Multiple choice

Directions: The given question is followed by two statements A and B. You have to determine which statement(s) is/are sufficient/necessary to answer the question. If 10 men and 9 women can complete a job in 10 days, then in how many days can 7 men and 2 women complete the same job? A. The efficiency of one woman is 200% of the efficiency of one man. B. 3 men and 2 women can complete the job in 40 days.

  1. Statement A alone is sufficient to answer the question, but statement B alone is not sufficient to answer the question.

  2. Statement B alone is sufficient to answer the question, but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A gives the ratio of efficiencies, which allows calculating the work done by any combination of men and women. Statement B provides a specific scenario that allows calculating the total work and the individual rates. Both are sufficient independently.

AI explanation

Statement A tells us one woman equals two men in efficiency, so 9 women can be treated as 18 men, making the total work equal to 280 men-days. Replacing the women in the target group using this ratio gives 11 men, which is sufficient to find the time is 280/11 days. Statement B provides a second equation (3 men and 2 women take 40 days) which can be solved simultaneously with the question's base data (10 men and 9 women take 10 days) to find the efficiency ratio of men and women, and subsequently the time for 7 men and 2 women. Because either statement alone unlocks the ratio needed to solve for the target group, either statement by itself is sufficient.

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