Question

How many daughters does A have? Statements: (I) B and C are only sisters of D whose father E is the husband of A. (II) P, Q are daughters of R who is a brother of D’s husband.

• A. Statement (I) alone is sufficient to answer the question, but (II) alone is not sufficient.
• B. Statement (II) alone is sufficient to answer the question, but (I) alone is not sufficient.
• C. Both the statements (I) and (II) are sufficient to answer the question, but neither statement alone is sufficient.
• D. Both the statements (I) and (II) together are not sufficient to answer the question and additional data are required.

Hint:

In family tree questions, words like husband/wife can reveal gender, which often helps complete the relation.

Answer 1

The Correct Option is C

Concept: In family relation problems, identify direct blood relations carefully. The question asks specifically about the number of daughters of A.

Step 1: Checking Statement (I).
Given: B and C are the only sisters of D. Also, D’s father is E. And E is the husband of A. So A and E are parents of D. Since B and C are sisters of D, they are also children of A and E. Thus: \[ B,\;C \] are daughters of A. But D’s gender is unknown. So A may have: \[ 2 \text{ or } 3 \text{ daughters} \] Hence Statement (I) alone is not sufficient.

Step 2: Checking Statement (II).
Given: P and Q are daughters of R. R is brother of D’s husband. This gives information about another family branch. No direct relation with A’s daughters. Thus Statement (II) alone is not sufficient.

Step 3: Checking both statements together.
From Statement (I), A definitely has B and C as daughters. From Statement (II), D’s husband is mentioned. This implies D is female. Since D is also child of A and E: \[ D \] is also A’s daughter. Thus total daughters of A: \[ B,\;C,\;D \] So number of daughters: \[ 3 \] Hence, both statements together are sufficient.