Multiple choice

Directions: The following question is accompanied by two statements A and B. You have to determine which statements(s) is/are sufficient/necessary to answer the question. If 23 unskilled and 20 skilled persons together can complete a project in 12 days, then 20 unskilled persons alone can complete the same project in how many days? (A) The skilled persons are 30% more efficient than the unskilled persons. (B) 25 unskilled and 26 skilled persons together can complete the same project in 10 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

Let U be the efficiency of an unskilled person and S be the efficiency of a skilled person. Statement A gives S = 1.3U. Statement B gives a second equation for the same project. Both statements allow solving for the efficiency ratio and the total work, making either sufficient.

AI explanation

Let the daily work of an unskilled person be U and a skilled person be S. The main equation is 23U + 20S = 1/12. Statement A gives S = 1.3U, which can be substituted into the main equation to find U and calculate the time for 20 unskilled workers. Statement B provides 25U + 26S = 1/10, which forms a system of two linear equations when paired with the main equation, allowing you to solve for U and find the required time. Either statement alone is sufficient.

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