SSC CGL (Prelims) General: Data Sufficiency questions with solutions

Q1. Instructions: Evaluate the following statements to determine whether the information provided is sufficient to answer the 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.

1. Statement I alone provides enough information to answer the question, but Statement II alone does not.
2. Statement II alone provides enough information to answer the question, but Statement I alone does not.
3. Both Statement I and Statement II combined are needed to answer the question, as neither statement on its own is sufficient.
4. Even when combined, the information in both Statement I and Statement II is not enough to answer the question.

Answer: Even when combined, the information in both Statement I and Statement II is not enough to answer the question.

Statement I gives the combined rate of Q and R, and Statement II gives the combined rate of P and R. But the rate of R alone is still unknown, so the total rate of P, Q, and R cannot be uniquely found. Therefore, even together the statements are insufficient.