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

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pranab223
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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
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A
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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

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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
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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   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] New post   06 Oct 2020, 01:43
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Hey, how about this approach to the solution?

Would like to know if there are any discrepancies with this:

1. First take the total volume of the glass to be 100ml. That gives you 20ml grape juice & 80ml apple juice.
2. Volume of Pitcher | As pitcher is 200% larger than a 100ml glass = 100 + 100 * (200/100) = 100ml + 200ml = 300ml.
3. Now the Remainder of the pitcher in our terms would be: Volume of Pitcher - Volume of juice transferred from glass = 300 - 100 = 200ml.
4. Now 200ml can be equated with 16 ounce of water, and as we have let 100ml = x = volume of glass, 200ml = 16 ounce;
5. 200 ml can be written as 2*x. Therefore, 2x = 16. x = 8 ounce, which is the volume of the glass.
6. Now, finally, to get the grape juice, we take 20% of 8 ounce = 1.6 ounce; which 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   06 Jun 2022, 16:06
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Glass = Grape 0.2x
Apple 0.8x
Total = x

Pitcher = 3x
3x-x = 2x
2x = 16
x = 8
Volume of grape 0.2 x 8
= 1.6 ounce
Answer A.
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Re: A full glass of juice is a mixture of 20% grape juice and 80 [#permalink]
06 Jun 2022, 16:06
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