Logic Breakdown

Passage Summary: If you take all the metal from one pile of cans and use it to make exactly half of a second pile of cans, the second pile must be twice as big as the first.

Conclusion: The new group of cans (M) contains exactly twice as many units as the original group (L).

Reasoning: All the aluminum from group L was used to create group M, and that recycled aluminum accounts for exactly half of the aluminum in group M.

Analysis: This argument relies on a mathematical gap regarding the efficiency of the recycling process. For the 2:1 ratio to be perfectly true, we must assume that no aluminum was lost or discarded when turning group L into group M. If even a small amount of aluminum was lost during processing, group M wouldn't be exactly twice the size of L. Look for an answer that guarantees that the total mass of aluminum from L is fully preserved in M.

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13.

The conclusion of the argument follows logically if which one of the following is assumed?

Correct Answer
C
If all of the aluminum in a can is recovered when recycled, then L contributes exactly L × a aluminum to M. Since that is 50% of M’s total aluminum, 0.5 × (M × a) = L × a, which yields M = 2L.
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