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After 360 liters of fuel were added to a container, the

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by AAPL » Sat Jun 23, 2018 6:23 am

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A

B

C

D

E

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After 360 liters of fuel were added to a container, the amount of fuel in the container was 5/8 of the tank's capacity. What is the capacity of the container?

1) After the 360 liters were added, the container had 108 liters less than of the tank's capacity.
2) Before the 360 liters were added, there were 180 liters of fuel in the container.

The OA is D.

Let the original amount of fuel in container = O
and let the capacity of container = C
360 liters of fuel were added to the container
O+ 360 = (5/8)C.

(1) After the 360 liters were added, the container had 108 liters less than of the tank's capacity.
(3/8)C = 108
C= 288. Sufficient

Though it seems that the first statement should be
(1) After the 360 liters were added, the container had 324 liters less than of the tank's capacity.

(2) Before the 360 liters were added, there were 180 liters of fuel in the container.
original amount , O = 180
180+ 360 = (5/8)C
=> 540 = (5/8)C
=> C = 864. Sufficient

Hence, D is the correct answer.

Has anyone another strategic approach to solve this PS question? Regards!
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Source: — Data Sufficiency |

by deloitte247 » Fri Jul 27, 2018 2:03 pm
Question Analysis;
* We need exact value of the container after 360 liters of fuel were added.
* Let capacity of container = C Liters.
* Before 360 Liters of fuel was added there were N Liters of fuel in the container.
$$\cdot\ After\ 360\ Liters\ of\ fuel\ were\ added,\ amount\ of\ fuel\ in\ the\ container\ was\ \frac{5}{8}\ of\ \tan k's\ capacity.$$
$$Thus\ N\ +\ 360\ =\ \frac{5}{8}C$$

$$Statement\ 1\ =\ After\ 360\ Liters\ were\ added\ the\ container\ had\ 108\ Liters\ less\ than\ \frac{3}{4}\ of\ the\ \tan k's\ capacity.$$
From the equation we have,
$$N\ +\ 360\ =\ \frac{3}{4}C\ -\ 180$$
$$Since\ N\ +\ 360\ =\ \frac{5}{8}C\ \left(from\ the\ equation\right)$$
$$\frac{5}{8}C\ =\ \frac{3}{4}C\ -\ 180\ $$
$$\frac{5}{8}C\ -\ \frac{3}{4}C\ =-\ 180\ $$
From the equation, we can get a definite value of C, hence, statement 1 is sufficient.

Statement 2 = Before the 360 Liters were added, there were 180 Liters of fuel in the container.
* After the 360 liters were added, there were 180 + 360 = 540 Liters.
$$Since\ after\ the\ 360\ liters\ were\ added,\ the\ amount\ of\ fuel\ in\ the\ container\ was\ 5-8\ of\ the\ \tan k's\ capacity.\$$
$$We\ have\ 540\ =\ \frac{5}{8\ }C\ dividing\ both\ side\ by\ Co-efficient\ of\ C\ will\ give\ us\ a\ definite\ value.\ Hence\ statement\ 2\ is\ also\ sufficient.$$
Final answer is Option D, because statement 1 and 2 are sufficient alone.
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