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A bag of trail mix is made by combining nuts and dried fruit by weight. What fraction of the mix, by weight, is nuts?
(1) The mix contains 3 pounds of nuts.
(2) The mix contains 2 pounds of dried fruit and nothing else besides nuts.
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Correct answer
C
The nut fraction is the nut weight divided by the total weight (nuts plus dried fruit).
Statement (1): 3 pounds of nuts, but the fruit weight and hence the total are unknown. Not sufficient.
Statement (2): 2 pounds of fruit (and only nuts otherwise), but the nut weight is unknown. Not sufficient.
Together: nuts 3, fruit 2, total 5, so the nut fraction is 3/5. Unique. Neither alone.
The (A)/(B) lure supplies one component weight; a part-of-total fraction needs both the part and the whole.
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