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05 Sep 2024, 01:30
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C
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17%
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An 80-ounce juice mix is made up of only apple, grape, and pomegranate juice. How many ounces of the mix is pomegranate juice?
(1) Increasing the amount of apple juice by 50 percent would yield a ratio of apple juice to grape juice of 2:1.
(2) Increasing the amount of apple juice by 50 percent would yield a juice mix of 100 ounces
(1) Increasing the amount of apple juice by 50 percent would yield a ratio of apple juice to grape juice of 2:1.
(2) Increasing the amount of apple juice by 50 percent would yield a juice mix of 100 ounces
Answer C.
Statements 1 nor 2 neither is alone sufficient as none gives no absolute value to work with.
But with both of them together, based on the increased weight and apple juice addition we can figure out total apple's weight, then grape's and finally the pomegranade's.
For detailed understanding the math breakdown is below -
Suppose before the increase Apple's weight ratio was x.
So as per statement 1's 50% increase, the increase in apple's amount is 3x/2.
Statement 2 says that increasing the apple's amount increases the overall juice weight by (100-80)=20 ounces, which only means that the 20-ounce increase happened only because 20 ounces of apple juice was added.
That takes us to -
(3x/2-x) = 20 => x/2 = 20 => x=40
Now after the addition of apple juice, the ratio stands -
2:1 for apple : grape
So after the addition of apple juice, the value stands -
60 : 60/2 ; [x+20 => 40+20 oz of apple]
60 : 30
Now the total increased weight is 100. So pomegranate juice amount = (100 - (60+30)) = 10 oz. (Ans. C)
If there's any setback in the solution or understanding, please do point it out. thanks!
Statements 1 nor 2 neither is alone sufficient as none gives no absolute value to work with.
But with both of them together, based on the increased weight and apple juice addition we can figure out total apple's weight, then grape's and finally the pomegranade's.
For detailed understanding the math breakdown is below -
Suppose before the increase Apple's weight ratio was x.
So as per statement 1's 50% increase, the increase in apple's amount is 3x/2.
Statement 2 says that increasing the apple's amount increases the overall juice weight by (100-80)=20 ounces, which only means that the 20-ounce increase happened only because 20 ounces of apple juice was added.
That takes us to -
(3x/2-x) = 20 => x/2 = 20 => x=40
Now after the addition of apple juice, the ratio stands -
2:1 for apple : grape
So after the addition of apple juice, the value stands -
60 : 60/2 ; [x+20 => 40+20 oz of apple]
60 : 30
Now the total increased weight is 100. So pomegranate juice amount = (100 - (60+30)) = 10 oz. (Ans. C)
If there's any setback in the solution or understanding, please do point it out. thanks!
06 Sep 2024, 03:45
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Hello! Thank you for your reply! I am a little confused why did you wrote x/2 should it be 1.5x because it is 50% increase of the amount of apple juice? Thank you for taking the time! Kindest!
