At the 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 test. Given that 40\% of the candidates are really capable, the proportion of capable college students is about
(a)68\%
(b)70\%
(c)73\%
(d)75\%
Answer
Answer (as printed): A
Explanation
Let the total number of candidates be $x$. Number of capable candidates who got admitted to college $80 \%$ of $40 \%$ of $x=\left(\frac{80}{100} \times \frac{40}{100} \times x\right)=\frac{8 x}{25}$. Number of incapable college students $=25 \%$ of $(100-40) \%$ of $x=\left(\frac{25}{100} \times \frac{60}{100} \times x\right)=\frac{3 x}{20}$. Total number of candidates who got admitted to college $$=\frac{8 x}{25}+\frac{3 x}{20}=\frac{47 x}{100} . \begin{aligned} \therefore \text { Required percentage } & =\left(\frac{8 x}{25} \times \frac{100}{47 x} \times 100\right) \% \\ & =\left(\frac{3200}{47}\right) \%=68.09 \% \approx 68 \% \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.