In a letter to number coding pattern, the single letter C is coded as 3 and the four letter word DASH is coded as 32. Assuming that the code for a word is obtained by summing the alphabetical positions of its letters (A = 1, B = 2, C = 3, and so on), what code will be assigned to the five letter word DANCE?

Introduction / Context:
This question again uses the simple yet widely used rule that each letter in a word is replaced by its position in the alphabet, and the code for the word is the sum of these values. The fact that C is coded 3 and DASH is coded 32 fits well with this letter sum system. Once we validate the pattern using DASH, we can apply the same method to calculate the code for the word DANCE.

Given Data / Assumptions:

• Alphabet positions: A = 1, B = 2, C = 3, …, Z = 26. • C = 3 is consistent with its position. • DASH = 32 under the code. • We must find the code for DANCE.

Concept / Approach:
We first verify that DASH = 32 by summing the positions of D, A, S, and H. If the sum matches 32, we can assume the same sum of positions rule applies to and then compute the value for DANCE. The task mainly involves recalling letter positions accurately and adding several small numbers correctly.

Step-by-Step Solution:
Step 1: Confirm the coding for DASH. Positions: D = 4, A = 1, S = 19, H = 8. Step 2: Add these: 4 + 1 = 5, 5 + 19 = 24, 24 + 8 = 32. This matches the given code, so the pattern is confirmed. Step 3: Now apply the same rule to DANCE. Identify the positions: D = 4, A = 1, N = 14, C = 3, E = 5. Step 4: Begin adding: 4 + 1 = 5. Step 5: Add N: 5 + 14 = 19. Step 6: Add C: 19 + 3 = 22. Step 7: Add E: 22 + 5 = 27. Step 8: Therefore DANCE is coded as 27.

Verification / Alternative check:
A quick alternative addition sequence, such as (4 + 14) + (1 + 3 + 5) = 18 + 9 = 27, confirms the same result. The total is reasonable for a five letter word whose letters mainly lie in the first half of the alphabet. This makes 27 a consistent and reliable answer.

Why Other Options Are Wrong:
Option 20 is too small and does not match the calculated sum. Option 25 is slightly smaller than the correct value and indicates incomplete addition. Option 26 is close but not equal to 27 and does not correspond to the exact positions. Option 23 is significantly below the correct sum and therefore incorrect.

Common Pitfalls:
Common errors include forgetting one letter while adding or misremembering the position of N or E. Careful writing of all letters with their corresponding numbers and a systematic addition eliminates these mistakes.

Final Answer:
Under the given letter sum coding rule, the word DANCE is coded as 27.