Data Sufficiency — Counting sons: How many sons does D have? Statements: I. A’s father has three children. II. B is A’s brother and the son of D.

Introduction / Context:
We must determine the exact number of sons of person D. Data sufficiency requires judging if the statements independently or jointly allow a unique answer, without making unstated assumptions about genders or parentage beyond what is explicit or standard in reasoning questions.

Given Data / Assumptions:

• I: A’s father has three children (no genders specified).
• II: B is A’s brother and is a son of D (so D is a parent of B, and B is male).
• “Brother” implies A and B share parents (at least one), but D’s gender is not stated.

Concept / Approach:
From II, D parents at least one son (B). From I, the father of A has three children; this reveals a total child count in that nuclear family, but it does not necessarily identify D as that father, nor does it identify the genders of the other children (including A). We must avoid presuming that the mother (if D) and father have identical child sets unless explicitly connected.

Step-by-Step Solution:
II ⇒ D has at least one son (B). A’s gender unknown.I ⇒ A’s father has three children; genders not given, and D is not explicitly identified as A’s father.Combining I and II does not guarantee that D is the same person as “A’s father,” nor does it reveal whether the other two children are sons or daughters.Therefore, the exact number of D’s sons cannot be determined uniquely.

Verification / Alternative check:
Even if one assumes D is the mother, the father’s three children might be the same three as D’s, but their genders remain unknown apart from B. Multiple consistent possibilities exist (e.g., one son; two sons; or even three sons), so no unique count is possible.

Why Other Options Are Wrong:

• I alone: Says nothing about D.
• II alone: Gives only a lower bound (at least one son).
• Either alone or both: Do not pin down a unique number.

Common Pitfalls:

• Assuming D is necessarily the father mentioned in I.
• Assuming “three children” implies a fixed gender split.

Final Answer:
Neither I nor II is sufficient