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07 Mar 2023, 11:41
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A
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38% (01:40) correct
62%
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wrong
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A pomegranate grower packages pomegranates in 10-pound and 20-pound boxes. If the grower fills more than twice as many 20-pound boxes as 10-pound boxes, which of the following could be the percentage of pomegranates, by weight, that are packaged in 10-pound boxes?
(A) 15%
(B) 20 %
(C) 25%
(D) 40%
(E) 60%
(A) 15%
(B) 20 %
(C) 25%
(D) 40%
(E) 60%
01 Apr 2023, 13:08
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Bunuel
To solve this question, let's try to dissect the information in steps.
Step 1 :
Let's assume that the pomegranate grower fills an equal number of 20-pound boxes as 10-pound boxes.
If that were the case, let's calculate the percentage of pomegranates, by weight, that is packaged in 10-pound boxes.
For the sake of simplicity, let's assume that the pomegranate grower fills one 20-pound box and one 10-pound box.
% of weight of 10 pound box = \(\frac{10 }{ 10 + 20}\) * 100 = 33.33%
So if the pomegranate grower were to fill an equal number of 20-pound boxes as 10-pound boxes, the percentage of pomegranates, by weight, that are packaged in 10-pound boxes would have been 33.33%. As the pomegranate grower fills more than twice as many 20-pound boxes as 10-pound boxes, the answer cannot exceed 33.33%.
At this point, we can safely eliminate any answer choice which has a value of more than 33.33%, i.e. eliminate answers D and E.
Step 2 :
Let's assume that the pomegranate grower fills exactly twice the number of 20-pound boxes as 10-pound boxes.
If that were the case, let's calculate the percentage of pomegranates, by weight, that is packaged in 10-pound boxes.
For the sake of simplicity, let's assume that the pomegranate grower fills two 20-pound boxes and one 10-pound box.
The two 20-pound boxes will have 2*20 = 40 pounds of pomegranate and the one 10-pound box will have 10 pounds of pomegranate.
% of weight of 10 pound box = \(\frac{10 }{ 10 + 40}\) * 100 = 20%
So if the pomegranate grower were to fill exactly twice the number number of 20-pound boxes as 10-pound boxes, the percentage of pomegranates, by weight, that are packaged in 10-pound boxes would have been an exact 20%.
From the question stem we know that the grower fills more than twice as many 20-pound boxes as 10-pound boxes, hence the percentage of pomegranates, by weight, that are packaged in 10-pound boxes will be less than 20%.
The only option that has a value of less than 20% is option A. Hence, Option A is our answer.
Option A
18 Dec 2024, 05:34
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