Data Sufficiency

Princeton Review

Hoses A, B, and C pump a swimming pool full of water. Hoses A and B working simultaneously can pump the pool full of water in 4 hours, and Pumps B and C working simultaneously can pump the pool full of water in 6 hours. How long does it take pump A working alone to fill the pool?

1) All three hoses working simultaneously can fill the pool in 3 hours and 36 minutes.
2) Hose A and Hose C working simultaneously can fill the swimming pool in twice the time it would take all three hoses together to fill the swimming pool.

OA D

Work done by hoses A and B in 1 hr = 1/4
Work done by hoses B and C in 1 hr = 1/6
How long does it take pump A working alone to fill the pool?
Statement 1
All the three hoses working together simultaneously can fill the in 3 hrs 36 mins
Workdone by hoses A,B and C in 1 hr = 1/3.6
i.e A + B + C = 1/3.6
Recall that A + B = 1/4 and B + C = 1/6
To find A
$$A+\left(B+C\right)=\frac{1}{3.6}$$
$$A+\frac{1}{6}=\frac{1}{3.6}$$
$$A=\frac{1}{3.6}-\frac{1}{6}$$
$$A=\frac{6-3.6}{21.6}$$
$$A=\frac{2.4}{21.6}$$

Statement 1 is SUFFICIENT.

Statement 2
Hose A and Hose C working simultaneously can fill the swimming pool in twice the time it would take all the three Hoses together to fill the swimming pool. Workdone by Hoses A and C in 1 hr
$$=\frac{1}{2}\left(A+B+C\right)$$
Recall that A + B = 1/4 ----eqn i
B + C = 1/6 ----eqn ii
B = 1/4 - A ----eqn iii

$$\left(\frac{1}{4}-A\right)+C=\frac{1}{6}$$
$$C=\frac{1}{6}-\frac{1}{4}+A=\frac{4-6}{24}+A$$
$$C=\frac{-2}{24}+A=-\frac{1}{12}+A----eqn\ iv$$
$$A+C=\frac{1}{2}\left(A+B+C\right)\ where\ B+C=\frac{1}{6}$$
$$A+C=\frac{1}{2}\left(A+\frac{1}{6}\right)\ $$
$$A+C=\frac{1}{2}A+\frac{1}{12}\ $$
from eqn iv C = -1/12 +A
$$A+\left(-\frac{1}{12}+A\right)=\frac{1}{2}A+\frac{1}{12}$$\
$$2A-\frac{1}{2}=\frac{1}{2}A+\frac{1}{12}$$
$$2A-\frac{1}{2}A=\frac{1}{12}+\frac{1}{2}$$
$$\frac{3}{2}A=\frac{2}{12}=\frac{1}{6}$$
$$A=\frac{\frac{1}{6}}{\frac{3}{2}}$$
$$A=\frac{1}{6}\cdot\frac{2}{3}=\frac{1}{9}$$
Statement 2 is also SUFFICIENT.
Both Statement alone are SUFFICIENT.

$$Answer\ is\ Option\ D$$