Working continuously 24 hours a day, a factory bottles Soda

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BTGmoderatorLU: Moderator; Posts: 2554; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon Feb 25, 2019 11:56 am

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Source: Manhattan Prep

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. 3/10
B. 5/6
C. 6/5
D. 8/3
E. 10/3

The OA is E

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Source: Beat The GMAT — Problem Solving | Mon Feb 25, 2019 11:56 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Feb 25, 2019 10:33 pm

BTGmoderatorLU wrote:Source: Manhattan Prep

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. 3/10
B. 5/6
C. 6/5
D. 8/3
E. 10/3

The OA is E

Since the question asks for the ratio and not the actual answer, we need not take 24 hours per day into consideration.

Ratio of Rate of filling Soda Q : Rate of filling Soda V :: 500 : 300 => 5 : 3.
Ratio of number of bottles of Soda Q : number of bottles of Soda V :: 2 : 1

Thus,

Ratio of the volume of a bottle of Soda Q to a bottle of Soda V = (5*2) : (3*1) = 10 : 3

Correct answer: E

Hope this helps.

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8152; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Mar 01, 2019 9:46 am

BTGmoderatorLU wrote:Source: Manhattan Prep

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. 3/10
B. 5/6
C. 6/5
D. 8/3
E. 10/3

The OA is E

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

1000/q = 300/v

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

1000/300 = q/v

q/v = 10/3

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Mar 02, 2019 1:24 pm

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

Contact Rich at [email protected]

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