gmatt1476 wrote:
Town X has 50,000 residents, some of whom were born in Town X. What percent of the residents of Town X were born in Town X ?
(1) Of the male residents of Town X, 40 percent were not born in Town X.
(2) Of the female residents of Town X, 60 percent were born in Town X.
DS34010.01
This is a weighted average problem. In the weighted arithmetic average form, the weights would be the number of male and the number of female residents. The values to be averaged would be partial part-to-whole ratios for the male and female residents, respectively.
The original question: What is the global ratio?
1) We know that the partial ratio for the male residents is 60 percent (born in Town X), but no information is given about the partial ratio for the female residents or about the weights. Thus, we can't get a unique value to answer the original question. \(\implies\)
Insufficient2) We know that the partial ratio for the female residents is 60 percent, but no information is given about the partial ratio for the male residents or about the weights. Thus, we can't get a unique value to answer the original question. \(\implies\)
Insufficient1&2) Since the partial ratios are equal for the subgroups, the global ratio cannot be different from these partial ratios. Even without knowing anything about the weights, we can determine that the global ratio in question is 60 percent. Thus, the answer to the original question is a unique value. \(\implies\)
SufficientAnswer: C
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