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Re: V07-18 [#permalink]
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Why can't A be the answer as the conclusion is concerned with the relative % decline in the WEIGHT of the plastic and aluminium cans.
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srishtigrover wrote:
Why can't A be the answer as the conclusion is concerned with the relative % decline in the WEIGHT of the plastic and aluminium cans.


Consider mathematically,

Previously the no. of plastic bottles in garbage = p and the no. of aluminium bottles in garbage = a

Now no. of plastic bottles in garbage = p' and no. of aluminium bottles in garbage = a'

say x = weight of each plastic bottle, y = weight of each aluminium bottle

(p-p')x = weight of recycled plastic (i.e. total reduction in weight of plastic bottles)
(a-a')y = weight of recycled aluminium (i.e. total reduction in weight of aluminium bottles)

Weight of plastic bottles in domestic garbage declined by a greater percentage than the weight of aluminum cans =>
(p-p')x/px > (a-a')y/ay
or 1-p'/p > 1 - a'/a
or p'/p < a'/a

Though aluminium recycling was more wide,i.e.
(a-a') > (p-p')

The question is: although (a-a') > (p-p'), why p'/p < a'/a ?

We have to explain why these two conditions happen together. The weights of the botlles (x and y) are not parameters in the aforesaid equations.

Option A: Plastic bottles are heavier than aluminium cans. i.e. x>y. This does not matter because the two equations to be explained do not contain x and y.


Now suppose the last sentence were as follows:
"....it was found that the weight of plastic bottles in domestic garbage declined by a greater percentage AMOUNT than the weight of aluminum cans.

Then the two statements required to be explained would be:
although (a-a') > (p-p'), why (p-p')x> (a-a')y?
Now option C is the right answer since the above two equations can be satisfied only when x>y.

The use of the word "percentage" makes all the difference.
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Re: V07-18 [#permalink]
Wow. loved the explanation.. i was reading e-gmat question today, and got stuck in a similar problem of absolute vs percentage.. Will highly appreciate if you could provide more material on this?

Thanks in advance!
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Re: V07-18 [#permalink]
I think this is a high-quality question and the explanation isn't clear enough, please elaborate.
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Re: V07-18 [#permalink]
IN OPTION C

Polymer is the superset, plastic is the subset of the superset.
So how can we infer that the plastic weight has gone down, plastic weight may be consistent.
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Re: V07-18 [#permalink]
sayantanc2k wrote:
srishtigrover wrote:
Why can't A be the answer as the conclusion is concerned with the relative % decline in the WEIGHT of the plastic and aluminium cans.


Consider mathematically,

Previously the no. of plastic bottles in garbage = p and the no. of aluminium bottles in garbage = a

Now no. of plastic bottles in garbage = p' and no. of aluminium bottles in garbage = a'

say x = weight of each plastic bottle, y = weight of each aluminium bottle

(p-p')x = weight of recycled plastic (i.e. total reduction in weight of plastic bottles)
(a-a')y = weight of recycled aluminium (i.e. total reduction in weight of aluminium bottles)

Weight of plastic bottles in domestic garbage declined by a greater percentage than the weight of aluminum cans =>
(p-p')x/px > (a-a')y/ay
or 1-p'/p > 1 - a'/a
or p'/p < a'/a

Though aluminium recycling was more wide,i.e.
(a-a') > (p-p')

The question is: although (a-a') > (p-p'), why p'/p < a'/a ?

We have to explain why these two conditions happen together. The weights of the botlles (x and y) are not parameters in the aforesaid equations.

Option A: Plastic bottles are heavier than aluminium cans. i.e. x>y. This does not matter because the two equations to be explained do not contain x and y.


Now suppose the last sentence were as follows:
"....it was found that the weight of plastic bottles in domestic garbage declined by a greater percentage AMOUNT than the weight of aluminum cans.

Then the two statements required to be explained would be:
although (a-a') > (p-p'), why (p-p')x> (a-a')y?
Now option A is the right answer since the above two equations can be satisfied only when x>y.

The use of the word "percentage" makes all the difference.



Suppose there were 1000kg of trash in 2000 in which 100g was Al and 400g of plastic.(As per option A)
Also let us suppose there were 4 no. of can each type.

Now After 10 years say 3 nos. of Al cans got recycled and only one remained in th trash.Also only 1 no. of Plastic can got recycled and 3 nos. remained in the trash.
This makes 25g of Al trash and 300g of Plastic trash(It is given that more aluminium cans got recycled).
Now plz check the %ge. Aluminium reduced by 7.5% and Plastic reduced by 10% which solves the paradox.

