How many children does M have? Statements: I. H is the only daughter of X, who…

Concept

A data-sufficiency question asks whether the given facts determine one unique answer; it does not ask whether they provide some related information.

Family-relation terms must be read at the correct generation. “Only daughter” limits female children, whereas “brother of M” describes M’s siblings.

Application

1. From Statement I, H is a daughter of X, and X is M’s wife. The statement fixes one daughter but gives no information about the number of sons, so M’s total number of children is not fixed.

2. From Statement II, K and J are M’s brothers. This tells us about M’s siblings and gives no count of M’s children.

3. Combining the statements adds the sibling facts to the one-daughter fact, but still leaves the number of sons unknown. Therefore the total cannot be uniquely calculated.

Cross-check and contrast

• “I alone is sufficient while II alone is not sufficient” conflicts with the unbounded number of sons in Statement I.

• “II alone is sufficient while I alone is not sufficient” uses sibling information that does not count children.

• “Both I and II are sufficient” still lacks a bound on sons after combination.

• “Neither I nor II is sufficient” reflects that neither statement determines a unique total.

Result: Neither I nor II is sufficient.