Among four friends A, B, C, and D, who is the heaviest? Consider the following statements: I. B is heavier than A but lighter than D. II. C is lighter than B.

Introduction / Context:
This data sufficiency problem is about comparing weights of four friends A, B, C, and D. The question asks who is the heaviest among them. Two statements provide partial information about relative weights. The goal is to determine which statements, alone or together, allow us to identify the heaviest friend without ambiguity.

Given Data / Assumptions:

• Statement I: B is heavier than A but lighter than D.
• Statement II: C is lighter than B.
• No two friends have exactly the same weight unless implied, and all inequalities are consistent.

Concept / Approach:
Each statement gives a set of inequalities on a weight scale. We want to know whether they jointly force one person to be at the top of this order. If one friend is heavier than all others based on the combined information, then that combination is sufficient. If any friend could still be heavier under some allowed arrangement, then the data are not sufficient.

Step-by-Step Solution:
Step 1: Translate statement I. B is heavier than A, so B > A. B is lighter than D, so D > B. Combining these, we get D > B > A. Step 2: Under statement I alone, we do not know the position of C in relation to D, B, or A. C could be heavier than D, lighter than A, or anywhere in between. For example, one possible order is C > D > B > A, where C is heaviest, and another is D > B > A > C, where D is heaviest. Hence statement I alone is not sufficient to identify the heaviest person. Step 3: Translate statement II. C is lighter than B, so B > C. We do not know where A or D stand relative to B or C from this statement alone, so II alone is not sufficient either. Step 4: Combine statements I and II. From I, D > B > A. From II, B > C. Combining these, we have D > B > A and D > B > C. Step 5: Put these together into a single order. We know that B is heavier than both A and C, and D is heavier than B. A and C might still be ordered either way relative to each other, but that does not affect who is heaviest. The crucial point is that D is heavier than B, and B is heavier than both A and C, so D is heavier than all three of A, B, and C. Step 6: Since there is no information suggesting any friend is heavier than D, and the inequalities show D above all others, D must be the heaviest. This conclusion relies on both statements I and II.

Verification / Alternative check:
To verify, attempt to construct any arrangement where someone other than D is heaviest while satisfying both statements. If we try to make B heaviest, we contradict D > B. If we try to make C heaviest, we contradict B > C and D > B. If we try to make A heaviest, we contradict B > A and D > B. Therefore, every consistent arrangement places D at the top, which confirms that the combined statements are sufficient to answer the question.

Why Other Options Are Wrong:
Option A, giving sufficiency to statement I alone, is wrong because C is unconstrained there and could be heavier than D. Option B, suggesting statement II alone is sufficient, is clearly incorrect since it does not involve D or A at all. Option C, claiming either statement alone is sufficient, fails for both reasons. Option E, which states that even both statements together are not sufficient, is false because the combined inequalities force D to be heaviest. Only option D correctly states that both statements together are necessary and sufficient.

Common Pitfalls:
Learners sometimes focus only on the explicit comparisons and overlook people not mentioned directly in a statement, leading to premature conclusions. Another frequent mistake is to fail to notice that, under statement I alone, C position is completely undetermined. Drawing a simple diagram or number line for weights when combining statements greatly reduces this kind of confusion.

Final Answer:
The data in both statements I and II together are necessary to answer the question, so the correct option is D.