In how many days can 14 men complete a piece of work? I. 18 women can complete the same work in 24 days. II. 28 children can complete the same work in 56 days. (No rate equivalence among men, women, children is given.)
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AStatement I alone is sufficient; Statement II alone is not
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BStatement II alone is sufficient; Statement I alone is not
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CEither Statement I alone or Statement II alone is sufficient
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DBoth statements together are necessary
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EEven both statements together are not sufficient
Answer
Correct Answer: Even both statements together are not sufficient
Explanation
Introduction / Context:We are asked for the completion time for 14 men. The statements give only women- and children-based work rates. No cross-equivalence is provided.
Given Data / Assumptions:
- I: 18 women finish in 24 days ⇒ women’s combined rate known.
- II: 28 children finish in 56 days ⇒ children’s combined rate known.
- No relation between a man’s rate and a woman’s/child’s rate.
Concept / Approach:To find men’s time, we need men’s rate (or a conversion factor to women/children). Absent any conversion, the unknown scale for men makes the target uncomputable.
Step-by-Step Reasoning:I alone: provides only women’s aggregate rate; tells nothing about men.II alone: provides only children’s aggregate rate; tells nothing about men.I + II: still no linkage to men, so men’s rate remains undetermined.
Why Other Options Are Wrong:Any option claiming sufficiency is incorrect because a key conversion (man↔woman/child) is missing.
Common Pitfalls:Assuming a conventional equivalence like “1 man = 2 women” without it being stated; data sufficiency disallows that.
Final Answer:Even both statements together are not sufficient.