When the numbers $2,3,4,5,6,7,8$ and 9 are placed in the boxes below such that each box contains a different number, all equalities are satisfied.
$$\begin{aligned} & \square \times \square = 12 \\ & A \div \square = 2 \\ & \square + \square = 12 \\ & B - \square = 2 \end{aligned}$$
Accordingly, what is the sum $A + B$?
A) 13 B) 14 C) 15 D) 16 E) 17

Let $a, b, c$ and $d$ be positive integers. $$\begin{aligned} & M = 6^{a} \cdot 5^{b} \\ & N = 10^{c} \cdot 9^{d} \end{aligned}$$ For the numbers $M$ and $N$ $$\begin{aligned} & \gcd(M, N) = 2^{3} \cdot 3^{2} \cdot 5 \\ & \text{lcm}(M, N) = 2^{5} \cdot 3^{3} \cdot 5^{5} \end{aligned}$$ are given. Accordingly, what is the sum $a + b + c + d$?
A) 8 B) 9 C) 10 D) 11 E) 12

A mathematics teacher asked students to find the decimal representation of the number $\frac{13}{20}$. Sude, who found this representation correctly, accidentally swapped the tenths and hundredths digits when writing the number she found on the board.
Accordingly, the number Sude wrote on the board is equal to which of the following?
A) $\frac{5}{8}$ B) $\frac{9}{20}$ C) $\frac{14}{25}$ D) $\frac{23}{40}$ E) $\frac{27}{50}$

The sum of five distinct prime numbers equals 100, and their product equals a six-digit natural number ABCABC.
Accordingly, what is the sum $A + B + C$?
A) 8 B) 11 C) 14 D) 17 E) 20

Let $a$, $b$ and $c$ be positive real numbers. The value of a certain notation is equal to the number $a \cdot (b + c)$.
If this is the case, what is $\times$?
A) 1 B) 2 C) 3 D) 4 E) 5

Let $x$ be a real number different from $-1, 0$ and $1$.
$$\left\{ x^{3}, x^{2}, x, -x, -\frac{1}{x} \right\}$$
When the elements of the set are arranged from smallest to largest, which element never occupies the exact middle position?
A) $x^{3}$ B) $x^{2}$ C) $x$ D) $-x$ E) $-\frac{1}{x}$

Some vehicles on a three-lane highway named lanes A, B, and C changed lanes during a certain time interval. During this time interval when there were no new vehicles entering the highway and no vehicles leaving the highway

• 5 vehicles from A to B;
• 4 vehicles from B to A, 1 to C;
• 3 vehicles from C to B

passed, and in the final state, the number of vehicles in these three lanes were equal to each other.
If the initial number of vehicles in lanes A, B, and C are $a$, $b$, and $c$ respectively, which of the following orderings is correct?
A) $a < b < c$ B) $a < c < b$ C) $b < a < c$ D) $b < c < a$ E) $c < a < b$

In a two-leg football match played between classes A and B at a school, let $x$ be the difference between the total number of goals scored in the first half and the total number of goals scored in the second half
$$|x - 4| < 3$$
the inequality is satisfied.
In the first half, class A scored 2 goals and class B scored 1 goal. In this match, the total number of goals scored by class A equals the total number of goals scored by class B.
Accordingly, which of the following cannot be the total number of goals scored by class A in this match?
A) 2 B) 3 C) 4 D) 5 E) 6

In the rectangular coordinate plane, the graphs of the functions $f + g$ and $f \cdot g$ defined on the closed interval $[0, 10]$ are shown below.
For the real numbers $a, b$ and $c$ in the closed interval $[0, 10]$,

• $f(a), f(b)$ and $g(b)$ values are positive,
• $g(a), f(c)$ and $g(c)$ values are negative.

Accordingly, which of the following is the correct ordering of $a, b$ and $c$?
A) $a < c < b$ B) $b < a < c$ C) $b < c < a$ D) $c < a < b$ E) $c < b < a$

For positive integers $a$, $b$, and $c$

• $\frac{a+b}{c}$ is an even integer,
• $\frac{a+c}{b}$ is an odd integer.

Accordingly
I. $a + b + c$ II. $a \cdot (b + c)$ III. $a \cdot b \cdot c$
which of the following expressions are always even?
A) Only II B) Only III C) I and II

Regarding the subsets $A, B$ and $C$ of the set of natural numbers, the propositions
$$\begin{aligned} & p : 9 \in A \cup B \\ & q : 9 \in A \cap C \\ & r : 9 \notin C \end{aligned}$$
are given. Given that the proposition $(p \Rightarrow q)' \wedge r'$ is true, which of the following statements are true?
I. $9 \in A$ II. $9 \in B$ III. $9 \in C$
A) Only I B) Only III C) I and II D) II and III E) I, II and III

A total of 35 fruits of five different types are packaged in 15 packages as shown in the figure.
Ayşenur, Cansu, Merve, Rabia, and Sibel shared these packages such that each person took 3 packages and each person's packages contained a total of 7 fruits. The fruits in the packages taken by Ayşenur are of exactly the same type as the fruits in the packages taken by Cansu, and the fruits in the packages taken by Merve are of completely different types from the fruits in the packages taken by Rabia.
Accordingly, what types of fruits are in the packages taken by Sibel?

