Regarding a two-digit natural number $AB$, the following propositions are given: p: The number $AB$ is even. q: The number $A^{AB}$ is prime. r: $A + B = 11$
If the proposition $(p \Rightarrow q) \wedge (q' \wedge r)$ is true, what is the product $A \cdot B$?
A) 18
B) 20
C) 24
D) 28
E) 30

The surface area of a rectangular prism with edge lengths $a, b$ and $c$ is calculated with the formula
$$A = 2(a \cdot b + a \cdot c + b \cdot c)$$
Two identical rectangular prisms are placed in three different ways such that they share one face each. The surface areas of the resulting Figure 1, Figure 2, and Figure 3 are calculated as 18, 20, and 22 square units respectively.
Accordingly, what is the surface area of one of the identical prisms in square units?
A) 12 B) 13 C) 14 D) 15 E) 16

Three faces of a square right prism-shaped board are painted white, and the other three faces are painted red. The sum of the areas of the white-painted faces is 76 square units, and the sum of the areas of the red-painted faces is 12 square units.
Accordingly, what is the volume of this board in cubic units?
A) 18 B) 24 C) 27 D) 32 E) 36

A toy bear, a toy horse, and a cactus plant are placed on 3 wall shelves, each at a different height from the ground, first as shown in Figure 1, and then as shown in Figure 2. The heights that are equal in Figure 1 and Figure 2 are shown with dashed lines. It is known that the sum of the heights of the toy bear, toy horse, and cactus plant is 15 units.
Given that the height of the leftmost shelf from the ground is 18 units, what is the sum of the heights of the other two shelves from the ground?
A) 45 B) 48 C) 51 D) 54 E) 57