Siblings — How many sisters does K have? Statements: I. M is a sister of K. II. K’s mother has three children.
Verbal Reasoning
Data Sufficiency
Difficulty: Medium
Choose an option
Answer
Correct Answer: Both Statements I and II together are not sufficient to answer the question.
Explanation
Introduction / Context:We need the exact count of K's sisters from family-size and one-known-sister facts.
Given Data / Assumptions:
- I: K has at least one sister (M).
- II: Total children of K’s mother = 3 (includes K).
Concept / Approach:Enumerate possibilities for the third child’s gender.
Step-by-Step Solution:
From I alone: #sisters ≥ 1, but could be 1 or 2; insufficient.From II alone: With 3 children total, the composition is unknown; #sisters for K could be 0, 1, or 2; insufficient.Together: We know one sister (M) and one additional sibling whose gender is unknown. Therefore, #sisters ∈ {1,2}. Not unique.Verification / Alternative check:Case A: (K male), siblings = {M (F), X (M)} → 1 sister. Case B: (K male), siblings = {M (F), X (F)} → 2 sisters. Both obey I & II.
Why Other Options Are Wrong:
- A/B/C/E: Neither statement alone suffices; even together they do not fix a unique number.
Common Pitfalls:Assuming genders not stated; presuming K’s own gender.
Final Answer:D — Together not sufficient.