In a certain letter coding system, each word is assigned a numerical value based on its letters. For example, the single letter S has the value 19, the word SUN has the value 54, and the word CAKE has the value 20. Using the same coding pattern, what numerical value should be assigned to the word MISTAKE?

Introduction / Context:
This problem is a classic example of a letter to number coding question, where each letter of the English alphabet is associated with its position number, and then those values are combined to obtain the code for a word. Such questions test your familiarity with alphabet positions and your ability to quickly add several numbers. Understanding this pattern makes it easy to handle many similar verbal reasoning questions.

Given Data / Assumptions:

• The letter S is coded as 19. • The word SUN is coded as 54. • The word CAKE is coded as 20. • We assume standard alphabet positions: A = 1, B = 2, C = 3, …, Z = 26. • The same rule must be applied to find the code for MISTAKE.

Concept / Approach:
The most natural approach is to check whether the codes are obtained by summing alphabet positions of each letter in the word. If this works for the given examples, we can safely apply the same rule to the target word. We therefore convert each letter into its positional value, add those values, and match the total with one of the options.

Step-by-Step Solution:
Step 1: Check S = 19. In the alphabet, S is the 19th letter, so this fits the pattern directly. Step 2: Check SUN = 54. Positions: S = 19, U = 21, N = 14. Sum = 19 + 21 + 14 = 54. The pattern is consistent. Step 3: Check CAKE = 20. Positions: C = 3, A = 1, K = 11, E = 5. Sum = 3 + 1 + 11 + 5 = 20. Again the pattern holds. Step 4: Apply the same to MISTAKE. Write down positions: M = 13, I = 9, S = 19, T = 20, A = 1, K = 11, E = 5. Step 5: Add these values: 13 + 9 = 22, 22 + 19 = 41, 41 + 20 = 61, 61 + 1 = 62, 62 + 11 = 73, 73 + 5 = 78. Step 6: The total value obtained for MISTAKE is 78.

Verification / Alternative check:
As a quick verification, compare the size of the word and the magnitude of the final value. MISTAKE has seven letters and the average position value is around 10 to 11, so a total near 70 to 80 is reasonable. This rough check supports the calculated result of 78. Also, none of the other options represent the correct sum of the letter values, so the answer is uniquely determined.

Why Other Options Are Wrong:
Option 68 is too small and would correspond to a lower overall sum of letter positions than actually present in MISTAKE. Option 59 is much smaller and clearly does not match the detailed addition. Option 48 is even further away from the computed total and does not fit the established pattern. Option 88 is larger than the correct sum and cannot be obtained from the given letter values.

Common Pitfalls:
Common mistakes include miscounting letter positions, especially confusing letters around the middle of the alphabet such as M, N, O, P, and mixing up the order of additions. Some learners rush and try to guess based on approximate length, which can easily lead to an incorrect option. It is safer to write the positions clearly and add them systematically.

Final Answer:
Using alphabet positions and summing them, the code for MISTAKE is 78.