Let $P_k$ represent the perimeter of a square with sides of length $k$. The value of the expression $P_1+P_2+P_3+\ldots+P_{10}$ is $\_\_\_\_$ .

The city of Atlantis was crafted by the God of the seas, Poseidon. It was made of alternating concentric circular rings of land (shaded) and water (not shaded) as represented in the figure (not to scale). The radius of Inner Island was 2.5 stades (a unit of length used in ancient Greece). The water surrounding Inner Island was one stade wide (length AB ). This was surrounded by two pairs of alternating rings of land and water. The first pair of land and water was two stades wide each (lengths BC and CD), and the outer pair is three stades wide each (lengths DE and EF).

The ratio of the surface area of the land to that of the water in the city of Atlantis is

$\_\_\_\_$ (round off to two decimal places).

A stick of length one meter is broken at two locations at distances of $b_1$ and $b_2$ from the origin (0), as shown in the figure. Note that 0<b $b_2<1$. Which one of the following is NOT a necessary condition for forming a triangle using the three pieces?

$$ \text { Note: All lengths are in meter. The figure shown is representative. } $$

The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT?

$$ \begin{array}{|c|c|c|c|} \hline \text { Nation } & \text { Gold } & \text { Silver } & \text { Bronze } \\ \hline \text { USA } & 40 & 44 & 41 \\ \hline \text { Canada } & 39 & 27 & 24 \\ \hline \text { Japan } & 20 & 12 & 13 \\ \hline \text { Australia } & 17 & 19 & 16 \\ \hline \text { France } & 16 & 26 & 22 \\ \hline \end{array} $$