1. An archipelago consists of a large, a medium, and a small island. The total area of the three islands is $23 \mathrm{~km}^{2}$. The difference between the areas of the large and the medium island turns out to be exactly $1 \mathrm{~km}^{2}$ more than the area of the small island. How many $\mathrm{km}^{2}$ is the area of the large island?
A) 10
B) 11
C) 12
D) 13
E) 14
A1. C) 12 The difference between the areas of the large and the medium island is 1 $\mathrm{km}^{2}$ more than the area of the small island. In other words, the area of the medium island plus the area of the small island is $1 \mathrm{~km}^{2}$ less than the area of the large island. Therefore, the sum of the areas of all three islands is $1 \mathrm{~km}^{2}$ less than twice the area of the large island. Twice the area of the large island is thus $23+1=24$, and the large island has an area of $12 \mathrm{~km}^{2}$.