In a letter coding system, each letter of the English alphabet is assigned a value equal to its position (A = 1, B = 2, C = 3, and so on). It is given that E has the value 5 and the word PEN has the value 35. Using the same coding rule, what is the value assigned to the word PAGE?

Introduction / Context:
This problem is another letter sum coding question, where each letter of a word is replaced by its alphabetical position and then those values are combined by addition. The relationship E = 5 and PEN = 35 is given to help confirm the coding rule. Once we are sure of the pattern, we apply exactly the same logic to a new word, PAGE, and compute its total value.

Given Data / Assumptions:

• Letter positions: A = 1, B = 2, …, Z = 26. • E = 5 is explicitly stated and matches its position. • PEN = 35 under this code. • We must find the value of PAGE under the same system.

Concept / Approach:
We check whether PEN = 35 comes from summing the position values of P, E, and N. If it does, we accept this as the rule and apply it to PAGE. The main skill required is quick and accurate recall of letter positions and careful addition of a few small integers.

Step-by-Step Solution:
Step 1: Confirm the rule using PEN. Positions: P = 16, E = 5, N = 14. Step 2: Add these values: 16 + 5 = 21, 21 + 14 = 35. This matches the given code PEN = 35. Step 3: Now apply the same rule to PAGE. Determine positions: P = 16, A = 1, G = 7, E = 5. Step 4: Add them step by step. First 16 + 1 = 17. Step 5: Then 17 + 7 = 24. Step 6: Finally 24 + 5 = 29. Step 7: Therefore, under this code, PAGE has the value 29.

Verification / Alternative check:
You can perform the total addition again in a different grouping, for example (16 + 7) + (1 + 5) = 23 + 6 = 29, which confirms the earlier result. Also, notice that PAGE has four letters, and each letter has a value less than or equal to 16 here, so a total just under 30 fits expectations. This supports the correctness of 29.

Why Other Options Are Wrong:
Option 27 is smaller and would require a lesser sum than the actual positions provide. Option 28 is close but still does not match the exact sum of 29. Option 30 is larger and again does not correspond to the computed sum. Option 26 is significantly smaller than required and cannot be obtained from these letter values.

Common Pitfalls:
Typical mistakes involve misidentifying the position of G or P, or accidentally omitting one of the letters when adding. Some learners also confuse this kind of code with letter product or other operations, but the verification with PEN clearly shows that we are dealing with a simple sum of positions.

Final Answer:
Using the same letter position sum code, the word PAGE is assigned the value 29.