Data sufficiency – counting sons of X from sibling statements How many sons does X have? Statements: (I) Q and U are brothers of T. (II) R is sister of P and U. (III) R and T are daughters of X.

Introduction / Context:This is a family-relation data-sufficiency problem. We must determine the exact number of sons of X using given sibling relationships and genders.

Given Data / Assumptions:

• I: Q and U are brothers of T (so Q and U are male and siblings of T).
• II: R is sister of P and U (so R is female, and P and U are R’s siblings).
• III: R and T are daughters of X (both female children of X).

Concept / Approach:Combine statements to list X’s children and their genders, then count sons. The key is whether P’s gender is determined or not.

Step-by-Step Solution:

Verification / Alternative check:No additional hidden constraints fix P’s gender. Therefore, even all three statements together do not yield a unique count of sons.

Why Other Options Are Wrong:

• Only I and II / Only II and III / All I, II and III: None can uniquely determine P’s gender; ambiguity remains.
• None of these: Incorrect because the correct conclusion is that insufficiency persists.

Common Pitfalls:Assuming 'sister of P' implies P is male. It does not; a person can be a sister of another sister as well. Do not infer extra facts.

Final Answer:I, II and III together are not sufficient