Question: How many sons does D have ? Statements: A's father has three…

Concept: A statement (or a combination of statements) is "sufficient" for a data-sufficiency question only when it pins down every fact the question asks for, with no ambiguity left. For a family-relationship question asking for a COUNT of sons, that means every child mentioned must be confirmed as belonging to the person in question AND every child's gender must be fixed — a statement that leaves even one child's gender or parentage open cannot be called sufficient.

Application:

1. Statement I alone: "A's father has three children" fixes the family size at three, but it never even names D, so it cannot answer how many of D's children are sons.

2. Statement II alone: "B is A's brother and son of D" confirms D has at least one son, B, but it says nothing about how many total children D has or whether A is also D's child, so the total son count stays unknown.

3. Combining I and II does not even guarantee that the father named in Statement I is the same person as D — Statement II only establishes that D is a parent of B, not necessarily the father, and being called A's "brother" does not guarantee A and B share the same father. Even under the most generous reading, where D is taken to be the father named in Statement I, D would have three children in total with only B confirmed male, while the genders of A and the third child are still never stated. Either way, the son count is never fixed.

Cross-check: Assign genders consistent with every given fact: A could be male or female, and the third child could be male or female, without contradicting Statement I or II. That freedom yields different possible son-counts (one, two, or three) that are all equally consistent with both statements together — so even combined, the data does not narrow down to a single count.

Result: Neither Statement I alone, nor Statement II alone, nor the two combined fix the number of sons D has — so neither I nor II is sufficient.