistencies. The reversed values for X-RAY add up exactly to 40, and A's reversed index is 26. No other simple coding scheme involving letter values would fit both pieces of information so neatly. Recomputing the sum for WHAT confirms that 56 is correct, and among the answer options, only 56 matches this computation.

Why Other Options Are Wrong:
Options 52, 54, 58 and 60 do not equal the sum of the reversed positions of W, H, A and T. To obtain any of these values, one would have to miscount one or more letter positions or apply an inconsistent rule. Since the code is clearly defined by A and X-RAY, and 56 is uniquely determined by that rule for WHAT, the other options cannot be correct.

Common Pitfalls:
A frequent mistake is to assume that the letters use their normal alphabetical positions and then to sum those. Another is to misinterpret A = 26 as a special case for A only, instead of seeing it as a clue that the entire alphabet is reversed. Some may also forget to include all letters in the word WHAT or miscalculate the arithmetic sum. Carefully computing 27 minus each normal position and adding the values step by step prevents these errors.

Final Answer:
Using the reversed alphabet coding rule, the value of WHAT is 56.