Instructions: Evaluate the following statements to determine if the information provided is sufficient to answer the question.
Question: If P, Q, and R work together, how many days will they take to complete a project?
Statement I: Q and R together can complete the project in 10 days.
Statement II: P and R together can complete the project in 15 days.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. Even when combined, the information in both Statement I and Statement II is not enough to answer the question.
We need the combined rate of P, Q, and R:
Statement I: Rate of (Q + R) = 1/10
Statement II: Rate of (P + R) = 1/15
Together, we still cannot find P + Q + R uniquely because the rate of R is unknown.
For example, if R is very fast, then P and Q are slower, but the sum changes.
Thus, even when combined, the information in both Statement I and Statement II is not enough to answer the question.