So my point is that if weight of plastic was Significantly high in the trash compared to aluminium, even minor reduction will lead to greater %ge change compared to lighter substance.
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Re: V07-18 [#permalink]
I don't understand why option A is wrong here. Lets say we have 5 Aluminum cans and 4 plastic bottles. The weight of the 5 Al cans is 5 kg, and the weight of the 4 plastic bottles is 10 kg. If we remove all of them, greater percentage of Al gets removed. But from a weight perspective, plastic bottles win. Then ?
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Re: V07-18 [#permalink]
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anish777 wrote:
I don't understand why option A is wrong here. Lets say we have 5 Aluminum cans and 4 plastic bottles. The weight of the 5 Al cans is 5 kg, and the weight of the 4 plastic bottles is 10 kg. If we remove all of them, greater percentage of Al gets removed. But from a weight perspective, plastic bottles win. Then ?
sayantanc2k


Hi. It would be correct that if you removed all or majority of the plastic bottles, the weight would go down. However, we have this condition:

Quote:
However, although aluminum recycling was more widely practiced in this period than plastic recycling,


And since the decline was in percentage terms, and not absolute, A is not the right answer…

PS. Please see numerous replies above. They explain each of the options quite well.
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Re: V07-18 [#permalink]
­We need to explain why the weight of plastic bottles in domestic garbage declined by a greater percentage than the weight of aluminum cans, even though aluminum recycling was more widespread.


A. Plastic bottles are significantly heavier than aluminum cans of comparable size.
The passage emphasizes the percentage decline in plastic bottle weight being greater than aluminum cans. Even if plastic bottles were heavier, a higher initial weight wouldn't necessarily translate to a larger decrease as a percentage.

B. Recycled aluminum cans were almost all beverage containers, but a significant fraction of the recycled plastic bottles had contained products other than beverages.
This might suggest a higher volume of recycled plastic bottles but does not directly address the decline in domestic garbage weight.

C. Manufacturers replaced many plastic bottles, but few aluminum cans, with polymer containers.
This indicates that many plastic bottles were no longer being used and were replaced by polymer containers. If fewer plastic bottles were being used, the amount of plastic bottle waste would decrease significantly, contributing to a greater percentage decline in plastic waste.

D. The total weight of plastic bottles purchased by domestics increased at a slightly faster rate than the total weight of aluminum cans.
This suggests a higher consumption rate for plastic but doesn't explain the decline in waste weight.

E. In many areas, plastic bottles had to be sorted by color of the plastic before being recycled, whereas aluminum cans required no sorting.
This option introduces complexity in recycling but does not explain the observed decline in waste weight.­
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Re: V07-18 [#permalink]
I think this the explanation isn't clear enough, please elaborate. GMATNinja could you please help with this question?
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Ishita2000 wrote:
I think this the explanation isn't clear enough, please elaborate. GMATNinja could you please help with this question?

­
There are 3-4 explanations offered by other users in addition to the official explanation. I think it would help if you could be more specific what you are not following from the explanation. Otherwise, already multiple explanations are here. 
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V07-18 [#permalink]
Bunuel bb nightblade354 GMATNinja Could you please help here, where I am wrong. I think both A and C help to answer the case. It just depends on the right numbers as I have mentioned below as an example:

Premise: However, although aluminum (50x) recycling was more widely practiced in this period than plastic recycling (5x). So a net 10x times more lets say
Which of the following, if true of the Brazil in the period 2000 to 2010, most helps to account for the finding?

A. Plastic bottles (50 kg/per bottle) are significantly heavier than aluminum cans (2 kg/per bottle) of comparable size. a net 25x times more
Here, it can be concluded that, the weight of plastic bottles in domestic garbage declined by a greater percentage than the weight of aluminum cans.

C. Manufacturers replaced many plastic bottles (50x), but few aluminum cans (2x), with polymer containers. a net 25x times more. In this case also, it can be concluded that, the weight of plastic bottles in domestic garbage declined by a greater percentage than the weight of aluminum cans.

 ­
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Hi. The question talks about percentage. Not raw weight. So even if plastic is significantly heavier, the percentage would not change in the same manner.

The passage talks about the weight change and unit change.

Quote:
the weight of plastic bottles in domestic garbage declined by a greater percentage than the weight of aluminum cans.

You can see a mathematical proof of this question above.


Ankit__7182 wrote:
Bunuel bb nightblade354 GMATNinja Could you please help here, where I am wrong. I think both A and C help to answer the case. It just depends on the right numbers as I have mentioned below as an example:

Premise: However, although aluminum (50x) recycling was more widely practiced in this period than plastic recycling (5x). So a net 10x times more lets say
Which of the following, if true of the Brazil in the period 2000 to 2010, most helps to account for the finding?

A. Plastic bottles (50 kg/per bottle) are significantly heavier than aluminum cans (2 kg/per bottle) of comparable size. a net 25x times more
Here, it can be concluded that, the weight of plastic bottles in domestic garbage declined by a greater percentage than the weight of aluminum cans.

C. Manufacturers replaced many plastic bottles (50x), but few aluminum cans (2x), with polymer containers. a net 25x times more. In this case also, it can be concluded that, the weight of plastic bottles in domestic garbage declined by a greater percentage than the weight of aluminum cans.

 ­


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