In a letter-value coding scheme, it is given that A = 1 and the word "AND" has a total value of 19. Using the same scheme, what is the total coded value of the word "ANT"?

Introduction / Context:
This question is about assigning numerical values to letters of the English alphabet and then finding the total value of a word by adding the values of its letters. We are told that A = 1 and that the code value of the word "AND" is 19. We must use this information to deduce the values of other letters and then compute the total for the word "ANT".

Given Data / Assumptions:

• A single letter A has the value 1.
• The word "AND" has a total coded value of 19.
• We are asked to find the coded value of "ANT".
• The usual assumption is that each letter corresponds to its position in the English alphabet (A = 1, B = 2, C = 3, and so on).
• The total value of a word is the sum of the values of its individual letters.

Concept / Approach:
First, we confirm that the standard alphabet-position rule fits the given information for "AND". If it does, we then apply exactly the same rule to "ANT". Under this system, we find the values of A, N and D from their positions in the alphabet, check their sum for "AND", and then similarly compute the value of "ANT".

Step-by-Step Solution:
Take the alphabet positions: A is the 1st letter, N is the 14th letter and D is the 4th letter of the alphabet. Using these positions as values gives A = 1, N = 14 and D = 4. Compute the total for "AND": 1 + 14 + 4 = 19. This matches the given information that "AND" has value 19, so our assumption about letter values is correct. Now we apply the same logic to the word "ANT". A = 1 and N = 14 as before. T is the 20th letter of the alphabet, so T = 20. Add the values: 1 + 14 + 20 = 35. Therefore, the coded value of "ANT" is 35.

Verification / Alternative check:
We can double-check by comparing any other word we might form from these letters. For example, "TAN" would have the value 20 + 1 + 14 = 35 as well. This confirms that our assignment of letter values is consistent and that we are correctly using alphabet positions.

Why Other Options Are Wrong:
Option 33 would correspond to a different sum, such as 1 + 12 + 20, which does not match A, N and T. Option 23 would require much smaller letter values, and option 19 is already the sum for "AND", not "ANT". None of these alternatives fit the standard A = 1, B = 2, C = 3 pattern for the letters A, N and T.

Common Pitfalls:
A common mistake is to assume a different pattern like doubling letter positions or using some other number system without checking against the given reference word. As soon as we see that "AND" matches the simple alphabet-position sum, we should stick to that rule rather than overcomplicate the pattern.

Final Answer:
Using the same coding scheme, the value of "ANT" is 35.