Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. P, Q and R can complete 1/3rd of the total work in 28/9 days and P alone can complete the whole work in 42 days. In how many days can Q alone complete 1/2 of the total work? (1) The efficiency of Q is 4/3 times of the efficiency of R. (2) R can complete the whole work in 28 days.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statementd (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Together, P, Q, and R work at 3/28 of the task per day, while P works at 1/42, so Q + R work at 1/12 per day. Statement 1 gives Q = 4R/3, which determines Q, and statement 2 directly gives R = 1/28, which also determines Q. Each statement alone is sufficient.

AI explanation

From the main question, the combined rate of P, Q, and R is 1/3 work in 28/9 days, so their daily rate is (1/3)/(28/9) = 3/28. P's daily rate is 1/42, making the combined daily rate of Q and R 3/28 - 1/42 = 1/12. Statement 1 gives the ratio of efficiencies, meaning if Q's rate is 4x, R's is 3x, so 7x = 1/12, yielding Q's rate of 1/21 to finish half the work in 10.5 days. Statement 2 gives R's rate as 1/28, so Q's rate is 1/12 - 1/28 = 1/21, yielding the same result. Each statement alone is sufficient.

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