A 6-round competition conducted over the internet has 1,000,000 competitors participating in the first round. At the end of each round, 1/5 of the competitors who participated in that round are eliminated, and only the remaining competitors in their entirety participate in the next round.
Accordingly, how many competitors remain at the end of the 6th round?
A) $2^{16}$
B) $2^{18}$
C) $2^{20}$
D) $2^{22}$
E) $2^{24}$

In the figure below consisting of 16 equal parts, a fraction is expressed by the ratio of the number of parts colored pink to the number of all parts.
How many of the uncolored parts should be colored pink to express the fraction equal to the square root of this fraction?
A) 1
B) 2
C) 3
D) 4
E) 5

Let A, B, and C be different digits other than zero,
ABC CAB BCA The three-digit natural numbers are divisible by 4, 5, and 9 respectively. Accordingly, what is the product A · B · C?
A) 150
B) 180
C) 200
D) 210
E) 240

When the numbers $1, 2, 3, 4, 5, 6, 7$ and 8 are placed in the boxes below such that each box contains a different number, all equalities are satisfied.
$\square : \square = 4$
$\square \times \square = 4$
$\square - \square = 4$
$\square + \square = A$
Accordingly, what is the number A?
A) 7
B) 8
C) 9
D) 10
E) 11

The value of an n-sided polygon symbol containing a natural number A is equal to the integer part of the decimal representation of the fraction $\frac{A}{n}$.
Example: $\widehat{6} = 9 = 2$
Let AB be a two-digit natural number, and
$$\langle \mathrm{AB} \rangle = 19 = \mathrm{AB}$$
Accordingly, what is the sum $\mathrm{A} + \mathrm{B}$?
A) 6
B) 7
C) 8
D) 9
E) 10

The following steps are applied to the number 123 in sequence to change the positions of its digits, and a three-digit number is obtained at each step.

1. In step 1, a number is obtained by switching the positions of the digits in the tens and hundreds places.
2. In step 2, a number is obtained by switching the positions of the digits in the ones and tens places of the number obtained in the previous step.

Continuing in this way, if the step number is odd, numbers are obtained by switching the positions of the digits in the tens and hundreds places of the number obtained in the previous step, and if the step number is even, by switching the positions of the digits in the ones and tens places of the number obtained in the previous step. Accordingly, which of the following is the number obtained after step 75?
A) 321
B) 312
C) 231
D) 213
E) 132

In the figure below, three points indicating the positions of apple, pear, and walnut trees in a garden located between a main street and a side street that intersect perpendicularly with each other and have straight edges are shown.
Of the trees in this garden, the one closest to the main street is the apple tree, and the one farthest is the pear tree.
Accordingly, which of the following is the correct ordering from the tree closest to the side street to the one farthest?
A) Pear - Walnut - Apple
B) Pear - Apple - Walnut
C) Walnut - Pear - Apple
D) Apple - Pear - Walnut
E) Apple - Walnut - Pear

On a table, there are three marbles in total: one red, one blue, and one yellow. These marbles are placed in bags A, B, and C with one marble in each bag, and p: ``There is no red marble in bag A.'' q: ``There is a blue marble in bag B.'' r: ``There is no yellow marble in bag C.'' propositions are given.
$$p \wedge ( q \vee r ) ^ { \prime \prime }$$
Given that the proposition is true; what are the colors of the marbles in bags A, B and C respectively?
A) Red - Blue - Yellow
B) Blue - Red - Yellow
C) Blue - Yellow - Red
D) Yellow - Red - Blue
E) Yellow - Blue - Red

Let $x$, $y$, and $z$ be positive integers, and
$$\frac{x - z}{y} = x$$
is given.
Accordingly,
I. If $x$ is odd, then $y$ is even.
II. If $x$ is even, then $z$ is even.
III. If $y$ is odd, then $z$ is even.
Which of the following statements are always true?
A) Only I
B) Only II
C) I and II
D) I and III
E) II and III

Two bottles each contain equal amounts of milk. The milk in the first bottle completely fills three identical empty cups and one identical empty saucer, while the milk in the second bottle completely fills two of these empty cups and three of these empty saucers.
Accordingly; the milk in a third bottle containing the same amount of milk completely fills how many of these saucers?
A) 6
B) 7
C) 8
D) 9
E) 10

On a radius of a circular park with center O and radius length 5 units, points dividing each 1 unit into five equal intervals are marked. Then, circular arcs with center O passing through these points are drawn as shown in the figure.
Ahmet throws 2 javelins from point O, with his first javelin landing at point A and his second javelin landing at point B.
If the distance from point A to point O is 54 meters, what is the distance from point B to point O in meters?
A) 63
B) 66
C) 72
D) 75
E) 81

Ayça starts from 56 and counts forward by sixes until she reaches a two-digit natural number AB, then counts backward by fives from this number she reached to arrive at the number 15.
Accordingly, what is the sum $\mathrm{A} + \mathrm{B}$?
A) 6
B) 7
C) 8
D) 9
E) 10

The difference between the largest and smallest digits of a three-digit natural number with distinct digits is called the digit range of that number.
According to this, how many numbers have a digit width of 8?
A) 70
B) 72
C) 78
D) 80
E) 84

