Aquafame Theme Park sells two types of tickets – for water park and for fun rides. On a certain day, 40% of the total

[BTGmoderatorDC]

Aquafame Theme Park sells two types of tickets – for water park and for fun rides. On a certain day, 40% of the total visitors had water park tickets as well as fun rides tickets. If 33.33% of the visitors with water park tickets did not buy fun rides tickets, then what percentage of the total visitors bought fun rides tickets?

A. 20%
B. 33.33%
C. 40%
D. 66.67%
E. 80%


OA E

Source: e-GMAT

[swerve]

Aquafame Theme Park sells two types of tickets – for water park and for fun rides. On a certain day, 40% of the total visitors had water park tickets as well as fun rides tickets. If 33.33% of the visitors with water park tickets did not buy fun rides tickets, then what percentage of the total visitors bought fun rides tickets?

A. 20%
B. 33.33%
C. 40%
D. 66.67%
E. 80%


OA E

Source: e-GMAT

Solved using 2x2 matrix

\begin{array}{|c|c|c|c|}
\hline
&\text{Water Park} & \text{Not Water Park} & \text{Total} \\ \hline
\text{Funride} & 40 & 40 & 80 \\ \hline
\text{Not Funride} & 20 & 0 & 20\\ \hline
\text{Total} & 60 & 40 & 100 \\ \hline
\end{array}

let total \(=100\)
So, \(33.33\%\) of the visitors with water park tickets did not buy fun rides tickets, then what percentage of the total visitors bought fun rides tickets
\(40+(40+x)\cdot 0.33= 40+x\)
\(x= 19.7 \approx 20\)

So, the total water park tickets \(= 40+20 = 60\)

Rest we can solve
We get a percentage of the total visitors bought fun rides tickets; \(80\%\)

Therefore, E