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An alloy, Alloy K, is made by mixing certain quantities of iron and lead. The total weight of the alloy is \(50\text{ kg}\). What is the ratio of the weight of iron to the weight of lead in Alloy K?
We need to find the ratio of the weight of iron to the weight of lead in Alloy K.
We need to find the ratio \(\mathrm{I:L}\) (or equivalently, \(\mathrm{I/L}\)). Since we know \(\mathrm{I + L = 50}\), if we can determine either I or L uniquely, we can find the other and thus determine the ratio.
For this question to be sufficient, we need to arrive at one specific ratio value.
Statement 1: If 4 kg of iron were to be replaced with 4 kg of lead, the percentage of lead, by weight, in Alloy K would become 40%.
This statement describes a hypothetical scenario. After replacing 4 kg of iron with 4 kg of lead:
Since lead would be 40% of 50 kg after the replacement:
[STOP - Sufficient!] We can determine a unique ratio.
Statement 1 is sufficient.
This eliminates choices B, C, and E.
Now let's forget Statement 1 completely and analyze Statement 2 independently.
Statement 2: The weight of iron per 100 cc is 0.7 times the weight of lead per 100 cc.
This tells us about the density relationship between iron and lead:
In other words, iron is less dense than lead (which makes sense physically).
While we know the density relationship, we don't know:
Think of it this way: If we have 50 kg total, we could have:
The density relationship alone doesn't tell us which combination we actually have, because we don't know the volumes involved.
Statement 2 is NOT sufficient.
This eliminates choices B and D.
Since Statement 1 alone is sufficient to determine the ratio, but Statement 2 alone is not sufficient, the answer is A.
Answer Choice A: "Statement 1 alone is sufficient, but Statement 2 alone is not sufficient."