Multiple choice

Directions: The following problem consists of a question and two statements numbers I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. Read the both the statements and mark your answer accordingly. Three employees A, B and C are working on an assignment. In how many days can they finish this assignment? Statement I: The time taken by employee A alone to complete the assignment is 24 days less than the time taken by employee C alone to finish the same assignment. Statement II: Employees A and B together can finish the assignment in 6 days. Employees B and C together can finish the assignment in 12 days. Employees C and A together can finish the assignment in 10 days.

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data in both statements I and II together is necessary to answer the question.

  4. The data in statement I alone or in statement II alone is sufficient to answer the question.

  5. The data in both statements I and II is not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II provides a system of equations: A+B=1/6, B+C=1/12, C+A=1/10. This is sufficient to solve for A, B, and C individually, and thus their combined rate. Statement I is insufficient on its own.

AI explanation

We evaluate the sufficiency of the statements to find the combined time of A, B, and C. Statement I only gives a relative time difference between A and C and lacks individual rates, making it insufficient. Statement II provides the pairwise completion times: A+B take 6 days, B+C take 12 days, and C+A take 10 days. Using the work formula, their combined one day work is 2*(A+B+C) = (1/6) + (1/12) + (1/10) = 3/10. Therefore, A+B+C can finish the work in 20/3 days using only Statement II. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient.

Keep practicing — related questions