Question

At a college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the tests. Of the candidates who are really capable, 80% pass the tests and of the incapable, 25% pass the tests. Given that 40% of the candidates are really capable, then the proportion of capable college students is about

• A. 73%
• B. 70%
• C. 68%
• D. 75%

Answer 1

The Correct Option is C

Let the total candidates be t and capable candidates be x and incapable be y.
Candidates passing the tests = \(0.8x + 0.25y\)
Candidates failing the test = \(0.2x + 0.75y\)
Given,
\(x = \frac{40}{100}\times t\) 
and \(y = 0.6t\)
Pass = \(0.8\times0.4t + 0.25\times0.6t = 0.32t + 0.15t = 0.47t\)
Proportion of capable college students who passed is = \(\frac{32}{47}\) = \(68\%\)