How many children does M have? Statements: I. H is the only daughter of X, who…
2023
How many children does M have?
Statements:
I. H is the only daughter of X, who is the wife of M.
II. K and J are brothers of M.
- A.
The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
- B.
The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
- C.
If the data in either statement I alone or statement II alone is sufficient to answer the question
- D.
If the data in both statements I and II together is not sufficient to answer the question
Show answer & explanation
Correct answer: D
CONCEPT: In a data-sufficiency question, a statement (or a combination of statements) is sufficient only when it uniquely pins down every quantity the question asks for. Partial information about one category, or information about an unrelated relationship, does not establish the total unless it explicitly rules out every other possibility.
APPLICATION: Statement I tells us H is the only daughter of X, who is M's wife — under the standard reading of such family-relation statements (X and M's children are taken as the same set), H is therefore the only daughter attributed to M. It says nothing about sons, so M could have zero, one, or several sons, leaving the total number of children undetermined from statement I alone. Statement II tells us K and J are M's brothers — this describes M's own siblings, a completely different relationship from M's children, so it adds no information about how many children M has. Combining both statements still leaves the number of sons completely open, since neither statement constrains it.
CROSS-CHECK: Since no combination of the two statements fixes a unique total number of children, the data — taken alone or together — is insufficient to answer the question.