BTGModeratorVI wrote: ↑Thu Nov 05, 2020 8:00 am
In a certain high school, 80 percent of the seniors are taking calculus, and 60 percent of the seniors who are taking calculus are also taking physics. If 10 percent of the seniors are taking neither calculus nor physics, what percent of the seniors are taking physics?
(A) 40%
(B) 42%
(C) 48%
(D) 58%
(E) 80%
Answer:
D
Source: Official guide
\(2\times 2\) Matrix
Consider total seniors as \(100S\)
\begin{array}{|c|c|c|c|}
\hline
& \text{Calculus} & \text{No Calculus} & \text{Total} \\ \hline
\text{Physics} & 48S & 10S & 58S \\ \hline
\text{No Physics} & 32S & 10S & 42S \\ \hline
\text{Total} & 80S & 20S & 100S \\ \hline
\end{array}
\(80\%\) takes calculus, so \(80S\) (Calculus) and \(20S\) (No Calculus)
\(60\%\) of those who take calculus also takes physics, so, \(60\%\) of \(80S= 48S\), takes both calculus and physics.
Therefore, \(32S\) takes only calculus and no physics.
\(10\%\) takes neither, so \(10S\) for no physics and no calculus.
Therefore, total physics \(= 58S\)
physics\(\%= \dfrac{58S}{100S} \Rightarrow 58\%\)
Hence,
D
