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A full glass of juice is a mixture of 20% grape juice and 80
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05 Aug 2017, 06:59
05 Aug 2017, 06:59
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Question Stats:
45% (02:09) correct
54% (02:05) wrong based on 35 sessions
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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
(A) 1.6 ounce
(B) 3.2 ounce
(C) 4.8 ounce
(D) 6.4 ounce
(E) 8 ounces
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Re: A full glass of juice is a mixture of 20% grape juice and 80
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29 Nov 2017, 09:34
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
(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
General Discussion
Re: A full glass of juice is a mixture of 20% grape juice and 80
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06 Aug 2017, 10:12
06 Aug 2017, 10:12
Expert Reply
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
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
