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Each of 60 mineral water bottles in a certain shipment is

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Each of 60 mineral water bottles in a certain shipment is

by BTGmoderatorLU » Thu May 17, 2018 4:24 pm

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Each of 60 mineral water bottles in a certain shipment is either 500ml or 1-liter and the average volume of the bottles in the shipment is 800ml. If the average volume of bottles is to be reduced 600ml by removing some 1-liter bottle. How many 1-liter bottles must be removed?

A. 24
B. 36
C. 20
D. 30
E. 40

The OA is D.

Please, can anyone assist me with this PS question? I don't have it clear. Thanks in advance.
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by Vincen » Fri May 18, 2018 2:56 am
Hello BTGmoderatorLU.
Each of 60 mineral water bottles in a certain shipment is either 500ml or 1-liter
Let's call

x - the number of bottles of 500ml.
y - the number of bottles of 1 liter = 1000 ml.

Then x+y=60.
the average volume of the bottles in the shipment is 800ml


$$800=\frac{500\cdot x+1000\cdot y}{60}\ \ \Leftrightarrow\ \ 48000=500\cdot x+1000\cdot y$$ $$\Leftrightarrow\ \ 96=x+2y.$$
If the average volume of bottles is to be reduced 600ml by removing some 1-liter bottle
Let's call

n - the number of bottles that need to be removed.

Then $$600=\frac{500\cdot x+1000\cdot\left(y-n\right)}{60-n}\ \ \Leftrightarrow\ \ \ 600\left(60-n\right)=500\left(x+2\left(y-n\right)\right)$$ $$\Leftrightarrow\ \ \ 6\left(60-n\right)=5\left(x+2y-2n\right)$$ $$\Leftrightarrow\ \ \ 360-6n=5\left(x+2y\right)-10n$$ $$\Leftrightarrow\ \ \ 4n=5\left(96\right)-360$$ $$\Leftrightarrow\ \ \ 4n=480-360$$ $$\Leftrightarrow\ \ \ 4n=120$$ $$\Leftrightarrow\ \ \ n=30.$$ Therefore, the number of bottles that need to be removed is 30.

Hence, the correct answer is the option [spoiler]D=30[/spoiler].

I hope it helps.
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bottles

by GMATGuruNY » Fri May 18, 2018 4:18 am
The addition of the word in red clarifies the intent of the problem:
BTGmoderatorLU wrote:Each of 60 mineral water bottles in a certain shipment is either 500ml or 1-liter, and the average volume of the bottles in the shipment is 800ml. If the average volume of the bottles is to be reduced TO 600ml by removing some 1-liter bottles, how many 1-liter bottles must be removed?

A. 24
B. 36
C. 20
D. 30
E. 40
Curren total volume = (number of bottles)(average volume per bottle) = 60*800 = 48,000 ml.

We can PLUG IN THE ANSWERS, which represent the number of 1000-ml bottles that must be removed to reduce the average volume per bottle to 600 ml.
Test B or D.
Since D is a rounder number than B, start with D.

D: 30 1000-ml bottles, for a total decrease of 30,000 ml
New total volume = 48,000 - 30,000 = 18,000.
New number of bottles = 60 - 30 = 30.
New average volume per bottle = 18,000/30 = 600.
Success!

The correct answer is D.
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hi

by Jeff@TargetTestPrep » Mon May 21, 2018 3:51 pm
BTGmoderatorLU wrote:Each of 60 mineral water bottles in a certain shipment is either 500ml or 1-liter and the average volume of the bottles in the shipment is 800ml. If the average volume of bottles is to be reduced 600ml by removing some 1-liter bottle. How many 1-liter bottles must be removed?

A. 24
B. 36
C. 20
D. 30
E. 40
We should first note that 1 liter = 1000 mL, so we can let x = the number of 500 mL bottles and y = the number of 1000 mL bottles and create the equations:

x + y = 60

x = 60 - y

and

800 = (500x + 1000y)/60

48000 = 500x + 1000y

480 = 5x + 10y

96 = x + 2y

Substituting x = 60 - y into 96 = x + 2y, we have:

96 = 60 - y + 2y

36 = y, thus x = 24

Now we let n = the number of 1000 mL bottles we need to remove and create the equation:

600 = [1000(36 - n) + 24(500)]/(60 - n)

600(60 - n) = 1000(36 - n) + 24(500)

6(60 - n) = 10(36 - n) + 24(5)

360 - 6n = 360 - 10n + 120

4n = 120

n = 30

Answer: D

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