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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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Re: V07-18 [#permalink]
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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 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.
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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.
Request your reply.
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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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