In how many days will Y alone complete the work? I. X and Y together finish in 8 days. II. Y and Z together finish in 10 days. III. X and Z together finish in 12 days.
Verbal Reasoning
Data Sufficiency
Difficulty: Easy
Choose an option
Answer
Correct Answer: I, II and III
Explanation
Introduction / Context:Identical structure to the prior rates problem; now solve for Y’s solo rate.
Solution Sketch:Let x, y, z be daily rates. We have x + y = 1/8, y + z = 1/10, x + z = 1/12. Then 2y = (1/8 + 1/10 − 1/12) = 17/120 ⇒ y = 17/240 ⇒ Y alone takes 240/17 days.
Sufficiency:All three equations are required to isolate y uniquely.
Final Answer:I, II and III.