Multiple choice

Directions: 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. Jenny and Kat together can complete a piece of work in 40/3 days while Ava and Emma together can complete the same piece of work in 300/11 days. In how many days Kat alone can complete the same work? (A) Jenny alone can complete the same piece of work in 20 days. (B) Ava alone can complete the same work in 50 days and Kat alone can complete the same work in 20 days less than Emma.

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

  4. Both the statements taken together are necessary to answer the questions, but neither of the statements alone 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
C Correct answer
Explanation

Statement A gives Jenny's rate, allowing us to find Kat's rate from the combined rate of Jenny and Kat. Statement B gives Ava's rate and a relationship between Kat and Emma, allowing us to find Kat's rate from the combined rate of Ava and Emma. Both statements are independently sufficient.

AI explanation

Using statement A, since Jenny and Kat complete the work in 40/3 days and Jenny alone takes 20 days, we solve 3/40 = 1/20 + 1/K to find Kat's time. Using statement B, we have the combined rates for Ava and Emma, and the individual rate for Ava, which lets us find Emma's time; since Kat takes 20 days less than Emma, her time can also be found directly. Since the time can be found using either statement alone, either statement by itself is sufficient to answer the question.

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