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

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

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 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

Eight digits from 1 to 8 are divided into two groups. It is known that the sum of the digits in the first group equals the sum of the digits in the second group, and the number of digits in each group equals one of the digits in that group.
Accordingly, which of the following digits is in the same group as digit 7?
A) 2 B) 3 C) 4 D) 5 E) 6

Ayşe, who read a page from a diary she had written in the past in 2020, saw that the date she wrote this was erased and, remembering the year the date was erased,
"My current age is equal to 3 times my age in the year I wrote this."
said. The diary entry mentioned that today her younger sibling started first grade in elementary school, that the sibling was very lucky to start school at age 6, and that Ayşe had started school at age 5 in the year her sibling was born.
In which year did Ayşe write this?
A) 1990 B) 1992 C) 1994 D) 1996 E) 1998

Cities A, B, C, D, and E are located on a straight road as shown in the figure, and the distance between cities A and E is 300 kilometers.
Ela, driving her vehicle, started moving from city A at a constant speed of 90 kilometers per hour and will go to city E using this road without taking a break. Her mother asked Ela to share her live location throughout the journey and occasionally checked this sharing to write down in the table below how many minutes after Ela left city A she was at which point.

Elapsed time	Current location
After 10 minutes	Exactly midway between cities A and B
After 40 minutes	Exactly midway between cities B and C
After 140 minutes	Exactly midway between cities D and E

According to this, what is the distance between cities C and D in kilometers?
A) 30 B) 35 C) 40 D) 45 E) 50

All of a certain quantity of balls are packaged in three types of packages, each containing either only 1 yellow ball, only 2 blue balls, or only 3 red balls. The distribution of these packages by type is shown in Figure 1, and the distribution of all balls in these packages by color is shown in the pie chart in Figure 2.
According to this, what percentage of the balls are red?
A) 60 B) 64 C) 66 D) 70 E) 72

On a straight street with a market at one end and a greengrocer at the other end, some of the 9 houses located between the market and greengrocer and standing side by side are gray, and the rest are pink. Arda, Burak, and Cem, each living in a different one of these houses, each left their home and went directly to either the market or the greengrocer. Along the way, excluding their own house:

• Arda passed 3 gray, 1 pink;
• Burak passed 1 gray, 2 pink;
• Cem passed 2 gray, 5 pink

colored houses.
According to this, what are the colors of the houses where Arda, Burak, and Cem live, respectively?
A) gray, gray, pink B) gray, pink, pink C) pink, pink, pink D) pink, pink, gray E) pink, gray, gray

Murat Teacher teaches 6 one-hour mathematics (Mat) and 5 one-hour geometry (Geo) classes per week. His weekly lesson schedule for a certain year's spring semester is given in the table.

Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
				Geo
Mat			Geo	Geo
Mat	Geo			Mat
	Geo		Mat	Mat
			Mat

In the determined year, according to this schedule, Murat Teacher taught a total of 26 hours of mathematics and 23 hours of geometry from the beginning of March 1 to the end of March 31. It is known that the teacher taught each of his classes on the days he had classes during these dates.
According to this, what day of the week is March 1 in the determined year?
A) Monday B) Saturday C) Wednesday D) Thursday E) Friday

The front face of a rectangular cabinet divided into identical square compartments has compartments numbered starting from 1 with consecutive natural numbers. This numbering process begins by numbering all compartments in the bottom row from left to right. In each subsequent row, all compartments are numbered in the opposite direction starting from the compartment directly above the last numbered compartment in the row below.
In this cabinet, part of which is visible as shown in the figure, what is the number of the compartment directly below compartment number 61?
A) 40 B) 44 C) 46 D) 50 E) 52

