In a residential complex consisting of two apartment buildings, one with units numbered 01 to 72 and the other with units numbered 01 to 88 with consecutive numbers, Onur, who lives there, sends a message to Engin, whom he has invited to his home, with the site address, apartment, and unit number.
According to this, what is the sum of the digits of Onur's apartment number?
A) 8 B) 10 C) 12 D) 14 E) 16

Seda, who has made an agreement with an organization company for cold and hot beverages to be served at a birthday party, informs the company that she estimates that between $\%52$ and $\%60$ of the guests will have cold drinks, between $\%67$ and $\%72$ will have hot drinks, and at most $\%4$ will not have any drinks, and asks them to make the necessary preparations.
According to Seda's estimate, between which two percentage values does the ratio of the number of guests who will have both a cold drink and a hot drink to the total number of guests lie?
A) $\%15 - \%24$ B) $\%16 - \%33$ C) $\%19 - \%36$ D) $\%22 - \%30$ E) $\%24 - \%29$

135 students at a school traveled to their homes and back during a holiday break using either bus company $A$ or $B$. While 75 students preferred company A for the outbound trip and 90 students preferred company B for the return trip, 86 students traveled with different companies for the outbound and return trips.
Accordingly, what is the total number of students who went with company B and returned with company A?
A) 22 B) 25 C) 28 D) 31 E) 34

At a workplace where there is work every day, a flexible work system has been implemented. The owner of this workplace asked some employees to come to the workplace every other day, while others to come every third day. After switching to this system, the number of employees coming to the workplace on the first four days was 22, 19, 28, and 26 respectively.
Accordingly, how many employees came to this workplace on the fifth day after switching to this system?
A) 12 B) 15 C) 18 D) 21 E) 24

Ali, standing on a flat ground, turns his direction north and walks 5 meters forward, then turns clockwise $126^{\circ}$ and walks 5 more meters, reaching the point where Berk is located.
Starting from his initial position, if Ali turns his direction north and walks 10 meters forward, then turns clockwise at least how many degrees and continues in that direction to reach the point where Berk is located?
A) 108 B) 117 C) 144 D) 153 E) 162

Triangles in which the length of one side equals the arithmetic mean of the lengths of the other two sides are called mean triangles.
Accordingly, which of these triangles can be mean triangles?
A) Only I B) Only III C) I and II D) II and III E) I, II and III

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

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

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

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

$a$, $b$ 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

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

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

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

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

For a two-digit natural number $AB$
$$\begin{aligned} & p: A + B = 5 \\ & q: A \cdot B = 6 \end{aligned}$$
Given these propositions.
If the proposition $(\mathbf{p} \vee \mathbf{q}) \Rightarrow (\mathbf{p} \wedge \mathbf{q})$ is false, what is the sum of the possible values of the number $AB$?
A) 106 B) 125 C) 144 D) 163 E) 182

A greengrocer has determined the kilogram selling price of each of six fruits as shown in the figure. The greengrocer has placed bananas in the back middle compartment of a counter consisting of six compartments as shown in the figure. The greengrocer asks his apprentice to place the remaining five types of fruit in the empty compartments of the counter such that each compartment contains a different type of fruit and the price of the fruit in each front compartment is cheaper than the price of the fruit in the compartment directly behind it.
Accordingly, in how many different ways can the apprentice arrange these fruits on the counter?
A) 18 B) 24 C) 30 D) 36 E) 42

A father, to encourage his son Kerem who is preparing for a math exam to study, changes the password of their wireless internet and leaves the following note next to the modem.
Accordingly, what is this internet password?
A) 45 B) 47 C) 51 D) 57 E) 63