Working continuously 24 hours a day, a factory bottles Soda Q at a rat

Question

Working continuously 24 hours a day, a factory bottles Soda Q at a rate of 500 liters per second and Soda V at a rate of 300 liters per second. If twice as many bottles of Soda V as of Soda Q are filled at the factory each day, what is the ratio of the volume of a bottle of Soda Q to a bottle of Soda V?

(A) \(\frac{3}{10}\)

(B) \(\frac{5}{6}\)

(C) \(\frac{6}{5}\)

(D) \(\frac{8}{3}\)

(E) \(\frac{10}{3}\)

(A)  \frac{3}{10}

(B)  \frac{5}{6}

(C)  \frac{6}{5}

(D)  \frac{8}{3}

(E)  \frac{10}{3}

EgmatQuantExpert · Accepted Answer

Solution

Given:  
 • Working continuously 24 hours a day, a factory bottles Soda Q at a rate of 500 liters per second and Soda V at a rate of 300 liters per second
• Twice as many bottles of Soda V as of Soda Q are filled at the factory each day

To find:  
 • The ratio of the volume of a bottle of Soda Q to a bottle of Soda V

Approach and Working:   
We assume that,
 • Number of bottles of Soda Q = n
• Number of bottles of Soda V = 2n

Therefore, we can write:
 • Volume of Soda per bottle of Q = V1 =  \frac{500 * 3600 * 24}{n} 
• Volume of Soda per bottle of V = V2 =  \frac{300 * 3600 * 24}{2n}

Hence, the ratio V1: V2 =  \frac{500 * 3600 * 24}{n}: \frac{300 * 3600 * 24}{2n}  = 500: 150 = 10: 3

Hence, the correct answer is option E.

Answer: E

WizakoBaskar · Answer

Because we are computing ratio of the volumes of the two types of bottles, whether we find it for 24 hours or 1 second, the answer will the same.

Let the number of bottles of soda Q bottled every second be 'n'
So, the number of bottles of soda V bottled every second will be '2n'

Each second 500 litres of soda Q are bottled. 
If in each second 'n' bottles of soda Q are bottled, volume of each bottle of soda Q =  \frac{500}{n}  litres. ---- (1)

Each second 300 litres of soda V are bottled.
Each second '2n' bottles of soda V are bottled.
So, volume of each bottle of soda V =  \frac{300}{2n} = \frac{150}{n}  litres. ---- (2)

Answer to question ratio of (1) and (2)
=  \frac{500}{n} / \frac{150}{n} 
=  \frac{500}{n} * \frac{n}{150} 
=  \frac{500}{150} = \frac{10}{3}

Choice E

fskilnik · Answer

Q:\,\,\,\,\frac{{500\,\,{	ext{liters}}}}{{1\,\,{	ext{second}}}}\,\,\,\,\,\,\,;\,\,\,\,\,\,\frac{{k\,\,{	ext{bottles}}}}{{\left( {{	ext{any}}\,\,{	ext{time}}\,\,{	ext{fixed,}}\,\,{	ext{say}}} ight)\,\,\,\,1\,\,\,{	ext{second}}}}

V:\,\,\,\,\frac{{300\,\,{	ext{liters}}}}{{1\,\,{	ext{second}}}}\,\,\,\,\,\,\,;\,\,\,\,\,\,\frac{{2k\,\,{	ext{bottles}}}}{{\left( {{	ext{same}}\,\,{	ext{time}}\,\,{	ext{fixed}}} ight)\,\,\,\,1\,\,\,{	ext{second}}}}

(We could explore a particular case, say k=1, it doesn´t matter. We left "k" so that you will have a "better feeling" of the whole structure!)

? = \frac{{{	ext{volume}}\,\,{	ext{bottle}}\,\,Q}}{{{	ext{volume}}\,\,{	ext{bottle}}\,\,V}}

Let´s use UNITS CONTROL, one of the most powerful tools of our method!

