At a contest with 1,500 participants, 1/2 of the people are aged 8 to 12. Next year, the number of people aged 8 to 12 will increase by 1/3. After this change, what percentage of the total 1,500 people will the 8- to 12-year-olds represent?
E. 66 2/3%
I just wanted to mention a couple of things here:
* this is a pure ratio question; the number 1,500 is completely irrelevant, and you can ignore it if you like. When we increase something by 1/3, we are multiplying it by 1 + 1/3 = 4/3, so the answer here must be (1/2)*(4/3) = 2/3 = 66 2/3 %.
* you can certainly take advantage of the answer choices to get the answer without any computation. The fraction of 8-12 year olds has clearly increased, so D and E are the only candidates. D would be the answer if the increase were 10%; it's more than 10% so the answer must be E.
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