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.