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

Answer: (C)

68%

Answer 2

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 = $\frac{32}{47}$ = $68\%$