On an internet site, the time remaining until the TYT starting at 10:15 on Saturday, June 21, 2025 is displayed as shown in the figure.
Can, viewing this site in Ankara at a specific time on a specific day, interprets the numbers in the day and hour sections as day and month respectively, and the four-digit number formed by placing the two-digit number in the seconds section to the right of the two-digit number in the minutes section as the year, and realizes that the date he viewed the site is written as day, month, and year.
According to this, on what day of the week and at what time did Can view the site?
A) Monday 04.54 B) Monday 05.55 C) Friday 03.54 D) Friday 04.54 E) Sunday 03.54

Eight line segments, each with one endpoint at point O, form angles $a$, $b$, $c$, $d$, $e$, $f$, $g$, and $h$ between them. The measures of these angles are directly proportional to 8 consecutive integers arranged from smallest to largest.
Given that points K, O, and R are collinear, what is the measure of the angle $\widehat{\mathrm{MOR}}$ shown in purple in the figure?
A) 108 B) 114 C) 120 D) 126 E) 132

A triangle with all side lengths being different integers measured in centimeters is called a scalene integer triangle.
According to this, what is the minimum perimeter of a scalene integer triangle in centimeters?
A) 6 B) 7 C) 8 D) 9 E) 10

Three identical isosceles triangle-shaped pieces in yellow, red, and blue colors are combined with their apex angles' vertices coinciding to form a fan. When the fan is opened, one side of each pair of adjacent pieces will be shared, and all pieces will be completely visible as shown in Figure 1.
When the fan is closed on a table, all pieces have one side on the table as shown in Figure 2.
According to this, what is the apex angle of the blue piece in degrees?
A) 18 B) 19 C) 20 D) 21 E) 22

Three right triangles with areas proportional to 1, 2, and 3 respectively in yellow, blue, and red colors are combined as shown in the figure such that one of the yellow triangle's legs coincides with one leg of the blue triangle, and the other leg coincides with one leg of the red triangle.
Given that the hypotenuse lengths of the yellow and blue triangles are 11 and 13 units respectively, what is the hypotenuse length of the red triangle in units?
A) 28 B) 29 C) 30 D) 31 E) 32

On the bottom edge of a rectangular advertisement board, two points are marked to divide this edge into three equal parts, and a lighting lamp is placed at each of these points. When on, each lamp illuminates a triangular region on the board as shown in the figure, with one vertex at the point where the lamp is located and the other two vertices at the endpoints of the board's top edge.
According to this, the area of the advertisement board that is not illuminated when only one lamp is on is how many times the area that is not illuminated when both lamps are on?
A) $\frac{4}{3}$ B) $\frac{5}{4}$ C) $\frac{6}{5}$ D) $\frac{7}{6}$ E) $\frac{8}{7}$

In an excavation, a historic artifact piece shaped like a right trapezoid with an area of 10 square meters was found, as shown in the figure.
The team conducting this excavation stated that they have not yet reached the missing right triangular part of this historic artifact, which was originally square-shaped and has an area of 6 square meters.
According to this, what is the perimeter of the found historic artifact piece in meters?
A) 10 B) 11 C) 12 D) 13 E) 14

Two of three identical squares are placed with their vertices coinciding, and the third square is placed such that part of it overlaps with the first square and part overlaps with the second square, as shown in the figure.
In the figure, the blue and red colored regions are squares, and the areas of the three yellow colored regions are given in square units.
According to this, what is the area of one of these identical squares in square units?
A) 96 B) 98 C) 100 D) 108 E) 121

The measure of an interior angle of a regular $n$-sided polygon is calculated as $\frac{(n-2) \cdot 180^{\circ}}{n}$.
Öykü draws a regular $k$-sided polygon with a red pen in her notebook. On each side of this polygon, she draws an equilateral triangle as shown in Figure 1, with one side length equal to the side length of the polygon.
Then Öykü connects the vertices of these triangles that are not on the red colored sides with a blue pen in a straight line. When she does this, she obtains another regular polygon, and she measures one of the resulting angles as $42^{\circ}$ as shown in Figure 2.
According to this, what is $k$?
A) 8 B) 9 C) 10 D) 11 E) 12