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I would appreciate it if someone could please help me understand what is being asked here and how to approach questions like the one below.

"At the college entrance exam, a candidate is admitted according to whether he has passed or failed the test. Of the candidates who are really capable, 80 % pass the test and of the incapable, 25 % pass the test. Given that 40 % of the candidates are really capable, then the proportion of the really capable students who can pass the test to the total students who can pass is?"

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    Are we to assume that every student is either "really capable" or "incapable", or is there also a group of "just adequately capable" students?2011-09-06
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    Out of all capable students, $80%$ pass, so since capable students are $40%$ of the total, they constitute $(.4)(.8)%$ of those who passed; similarly, out of the $60%$ that is incapable, $25%$ passed, so they form $15%$ of the total who passed. You can do this problem assuming there are 100 students and the solution will generalize to any number.2011-09-06
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    I don't know how to describe the general category, but maybe weighted averages fits reasonably-well.2011-09-06
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    This is a CAT question. This was just what was given2011-09-07
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    but I think your solution there makes a lot of sense. The final answer was 68% though.2011-09-07

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