Multiple choice

Directions: The following item contains two statements, I and II, giving certain data. Select the correct answer from (1) to (4) depending on the sufficiency of the data given in the statements to answer the question. P and Q started working on an assignment together. But due to some heath problems, after 3 days, Q had to leave the assignment, and P alone completed the remaining assignment. In how many days was the whole assignment completed? Statement I: P alone can complete the whole assignment in 21 days. Statement II: Q alone can complete the whole assignment in 14 days.

  1. I alone is sufficient but II alone is not sufficient to answer the question.

  2. II alone is sufficient but I alone is not sufficient to answer the question.

  3. Both I and II together are sufficient but neither statement alone is sufficient to answer the question.

  4. Both I and II together are not sufficient to answer the question, and additional data, specific to the question, is needed.

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives P's rate as 1/21 of the assignment per day, while statement II gives Q's rate as 1/14 per day. Both rates are needed to determine the work completed together during the first 3 days and the remaining time taken by P. Therefore, both statements together are sufficient, but neither alone is sufficient.

AI explanation

To find the total completion time, you must know the daily work rate of both P and Q. Statement I provides P's rate but leaves Q unknown, while Statement II provides Q's rate but leaves P unknown. By combining both statements, we calculate that P's rate is 1/21 and Q's rate is 1/14, giving a combined rate of 5/42 per day. The total time is the 3 days they worked together plus the remaining 27/42 of the job divided by P's individual rate of 1/21, which requires both statements to calculate. Therefore, both statements together are sufficient but neither statement alone is sufficient.

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