What will be the total weight of 10 poles if each pole has the same weight? Statement I: One fourth of the weight of a pole is 5 kilograms. Statement II: The total weight of three poles is 20 kilograms more than the total weight of two poles.

Introduction / Context:
This is a straightforward arithmetic data sufficiency question involving equal weights. You are asked to find the total weight of 10 identical poles. Two statements provide different ways of expressing the weight of a single pole. The primary goal is to determine whether one or both of the statements are sufficient to compute the total weight, not to perform unnecessary extra calculations.

Given Data / Assumptions:
- All 10 poles have the same weight.
- Question: What is the total weight of 10 such poles?
- Statement I: One fourth of the weight of a pole is 5 kilograms.
- Statement II: The total weight of three poles is 20 kilograms more than the total weight of two poles.
- We assume basic algebra holds and weights add linearly.

Concept / Approach:
If we denote the weight of one pole by w kilograms, then the total weight of 10 poles is 10w. Each statement gives a linear equation involving w. If any single statement allows us to solve uniquely for w, then that statement alone is sufficient. If both statements individually allow us to solve for w, then either statement alone is sufficient and we choose the appropriate data sufficiency option accordingly.

Step-by-Step Solution:
Step 1: Analyze statement I. It states that one fourth of the weight of a pole is 5 kilograms. In algebraic form, this is (1/4) * w = 5. Step 2: Solving for w gives w = 5 * 4 = 20 kilograms. Then the total weight of 10 poles is 10 * 20 = 200 kilograms. Hence, statement I alone is sufficient to answer the question. Step 3: Now analyze statement II. It states that the total weight of three poles is 20 kilograms more than the total weight of two poles. In algebraic form, 3w = 2w + 20. Step 4: Subtracting 2w from both sides yields w = 20 kilograms. Again, the total weight of 10 poles is 10 * 20 = 200 kilograms. Therefore, statement II alone is also sufficient to answer the question. Step 5: Since each statement alone leads to a unique value of w and hence the total weight of 10 poles, either statement alone is sufficient, and using both together is not necessary.

Verification / Alternative check:
We can confirm that both statements give the same weight for one pole. From both I and II we obtain w = 20 kilograms. This consistency reassures us that there is no hidden contradiction and that both statements describe the same situation in different ways. Furthermore, once w is known, the total weight of 10 poles is uniquely determined as 200 kilograms.

Why Other Options Are Wrong:
- Option a is wrong because it claims only statement I is sufficient, ignoring that statement II alone is also adequate.
- Option b is wrong for the symmetric reason: it credits only statement II while statement I is equally sufficient.
- Option d is incorrect because we do not need to combine the statements; either alone suffices.
- Option e is wrong because the data are not insufficient or contradictory; each statement individually gives a clear answer.

Common Pitfalls:
Some students assume that if two statements are given, both must be used together, which is not the case in data sufficiency problems. Others may fail to translate the verbal descriptions into algebra correctly. For instance, misunderstanding "20 kilograms more than the total weight of two poles" may lead to incorrect equations. Carefully forming and solving the linear equations for each statement separately avoids these errors.

Final Answer:
Either statement I alone or statement II alone is sufficient to determine the total weight of 10 poles, which is 200 kilograms. Therefore, the correct data sufficiency choice is option C.