In a data set where not all values repeat equally, each value that repeats most frequently is called the mode of this data set.
All 48 students in a class took a mathematics exam, and the numerical distribution of the scores these students received from this exam is given in the column graph below.
The modes of the data set formed by the scores from this exam were found, and the total number of students with scores equal to these values was 32. Additionally, the number of students in this class who scored above 70 on this exam was calculated as 38.
Accordingly, how many students in this class scored 65 on this exam?
A) 2
B) 3
C) 4
D) 5
E) 6

After completing a market purchase, Arda goes to the cashier and is told by the cashier that the total cost of the items he bought is 45 TL, but that he can buy some items 2 TL cheaper for purchases of 50 TL and above.
Thereupon, Arda buys one more item, and with this discount applied to only five of the items he had previously bought, he pays the cashier a total of 43 TL.
Accordingly, what is the price of the item Arda bought last?
A) 5
B) 6
C) 7
D) 8
E) 9

Two views of the sign at the entrance of a two-story parking lot showing the date, time, and the number of empty parking spaces on each floor are given below.

98.05.99	$22 : 08$
	Empty
1st Floor	92
2nd Floor	89

It is known that all vehicles entering this parking lot are parked, and the sum of the number of vehicles entering the parking lot and the number of vehicles leaving the parking lot between these two times is 51.
Accordingly, how many vehicles entered the parking lot between these two times?
A) 12
B) 20
C) 28
D) 36
E) 44

Defne's 7 friends decided to buy a joint gift for Defne and planned to share the cost equally among themselves. Since Ali, Buse, and Can did not have enough money, each of them could only contribute half of their share. Thereupon, the other four friends divided the remaining cost of the gift equally among themselves.
Given that each of these four friends paid 6 TL more than planned, what is the cost of the gift purchased?
A) 112
B) 126
C) 140
D) 147
E) 154

Deniz and Eylül mix the eggs they have and the oil in bottles each containing 60 milliliters of oil in the order and ratio given below to obtain hair mask mixtures.
While obtaining these two mixtures, each containing only two types of oil, Deniz used all of 1 bottle of argan oil, and Eylül used all of 2 bottles of olive oil.
Accordingly, what is the total number of eggs used for these two mixtures?
A) 4
B) 5
C) 6
D) 7
E) 8

A gardener has 30 identical empty wooden crates and 20 identical empty plastic crates. When the gardener fills all the wooden crates using only wooden crates, 60\% of the tomatoes collected are placed in crates, and when filling all the plastic crates using only plastic crates, 65\% of the tomatoes collected are placed in crates.
Given that a full wooden crate contains 8 kilograms of tomatoes, how many kilograms of tomatoes are in a full plastic crate?
A) 9
B) 10
C) 11
D) 12
E) 13

A bed company produces and sells three types of beds: A, B, and C, and some of these beds sold are returned by customers to the company. The numerical distribution of the company's sales of these beds over one month is shown in the pie chart in Figure 1, and the return percentages of these sold beds are shown in the column graph in Figure 2.
600 type A beds were sold this month, and 168 of the type B beds sold this month were returned.
Accordingly, how many type A and C beds sold this month were returned in total?
A) 90
B) 105
C) 120
D) 135
E) 150

An elevator gives a warning if the total weight of the people inside exceeds its weight capacity. When five people weighing 25, 40, 50, 60, and 63 kilograms enter this empty elevator, the elevator gives a warning regardless of which four of them enter, but does not give a warning regardless of which three of them enter.
Accordingly, which of the following could be the weight capacity of this elevator in kilograms?
A) 170
B) 172
C) 174
D) 176
E) 178

Barış has one weight each of 3, 4, 5, 6, and 10 kilograms, and several weights of 1 kilogram. Barış places all these weights on the pans of an equal-arm balance, which is initially empty, such that the product of the weights on each pan is equal to each other, and the balance reaches equilibrium.
Accordingly, what is the minimum number of 1-kilogram weights that Barış has?
A) 1
B) 2
C) 3
D) 4
E) 5

Aylin has sufficient numbers of stones in yellow, blue, and red colors. She strung 3 yellow, 2 blue, and 1 red stone on a string in that order, then repeated this process a certain number of times while preserving this color sequence of the stones to make a bracelet. When Aylin placed this bracelet in an empty jewelry box, she saw that some stones in the bracelet were inside the box and others were outside the box as shown in the figure.
Given that the number of yellow stones inside the box is 2 more than the number of blue stones inside the box, what is the total number of stones used in the bracelet?
A) 30
B) 36
C) 42
D) 48
E) 54

Kerem, who lives in city A, wants to visit Aslı in city B. After determining the route between these two cities from a map, Kerem calculates that if he leaves at a planned time and drives at 100 km/h, he will arrive in city B at 09:00, and if he drives at 60 km/h, he will arrive at 11:00 on the same day.
Accordingly, if Kerem leaves at the planned time and arrives in city B at 10:00 on the same day, what should be the speed of his vehicle in km/h?
A) 72
B) 75
C) 80
D) 85
E) 88

Esra measures the side lengths of a rectangular cardboard with a perimeter of 320 cm using a rectangular bookmark and wants to calculate the side lengths of this bookmark. Esra measures that the long side of the cardboard is 10 times the long side of the bookmark and 25 times the short side of the bookmark, and calculates that the short side of the cardboard is 15 times the short side of the bookmark.
Accordingly, what is the perimeter of the bookmark in cm?
A) 20
B) 24
C) 28
D) 32
E) 36