Directions: Each of the questions given below consists of a statement and/or a question followed by two statements labelled I and II. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. How many women can complete a piece of work in 15 days? (Bank P.O., 2009) I. 12 women can complete the same piece of work in 20 days. II. 10 men can complete the same piece of work in 12 days.
Verbal Reasoning
Data Sufficiency
Difficulty: Easy
Choose an option
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Aif the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question;
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Bif the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question;
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Cif the data either in Statement I or in Statement II alone are sufficient to answer the question;
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Dif the data even in both Statements I and II together are not sufficient to answer the question;
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Eif the data in both Statements I and II together are necessary to answer the question.
Answer
Correct Answer: if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question;
Explanation
### Concept & Chain Rule
This is a standard "Time and Work" problem that can be solved using the fundamental principle that Total Work is constant. We use the formula:
$$ M_1 \times D_1 = M_2 \times D_2 $$
where $M$ represents the number of workers (women) and $D$ represents the number of days.
### Step-by-Step Solution
We need to find $M_2$ (number of women) when $D_2 = 15$ days.
From Statement I:
* We are given $M_1 = 12$ women and $D_1 = 20$ days.
* According to the formula: $12 \times 20 = M_2 \times 15$.
* We can easily solve for $M_2$: $M_2 = \frac{12 \times 20}{15} = 16$.
* Therefore, Statement I alone is sufficient to find the exact number of women.
From Statement II:
* We are given information about men ($M_1 = 10$ men, $D_1 = 12$ days).
* Since we do not know the relative efficiency between men and women (e.g., 1 man = how many women?), we cannot use this data to find the number of women needed.
* Therefore, Statement II alone is insufficient.
### Exam Strategy & Shortcut
When the question asks for a specific demographic (women) and a statement provides the complete initial conditions for that exact demographic, you can instantly confirm sufficiency. You don't actually need to calculate the final answer (16) to know that the formula $M_1D_1 = M_2D_2$ will work.
### Common Pitfall
A common mistake is trying to force a relationship between men and women from Statement II to use the data. Unless an efficiency ratio is explicitly given, demographics cannot be interchanged in work equations.
### Final Answer
Therefore, the correct answer is **if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question;**