How many brothers does A have? I. A, who is B's brother, has two siblings. II. D is a brother of A and is the youngest in the family.

Difficulty: Medium

Statement I alone is sufficient; Statement II alone is not.
Statement II alone is sufficient; Statement I alone is not.
Either Statement I alone or Statement II alone is sufficient.
Both statements together are NOT sufficient.
Both statements together are sufficient, but NEITHER alone is sufficient.

Correct Answer: Both statements together are NOT sufficient.

Explanation:

Introduction / Context:
The task is to determine the exact number of A's brothers from two familial statements. In Data Sufficiency, we do not compute every possibility; we judge whether the information fixes a unique answer.

Given Data / Assumptions:

I: A is B's brother (so A is male) and A has exactly two siblings in total.
II: D is a brother of A and is the youngest.
“Sibling” means brother or sister; genders of unspecified siblings are unknown unless stated.

Concept / Approach:
Translate each statement into structure and test whether the number of A's brothers is uniquely determined. If more than one consistent family composition fits the statements, sufficiency fails.

Step-by-Step Solution:

1) I alone: A has two siblings. One named sibling is B (gender unknown). The other sibling is unnamed and gender unknown. Thus, the number of A’s brothers could be 1 (if only one of {B, other} is male) or 2 (if both are male). I alone is not sufficient.2) II alone: We only learn that D is a brother of A and the youngest. Others (including B) may be brother(s) or sister(s); the total sibling count is unknown. II alone is not sufficient.3) I + II: From I, A has exactly two siblings: {B, X}. Statement II forces one sibling (say D) to be a brother; this pins either B = D or X = D. We still cannot determine B’s gender. Therefore A’s brothers = 1 (if B is sister) or 2 (if B is brother). Not unique.

Verification / Alternative check:
Construct two consistent families: Case 1: Siblings {D (brother), B (sister)} ⇒ brothers = 1. Case 2: {D (brother), B (brother)} ⇒ brothers = 2.

Why Other Options Are Wrong:

A/B/C: Neither statement alone nor “either alone” is enough.
E: Together still ambiguous.

Common Pitfalls:
Assuming B's gender; overlooking that I limits total siblings to exactly two, not enabling gender resolution.

Final Answer:
Both statements together are NOT sufficient.

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How many brothers does A have? I. A, who is B's brother, has two siblings. II. D is a brother of A and is the youngest in the family.

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