Question: How many sons does X have? Statements: I. Q and U are brothers of T.…
2023
Question: 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.
- A.
Only I and II
- B.
Only II and III
- C.
All I, II and III
- D.
I, II and III together are not sufficient
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Concept: A set of statements is sufficient for a data-sufficiency question only when it lets you uniquely fix every fact the question needs — here, both WHO belongs to X's family and the GENDER of each of those people, since the question asks for an exact count of sons.
Statement I (Q and U are brothers of T) fixes Q and U as male and as siblings of T, but on its own does not connect T to X.
Statement III (R and T are daughters of X) fixes R and T as female children of X, and since T is a sibling of Q and U (from I), all of Q, R, T, U become children of X.
Statement II (R is sister of P and U) adds P as a sibling of R and U, so P also becomes a child of X — but 'sister of P' only tells us R's relationship to P, not P's own gender.
Cross-check: with all three statements combined, X's children are P, Q, R, T and U; Q and U are confirmed sons and R and T are confirmed daughters, but P could be male or female — the son count is either two or three depending on a fact that is never given.
Since even the full combination of I, II and III cannot pin down P's gender, the three statements together are not sufficient to answer how many sons X has.