An unequal-armed seesaw has been constructed from a straight rod and a support placed perpendicular to the ground on this rod. When the left end of this seesaw placed on a flat ground touches the ground as shown in Figure 1, the height of the right end from the ground is 180 cm. When the right end of the seesaw touches the ground as shown in Figure 2, the height of the left end from the ground is 90 cm.
Accordingly, what is the length of the support placed on the seesaw in cm?
A) 45 B) 54 C) 60 D) 75 E) 81

Regarding a triangle $ABC$ and a point D taken on the side $AB$ of this triangle, it is known that two of the following four statements are true and two are false.
I. $\mathrm{AB} \perp \mathrm{CD}$ II. $|\mathrm{AD}| = |\mathrm{BD}|$ III. $m(\widehat{ACD}) = m(\widehat{BCD})$ IV. $A(\stackrel{\triangle}{\mathrm{ACD}}) = A(\stackrel{\triangle}{\mathrm{BCD}})$
Accordingly, which of the following are the true statements for this triangle?
A) I and II B) I and III C) I and IV D) II and III E) II and IV

Ayşe and Ferhat enter a store to buy pizza. From a whole pizza divided into 13 circular slices in this store; the 2 slices that Ayşe buys are identical to each other, while the 11 slices that Ferhat buys are also identical to each other.
Later, they combine three of these slices to obtain a semicircular pizza.
Accordingly, what is the measure of the central angle of one of the larger slices in degrees?
A) 90
B) 81
C) 75
D) 72
E) 60

A rubber band fixed at both ends to the ground is pulled from its midpoint and stretched upward perpendicular to the ground. When the rubber band is pulled x units above the ground, the angle formed is $120^{\circ}$, when pulled y units further up from this position, the angle formed is $90^{\circ}$, and finally when pulled z units further up from the second position, the angle formed is $60^{\circ}$.
Accordingly, which of the following is the correct ordering of the values x, y, and z?
A) $x < y < z$ B) $y < x < z$ C) $y < z < x$ D) $z < x < y$ E) $z < y < x$

When Mehmet throws a tennis ball shaped like a sphere with radius 2 cm at a wire mesh with a pattern made of identical shapes, the ball passes through the wire mesh without touching it.
Accordingly, the appearance of this wire mesh could be which of the following?
A) Only I
B) Only II
C) Only III
E) I and III

The measure of an interior angle of a regular n-sided polygon is calculated as $\frac{(n-2) \cdot 180^{\circ}}{n}$.
ABCDEFGHI is a regular nonagon, $P \in [FB]$, $|FD| = |FP|$, $\mathrm{m}(\widehat{\mathrm{APB}}) = x$.
According to the given information above, what is the measure of angle x in degrees?
A) 40 B) 45 C) 50 D) 55 E) 60

In Figure 1, a photograph taken by Selim while watching the sunset, the sun appears as a semicircle above the sea, and the distance from the highest point of the sun to the sea is measured as $3{,}9$ cm.
Some time after taking the photograph in Figure 1, Selim takes the photograph in Figure 2 from the same point. In this photograph, the distance from the highest point of the sun to the sea is measured as $0{,}3$ cm.
Accordingly, what is the length marked with ? in Figure 2 in cm?
A) 2
B) 2{,}5
C) 3
D) 3{,}5
E) 4

For a structure to be built on a rectangular plot of land with sides of at least 4 meters, a distance of two meters is left from each side of the plot as shown in the figure, and the area shown in gray is determined as the development area and development permission is granted for this area.
For this plot with a perimeter of 42 meters, if the determined development area is $24\,\mathrm{m}^2$, what is the length of a diagonal of the determined development area in meters?
A) 10 B) 11 C) 12 D) 13 E) 14

Burcu, who makes a ship from a deltoid with one face area of 48 square units according to the procedure above, finds that the two lengths shown in the figure on her ship are equal.
Accordingly, what is the area of the visible face of Burcu's ship in square units?
A) 20 B) 24 C) 28 D) 32 E) 36

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

A pencil with one end sharpened has the unsharpened part shaped like a right circular cylinder and the sharpened end shaped like a right circular cone with height 1 unit, as shown in the figure.
When the other end of the pencil is sharpened to be identical to the sharpened end and the total length of the pencil remains unchanged, the total volume of the pencil decreases by 5\%.
Accordingly, what is the total length of the pencil in units?
A) 12
B) 14
C) 16
D) 18
E) 20

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

The table below shows some musical note symbols and the duration lengths of these note symbols.
Accordingly, what is the sum of the duration lengths of the musical note symbols given above?
A) $\frac{3}{2}$ B) $\frac{7}{4}$ C) $\frac{5}{4}$ D) $\frac{13}{8}$ E) $\frac{15}{8}$

