In a word to number coding system, the value of a word is obtained by adding the alphabetical positions of its letters (A = 1, B = 2, …, Z = 26). If REDUCE has value 56 and RECYCLE has value 71 under this system, what is the value of REUSE?

Introduction / Context:
This is a straightforward coding question where words are converted into numbers by summing the positions of their letters in the English alphabet. You are told that REDUCE equals 56 and RECYCLE equals 71 in this system, and you must find the corresponding value for REUSE. This tests your familiarity with letter positions and basic addition.

Given Data / Assumptions:

• Alphabet positions: A = 1, B = 2, …, Z = 26.
• REDUCE has value 56.
• RECYCLE has value 71.
• The code value of a word is the sum of the positions of its letters.
• We need to find the value of REUSE.

Concept / Approach:
To confirm the coding rule, we compute the sum of letter positions for REDUCE and RECYCLE and check that they match the given values. Once verified, we apply exactly the same procedure to REUSE. The main tasks are to recall or determine the numeric position of each letter and to add these values accurately.

Step-by-Step Solution:
Step 1: Check the rule with REDUCE. Letters: R, E, D, U, C, E. Positions: R(18), E(5), D(4), U(21), C(3), E(5). Sum: 18 + 5 = 23, 23 + 4 = 27, 27 + 21 = 48, 48 + 3 = 51, 51 + 5 = 56. This matches the given value 56. Step 2: Check the rule with RECYCLE. Letters: R, E, C, Y, C, L, E. Positions: R(18), E(5), C(3), Y(25), C(3), L(12), E(5). Sum: 18 + 5 = 23, 23 + 3 = 26, 26 + 25 = 51, 51 + 3 = 54, 54 + 12 = 66, 66 + 5 = 71. This matches the given value 71. Step 3: Now apply the same rule to REUSE. Letters: R, E, U, S, E. Positions: R(18), E(5), U(21), S(19), E(5). Step 4: Add these values. 18 + 5 = 23. 23 + 21 = 44. 44 + 19 = 63. 63 + 5 = 68.

Verification / Alternative check:
Since the sums for REDUCE and RECYCLE match the given values exactly, the coding rule of summing letter positions is fully confirmed. The computation for REUSE uses the same positions and simple additions, so there is no ambiguity in obtaining 68. You can quickly re add 18 + 5 + 21 + 19 + 5 on a calculator or by grouping as (18 + 21) + (5 + 19 + 5) to double check that the result is 39 + 29 = 68.

Why Other Options Are Wrong:
Options 65, 69, 70 and 72 are all close to the correct value but do not match the exact sum of the letter positions for REUSE. Choosing any of these would reflect either a misremembered letter position or a small arithmetic mistake, such as adding 19 as 20 or miscounting the total. Because the rule is precise and the calculation is straightforward, only 68 fits the definition exactly.

Common Pitfalls:
A common pitfall is misassigning positions to letters near the middle or end of the alphabet, for example treating S as 20 instead of 19. Another is rushing through the addition and making a small mistake. Writing down each intermediate partial sum as shown and grouping numbers cleverly can help prevent simple arithmetic errors, especially under time pressure.

Final Answer:
Therefore, under this letter position coding system, the value of REUSE is 68.