Multiple choice

The following questions are accompanied by two statements A and B. You have to determine which statements(s) is/are sufficient/necessary to answer the questions. In how many days A will complete the work, if B takes 10 more days than A and C takes 4 less days than B to do the same work. (A) Time taken by B & C together is 10/9 less days than that by A alone. (B) A & C together will take less time than the taken by B & C together

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

  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 questions, 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.
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A Correct answer
Explanation

Let A's time be x. B's time is x + 10. C's time is (x + 10) - 4 = x + 6. Statement A provides the relationship between the combined work rate of B and C and A's work rate, which is sufficient to solve for x. Statement B is a qualitative comparison and does not provide enough numerical data to solve for x.

AI explanation

Let the time taken by A be x days, making B's time x + 10 and C's time x + 6. Statement A provides the combined work rate equation for B and C by stating their time is 10/9 days less than A's time, which translates directly to 1 / (1/(x+10) + 1/(x+6)) = x - 10/9. Solving this single quadratic equation yields the value of x, showing Statement A is entirely sufficient. Statement B only provides a qualitative comparison of combined speeds, offering no numerical data to form an equation. Therefore, Statement A alone is sufficient to answer the question.

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