Q:\,\,\,\,\,\,\,\frac{{500\,\,{	ext{liters}}}}{{1\,\,{	ext{second}}}}\,\,\,\left( {\frac{{1\,\,\,{	ext{second}}}}{{\,k\,\,{	ext{bottles}}\,}}\,\,\begin{array}{*{20}{c}}
 
earrow \ 
 
earrow 
\end{array}} ight)\,\,\, = \,\,\,\frac{{500\,\,\,{	ext{liters}}}}{{k\,\,\,{	ext{bottles}}}} = \frac{{\frac{{500}}{k}\,\,\,{	ext{liters}}}}{{1\,\,\,{	ext{bottle}}}}

V:\,\,\,\,\,\,\,\frac{{300\,\,{	ext{liters}}}}{{1\,\,{	ext{second}}}}\,\,\,\left( {\frac{{1\,\,\,{	ext{second}}}}{{\,2k\,\,{	ext{bottles}}\,}}\,\,\begin{array}{*{20}{c}}
 
earrow \ 
 
earrow 
\end{array}} ight)\,\,\, = \,\,\,\frac{{300\,\,\,{	ext{liters}}}}{{2k\,\,\,{	ext{bottles}}}} = \frac{{\frac{{150}}{k}\,\,\,{	ext{liters}}}}{{1\,\,\,{	ext{bottle}}}}

Obs.: arrows indicate  licit converters .

? = \frac{{\,\,\,\frac{{500}}{k}\,\,\,}}{{\frac{{150}}{k}}} = \frac{{50}}{{15}} = \frac{{10}}{3}

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

EMPOWERgmatRichC · Answer

Hi All,

We're told that working continuously 24 hours a day, a factory bottles Soda Q at a rate of 500 liters per second and Soda V at a rate of 300 liters per second and that TWICE as many bottles of Soda V as of Soda Q are filled at the factory each day. We're asked for the ratio of the volume of a bottle of Soda Q to a bottle of Soda V. This question is all about ratios, so you can approach the math in a variety of different ways. You might also find it useful to TEST VALUES.

The fact that this scenario takes place in a 24-hour day is actually irrelevant to the math involved. Since the number of bottles created is an unknown, we can TEST VALUES to define the overall ratios involved.

IF... 1 bottle of Soda Q is created each second, then 2 bottles of Soda V are created each second. 
Thus, 1 bottle of Soda Q is 500 liters and the 2 bottle of Soda V TOTAL 300 liters (meaning that each bottle is 300/2 = 150 liters).

The ratio of a bottle of Soda Q to a bottle of Soda V = 500:150 = 500/150 = 10/3

Final Answer:  E

GMAT assassins aren't born, they're made, 
Rich

T1101 · Answer

Different way of looking at this problem:

The ratio of liters per day will alwys be  \frac{Q}{V} = \frac{5}{3} .

Lets assume there are only  5  liters of  Q  and  3  liters of  V . To make things easier lets use the LCM as the number of bottles of  Q .

So  15  bottles of  Q , therefore  30  bottles of  V .

Liters per bottle for  Q :  \frac{5}{15}   -->   \frac{1}{3}

Liters per bottle for  V :  \frac{3}{30}   -->   \frac{1}{10}

Ratio bottles volume  Q:V  --> \frac{1}{3}/\frac{1}{10}   -->   \frac{1}{3}*\frac{10}{1}   -->   \frac{10}{3}

ScottTargetTestPrep · Answer

Let the volume of a bottle of Soda Q be q and the volume of a bottle of Soda V be v. Note that if twice as many bottles of Soda V are filled each day, the same must be true for the number of bottles filled each second; so we will compare those quantities instead.

In one second, 500/q bottles of Soda Q and 300/v bottles of Soda V are filled. Thus, we can create the equation:

2 x 500/q = (300/v)

Multiplying both sides of the equation by q/300, we have:

1000/300 = q/v

q/v = 10/3

Answer: E

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Working continuously 24 hours a day, a factory bottles Soda Q at a rat

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