Data sufficiency — How many daughters does W have? Statements: A. B and D are sisters of M. B. M's father T is the husband of W. C. Out of three children which T has, only one is a boy. Find which statements suffice to determine the number of W's daughters.

Introduction / Context:We must determine the exact number of daughters of W using standard family-relation logic and data sufficiency reasoning. Pay attention to how each statement contributes.

Given Data / Assumptions:

• A: B and D are sisters of M (so B and D are female; all three are siblings).
• B: M’s father is T, and T is the husband of W (so W is M’s mother).
• C: T has exactly three children and only one is a boy.

Concept / Approach:Translate the statements into counts. If T has three children and only one is a boy, then two are girls. Using A, identify which of B, D, M are girls and which could be the boy.

Step-by-Step Solution:

Verification / Alternative check:If M were also a girl, there would be zero boys, contradicting C. If either B or D were not W’s child, B would be violated (which ties M to W) plus A would no longer align with C’s total count under the shared-parent assumption. Thus the two-daughter conclusion holds only when all three statements are used together.

Why Other Options Are Wrong:

• Only A and C: Without B, we cannot link W to these children.
• Only B and C: The specific identity of the two girls (and count) is unclear without A.
• Only A and B: Lacks the crucial “one boy” constraint.
• Only C: Gives a ratio, not identities or link to W.

Common Pitfalls:Assuming A alone ties children to W; forgetting that C is needed to fix genders; ignoring that B links W to the sibling group.

Final Answer:All A, B and C.