In a certain code language, the word "TIRED" is written as the number 56 and the word "BRAIN" is written as the number 44. Using the same rule, what number represents the word "LAZY"?

Introduction / Context:
This coding question converts words into numbers. The numeric code is based on the positions of letters in the alphabet, but the operation is not concatenation; rather, it is a total sum. The example words TIRED and BRAIN and their codes 56 and 44 hint at this pattern. We must find the code for LAZY under the same rule.

Given Data / Assumptions:

• TIRED is coded as 56.
• BRAIN is coded as 44.
• We must determine the code for LAZY.
• Letters are associated with their alphabet positions: A is 1, B is 2, up to Z which is 26.
• The code likely equals the sum of the positions of all letters in the word.

Concept / Approach:
To confirm the rule, convert each letter of TIRED and BRAIN into its alphabetical position and sum them. If the result matches the given code, then the pattern is established as a letter sum. Once confirmed, repeat the same process for LAZY. This type of question checks whether the candidate can move comfortably between letters and numbers and see patterns across multiple examples.

Step-by-Step Solution:
Step 1: Convert TIRED into letter positions: T, I, R, E, D. Step 2: T is 20, I is 9, R is 18, E is 5 and D is 4. Step 3: Sum these: 20 + 9 + 18 + 5 + 4 = 56, which matches the code for TIRED. Step 4: Now convert BRAIN into letter positions: B, R, A, I, N. Step 5: B is 2, R is 18, A is 1, I is 9 and N is 14. Step 6: Sum these: 2 + 18 + 1 + 9 + 14 = 44, matching the code given for BRAIN. The rule is confirmed. Step 7: Apply the same rule to the word LAZY. Step 8: L is 12, A is 1, Z is 26 and Y is 25. Step 9: Sum them: 12 + 1 + 26 + 25 = 64. Step 10: Therefore LAZY is coded as 64.

Verification / Alternative check:
As a quick check, consider whether any alternative pattern such as product or difference could yield the same results. Products of letter positions would be extremely large, so they are unlikely. Differences would be small or negative and do not match the given positive codes. Simple addition fits both example words exactly, so it is the most reasonable and consistent pattern.

Why Other Options Are Wrong:
Options 61, 54 and 51 result from partial sums, omitted letters or miscounted positions. Because the mapping from letters to numbers is well defined and the addition rule has been confirmed twice, only the exact sum 64 can be correct. Any other total indicates a mistake at some stage in converting or adding the letter values.

Common Pitfalls:
Errors often occur when counting letter positions, especially for letters near the end of the alphabet like Y and Z. Another pitfall is misreading the pattern and trying to concatenate digits instead of summing values. Writing out the alphabet with positions or double checking suspicious letters helps avoid such errors.

Final Answer:
Using the same letter position sum rule that maps TIRED to 56 and BRAIN to 44, the word "LAZY" is coded as 64.