(1) 60% of the bipeds in the exhibit were not carnivores, and 60% of the carnivores in the exhibit were bipeds.Using a 3x3 matrix to plot the provided info and solve any of the other spaces:
\begin{tabular}{|l|l|l|l|}
\hline
~ & B & nB & Total \\ \hline
C & \(\frac{4}{10}\)b /\(\frac{6}{10}\)c & \(\frac{4}{10}\)c & c \\ \hline
nC & \(\frac{6}{10}\)b & ~ & ~ \\ \hline
Total & b & ~ & 100 \\ \hline
\end{tabular}
Without knowing the number of non-carnivores non-bipedal dinosaurs in the exhibit one will not be able to solve for the percentage of the dinosaurs in a certain museum exhibit were both bipeds and carnivores.
INSUFFICIENT(2) Every dinosaur in the exhibit was a biped, a carnivore, or both.No numeric values are given by this statement, which in itself means the statement alone will be insufficient. However, the most important piece of info which one can extract from this statement is that there are no dinosaurs in the exhibit which are non-carnivores and non-bipedal.
INSUFFICIENT(1+2)Putting the two statements together, one now can complete the 3x3 matrix to look like:
\begin{tabular}{|l|l|l|l|}
\hline
~ & B & nB & Total \\ \hline
C & \(\frac{4}{10}\)b /\(\frac{6}{10}\)c & \(\frac{4}{10}\)c & c \\ \hline
nC & \(\frac{6}{10}\)b & 0 & \(\frac{6}{10}\)b \\ \hline
Total & b & \(\frac{4}{10}\)c & 100 \\ \hline
\end{tabular}
One has \(b + \frac{4}{10} = 100 \) and \(c + \frac{6}{10}b = 100\).
Making them equal one another: \(b + \frac{4}{10} = c + \frac{6}{10}b\)
\(\frac{4}{10}b = \frac{6}{10}c\)
\(4b = 6c\)
\(\frac{b}{c} = \frac{6}{4}\)
Which means of the total dinosaurs in the exhibit \(\frac{4}{10}\) or \(40\)% are bipedal and \(\frac{6}{10}\) or \(60%\) are carinovers.
The number of dinosaurs in the exhibit which are both carnivores and bipedal is \(\frac{4}{10}b\), which is \(60\)% of the total dinosaurs. Therefore, the percentage of the dinosaurs in a certain museum exhibit were both bipeds and carnivores: \(24\)%
SUFFICIENT
ANSWER C