Regarding the sets $A, B, C, K$ and $L$, $$K = A \times B$$ $$L = B \times C$$ are given.
Given that $K \cup L = \{(1,2), (1,3), (2,2), (3,2), (3,3)\}$, which of the following is the set $K \cap L$?
A) $\{(1,2)\}$ B) $\{(1,3)\}$ C) $\{(2,2)\}$ D) $\{(3,2)\}$ E) $\{(3,3)\}$

Let $A$ and $B$ be two sets

• $8 \in A \cap B$
• $9 \in A \cup B$
• $10 \in A \setminus B$

it is known that.
Accordingly, set $B$
I. all even numbers II. all single-digit natural numbers III. all natural numbers divisible by 4
which of the following sets can it be?
A) Only I B) Only II C) Only III D) I and II E) II and III

Regarding Beyza
$p$: She was born on the first day of the month. $q$: She was born in September. $r$: She was born in 2000
propositions are given.
$$(p \Rightarrow q) \Rightarrow (r \Rightarrow q)$$
If the proposition is false, which of the following could be Beyza's date of birth?
A) December 4, 2000 B) September 4, 1999 C) December 1, 1999 D) September 1, 2000

If a natural number is itself a prime number but none of its digits are prime numbers, this number is called a primeless number. For example, 109 is a primeless number.
Accordingly, what is the sum of all two-digit primeless numbers?
A) 145 B) 163 C) 189 D) 207 E) 221

In the rectangular coordinate plane, the graphs of $f$, $g$, and $h$ linear functions defined on the closed interval $[0,1]$ are given in the figure.
Let $a$ and $b$ be real numbers in the open interval $(0,1)$ and
$$f(1) = g(1)$$
$$f(a) = g(b) = h(b)$$
equalities are satisfied.
Accordingly, which of the following orderings is correct?
A) $f(a) < h(a) < g(a)$ B) $g(a) < f(a) < h(a)$ C) $g(a) < h(a) < f(a)$ D) $h(a) < f(a) < g(a)$ E) $h(a) < g(a) < f(a)$

The remainder when the four-digit natural number $\overline{A34B}$ is divided by 5 equals the remainder when divided by 9.
Accordingly, what is the sum of the different values that digit $A$ can take?
A) 8 B) 10 C) 12 D) 14 E) 16

Sena has chosen a series A consisting of three films and a series B consisting of three films to watch a different film each of six specific evenings. For each series, Sena will not watch the second film without watching the first film of that series, and will not watch the third film without watching the second film of that series.
Accordingly, in how many different ways can Sena determine the order in which she will watch these six films?
A) 20 B) 24 C) 27 D) 30 E) 32

From five consecutive two-digit odd natural numbers written on a paper, the sum of the digits of each is written on the board. Then it is observed that the sum of these five numbers written on the board is 42.
Accordingly, what is the product of the digits of the largest of these five numbers written on the paper?
A) 4 B) 9 C) 12 D) 18 E) 21

In front of the two doors of a shopping mall, there are 2 parking lots named Blue and Red in front of the first door, and 3 parking lots named Yellow, Orange and Green in front of the second door. Kartal, who came to this shopping mall, randomly came in front of one of the doors and randomly parked his car in one of the parking lots in front of that door and entered the shopping mall. When leaving the shopping mall, since Kartal forgot which parking lot he parked his car in and which door he entered the shopping mall from, he exited from one of the doors randomly and searched for his car in one of the parking lots in front of that door randomly.
Accordingly, what is the probability that the parking lot where Kartal searched for his car is the parking lot where he parked his car?
A) $\frac{1}{5}$ B) $\frac{5}{24}$ C) $\frac{6}{25}$ D) $\frac{7}{36}$ E) $\frac{11}{48}$

In a data group, when the numbers are arranged from smallest to largest, if the number of terms in the group is odd, the median is the middle number; if it is even, the median is the arithmetic mean of the two middle numbers.
Let $A$ and $B$ be two sets. From the number of elements of the sets $A$, $B$, $A \cap B$, $A \cup B$ and $A \setminus B$, the numbers in the data group are arranged from smallest to largest as
$$s(B),\ s(A \cap B),\ s(A \setminus B),\ s(A \cup B),\ s(A)$$
in this form.
If the arithmetic mean of this data group is 5, what is the median?
A) 3 B) 4 C) 5 D) 6 E) 7

Melek, who entered a store, bought 1 bunch of arugula, 2 bunches of parsley, and 3 bunches of dill and went to the cashier to pay. The cashier, who confused arugula and dill, calculated 1 bunch of arugula price instead of 1 bunch of dill price, and 3 bunches of arugula price instead of 3 bunches of dill price. Due to this miscalculation, Melek paid 4 TL less than she should have paid and paid a total of 100 TL.
If the price of 1 bunch of parsley in this store is 15 TL, what is the price of 1 bunch of dill in TL?
A) 18 B) 19 C) 20 D) 21 E) 22

Efe made six shots in a basketball practice. After each shot, Efe noted what fraction of his shots up to that point had been successful. The largest of these six numbers that Efe noted is $\frac{3}{4}$.
If exactly four of Efe's shots were successful, which shots were not successful?
A) 1st and 4th B) 1st and 5th C) 1st and 6th D) 2nd and 5th E) 2nd and 6th

After marking the pages to be printed on a computer and starting the printing process, the computer screen shows what percentage of the marked pages have been sent to the printer, and the printer screen shows what percentage of the pages sent to the printer have been completed.
While there was some paper in the printer, a certain number of pages were marked on the computer and the printing process was started so that each page would be printed on a different sheet of paper.
When the computer screen and printer display are as shown in the figure, the printer runs out of paper. Then 39 sheets of paper were added to the printer, and when both screens showed 80\%, these papers also ran out.
Accordingly, how many pages were marked to be printed at the beginning?
A) 50 B) 65 C) 75 D) 90 E) 100