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A full glass of juice is a mixture of 20% grape juice and 80

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A full glass of juice is a mixture of 20% grape juice and 80 [#permalink] New post 05 Aug 2017, 06:59
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A full glass of juice is a mixture of 20% grape juice and 80% apple juice. The contents of the glass are poured into a pitcher that is 200 percent larger than the glass. The remainder of the pitcher is filled with 16 ounces of water. What was the original volume of grape juice in the mixture?

(A) 1.6 ounce
(B) 3.2 ounce
(C) 4.8 ounce
(D) 6.4 ounce
(E) 8 ounces
[Reveal] Spoiler: OA

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Re: A full glass of juice is a mixture of 20% grape juice and 80 [#permalink] New post 06 Aug 2017, 10:12
Expert's post
The first sentence about juice grape and apple actually is irrelevant.

Our glass is X. Then the new pitcher is 2 X. Clearly, we have a total of 3; 2 + X = 3 units of the container. The first glass considering that is 20% of grape and 80% apple it must be of 100.
So, if our 200 pitcher is full of 16 ounces, our first glass must be 16/100 = 1.6

A is the answer
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Re: A full glass of juice is a mixture of 20% grape juice and 80 [#permalink] New post 29 Nov 2017, 09:34
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pranab01 wrote:
A full glass of juice is a mixture of 20% grape juice and 80% apple juice. The contents of the glass are poured into a pitcher that is 200 percent larger than the glass. The remainder of the pitcher is filled with 16 ounces of water. What was the original volume of grape juice in the mixture?

(A) 1.6 ounce
(B) 3.2 ounce
(C) 4.8 ounce
(D) 6.4 ounce
(E) 8 ounces


The contents of the glass are poured into a pitcher that is 200 percent larger than the glass. The remainder of the pitcher is filled with 16 ounces of water.
Many students read "200 percent larger" and mistakenly conclude that the pitcher's volume is TWICE the glass's volume.
This is not true.

EXAMPLE: If the glass holds 5 liters of water, then 200% of 5 = 10
So, 200% LARGER = 5 + 10 = 15 liters.
In other words, 15 liters is 200% MORE than 5 liters.

Likewise, if the glass holds 8 liters of water, then 200% of 8 = 16
So, 200% LARGER = 8 + 16 = 24 liters.
In other words, 24 liters is 200% MORE than 8 liters.

Notice, that in the last example, we can see that, if we start with 8 liters and add 16 liters, the resulting volume is 200% more than the starting volume.
This is EXACTLY what's happening in the question.
So, we can conclude that the glass must contain 8 liters of juice.

A full glass of juice is a mixture of 20% grape juice and 80% apple juice.
If the 8 liters of juice is 20% grape juice, then...
Volume of grape juice = 20% of 8
= 1.6 liters

Answer: A

Cheers,
Brent
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Re: A full glass of juice is a mixture of 20% grape juice and 80 [#permalink] New post 25 Apr 2018, 08:30
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Hi There,

Will it be wrong to solve like this - that 16 is 200% of glass. then 16/2 = 8 must be 100% which was the orignal solution therefore 0.2*8 =1.6 hence answer A.

Please clarify if I am wrong.
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Re: A full glass of juice is a mixture of 20% grape juice and 80 [#permalink] New post 25 Apr 2018, 08:34
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Flexibility to solve a question in different manner is king.

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Re: A full glass of juice is a mixture of 20% grape juice and 80 [#permalink] New post 03 May 2018, 15:29
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pranab01 wrote:
A full glass of juice is a mixture of 20% grape juice and 80% apple juice. The contents of the glass are poured into a pitcher that is 200 percent larger than the glass. The remainder of the pitcher is filled with 16 ounces of water. What was the original volume of grape juice in the mixture?

(A) 1.6 ounce
(B) 3.2 ounce
(C) 4.8 ounce
(D) 6.4 ounce
(E) 8 ounces


Let’s let the capacity of the glass = n. Since the volume of the pitcher is 200% larger than that of the glass, we see that the volume of the pitcher is 3n. We can now create the equation:

n + 16 = 3n

16 = 2n

8 = n

Thus, there are 8 ounces of juice in the glass and since grape juice is 20% of it, grape juice is 8 x 0.2 = 1.6 ounces.

Alternate Solution:

The problem states that the pitcher needs 16 ounces of water to fill it, after the juice has been poured into it. Thus, 16 ounces is twice the capacity of the glass, so the capacity of the glass is 8 ounces. Since grape juice is 20% of the original juice in the glass, grape juice is 8 x 0.2 = 1.6 ounces.

Answer: A
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Re: A full glass of juice is a mixture of 20% grape juice and 80   [#permalink] 03 May 2018, 15:29
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