# GMAT Challenge Series (700+): Q25

Question:

Three employees, A, B and C, clean a certain conference room each day. Working together, A and B can clean the conference room in 3 hours, whereas A and C together can do it in 2 and 1/2 hours. Can A, B and C working together clean the conference room in less than 2 hours?

1) B cleans faster than A.
2) Working alone, C can clean the conference room in less than 5 hours.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

$$\textit{rate} = {\textit{work} \over \textit{time}}$$  $$\text{We know that:}$$ $$\text{A} + \text{B} = \frac{1}{3}$$ $$\text{A} + \text{C} = \frac{2}{5}$$  $$\text{We need to figure out if:}$$ $$\text{A} + \text{B} + \text{C} > \frac{1}{2}$$ $$\text{or}$$ $$\text{B} > \frac{1}{10}$$ $$\text{or}$$ $$\text{C} > \frac{1}{6}$$  $$\text{Statement 1:}$$ $$\text{If:}$$ $$\text{A} + \text{B} = \frac{1}{3}$$ $$\text{and}$$ $$\text{B} > \text{A}$$ $$\text{then:}$$ $$\text{B} > \frac{1}{6} > \frac{1}{10}$$ $$\text{Statement 1 is SUFFICIENT}$$  $$\text{Statement 2:}$$ $$\text{C} > \frac{1}{5} > \frac{1}{6}$$ $$\text{Statement 2 is SUFFICIENT}$$