The value of an n-sided polygon symbol with circles at its corners and a natural number A written inside is equal to the sum of n times the sum of the natural numbers written inside the circles at the corners and the number A.
Given that, what is x?
A) 10 B) 11 C) 12 D) 13 E) 14

A flower bed with a height of 1.2 meters has five shelves at equal intervals in its left compartment and six shelves at equal intervals in its right compartment. The shelves at the bottom and top of these two compartments are at equal heights. A flower has been placed on the 4th shelf in the left compartment and on the 3rd shelf in the right compartment of the flower bed as shown in the figure.
Accordingly, what is the sum of the heights from the ground of the shelves where the flowers are located in meters?
A) 1.38 B) 1.36 C) 1.34 D) 1.32 E) 1.30

$a$, $b$ and $c$ are distinct digits,
$$\begin{aligned} & a \cdot b < 8 \\ & a \cdot c > 10 \\ & b \cdot c = 12 \end{aligned}$$
Given these statements.
Accordingly, what is the sum $\mathbf{a} + \mathbf{b} + \mathbf{c}$?
A) 9 B) 11 C) 13 D) 15 E) 17

Let $p$, $q$ and $r$ be prime numbers,
$$5pqr - 2p - 10r = 270$$
Given this equality.
Accordingly, what is the sum $p + q + r$?
A) 14 B) 15 C) 16 D) 17 E) 18

Let $a, b, c$ and $d$ be positive real numbers; the value of the first notation equals the number $\frac{a+d}{b+c}$, and the value of the second notation equals the number $\frac{a \cdot d}{b \cdot c}$.
Given that the above holds, what is x?
A) 12 B) 16 C) 24 D) 36 E) 48

For real numbers $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$
$$\begin{aligned} & |a + b + c| = a + b \\ & |(a + b) \cdot c| = 8 \\ & |a - b - 8| = 0 \end{aligned}$$
Given that this holds, what is the product $\mathbf{a} \cdot \mathbf{b} \cdot \mathbf{c}$?
A) 48 B) 50 C) 52 D) 56 E) 60

The figure below shows a lamp and the appearance of a string that operates this lamp. The lamp;

• when closed, if the string is pulled and released, it gives dim light,
• when giving dim light, if the string is pulled and released, it gives daylight,
• when giving daylight, if the string is pulled and released, it gives bright light,
• when giving bright light, if the string is pulled and released, it turns off.

Initially, this lamp was closed. The string was pulled and released A times and the lamp was observed to give bright light. Then, the lamp's string was pulled and released B more times and the lamp was observed to give daylight. Later, the lamp's string was pulled and released C more times and the lamp was observed to turn off.
Accordingly, which of the following is an even number?
A) $A \cdot B + C$ B) $B \cdot C + A$ C) $A \cdot (B + C)$ D) $B \cdot (A + C)$ E) $C \cdot (A + B)$

Let $A$, $B$, $C$ and $D$ be digits;

• the four-digit number $ABCD$ is divisible by 20,
• the three-digit number $ADB$ is divisible by 18,
• the three-digit number $CDA$ is divisible by 15.

Accordingly, what is the sum $A + B + C + D$?
A) 10 B) 11 C) 12 D) 13 E) 15

Two balloons are hung on a string stretched between two walls as shown in the figure. Between these two balloons, 2 white balloons or 4 yellow balloons are to be hung such that the distance between the points where any two adjacent balloons are attached to the string is equal.
The distance between the points where any two adjacent balloons are attached to the string is 18 cm more when white balloons are hung compared to when yellow balloons are hung.
Accordingly, what is the distance in cm between the points where the two initially hung balloons are attached to the string?
A) 135 B) 144 C) 153 D) 162 E) 171

Let $A$, $B$ and $C$ be digits different from zero and from each other. If both two-digit natural numbers $AB$ and $BC$ are prime numbers, then the three-digit natural number $ABC$ is called a primish number.
Accordingly, what is the sum of the smallest primish number and the largest primish number?
A) 1034 B) 1050 C) 1110 D) 1154 E) 1170

At the entrance of a hotel, there are three digital wall clocks showing the local times of cities $\mathrm{A}, \mathrm{B}$ and C. A customer looking at these clocks observed that the local time difference between cities A and B is 4 hours, and the local time difference between cities B and C is 3 hours.
When the clock showing the local time of city A reads 14.00, which of the following cannot be the time shown on the clock for city C?
A) 07.00 B) 13.00 C) 15.00 D) 17.00 E) 21.00

Regarding sets $A$, $B$ and $C$
$$\begin{aligned} & s(A) = s(C) = 5 \\ & s(A \times (B \cup C)) = 30 \\ & s(B \times (A \cup C)) = 16 \end{aligned}$$
Given these equalities.
Accordingly, how many elements does the set $B \cap C$ have?
A) 1 B) 2 C) 3 D) 4 E) 5