Three friends who met at university had an average age of 20 at the time they met. After a certain period of time, these three friends gathered together with one child each, and it was observed that the average age of these six people was again 20.
It is known that the age differences between these three friends and their children are 28, 30, and 32.
Accordingly, how many years after the three friends met did they gather together?
A) 15
B) 16
C) 18
D) 20
E) 21

A grocer sells cherries at $K$ TL per kilogram and bananas at $M$ TL per kilogram. A customer who comes to the grocer buys 3 kg of cherries and 3 kg of bananas and gives the grocer 30 TL. Then the following conversation takes place between the grocer and the customer.
Grocer: "I don't have any change. Instead, let me give you 1 kg more cherries." Customer: "I don't want more cherries. Instead, give me 1 kg more bananas, and I'll give you 3 TL more."
Accordingly, what is the sum $\mathbf{K} + \mathbf{M}$?
A) 7
B) 7.5
C) 8
D) 8.5
E) 9

In a sports hall containing a certain number of balls of brands A, B, and C, each ball of the same brand has equal weight. The numerical distribution of these balls is shown in the 1st graph, and the distribution of their total weights is shown in the 2nd graph.
If the weights of balls of brands A, B, and C are $K_A$, $K_B$, and $K_C$ respectively, which of the following orderings is correct?
A) $\mathrm{K}_{\mathrm{A}} < \mathrm{K}_{\mathrm{B}} < \mathrm{K}_{\mathrm{C}}$
B) $\mathrm{K}_{\mathrm{A}} < \mathrm{K}_{\mathrm{C}} < \mathrm{K}_{\mathrm{B}}$
C) $\mathrm{K}_{\mathrm{B}} < \mathrm{K}_{\mathrm{A}} < \mathrm{K}_{\mathrm{C}}$
D) $\mathrm{K}_{\mathrm{B}} < \mathrm{K}_{\mathrm{C}} < \mathrm{K}_{\mathrm{A}}$
E) $\mathrm{K}_{\mathrm{C}} < \mathrm{K}_{\mathrm{B}} < \mathrm{K}_{\mathrm{A}}$

In a shoe factory, there is a linear relationship between the size values of each shoe produced according to standards A and B.
In this factory, the smallest shoe produced has a size value of 34 in standard A and 7 in standard B; the largest shoe has a size value of 46 in standard A and 13 in standard B.
Accordingly, what is the size value in standard A of a shoe with a size value of 11.5 in standard B?
A) 43
B) 42
C) 41
D) 40
E) 39

Defne adds 29 to a two-digit natural number on the calculator on the left.
Defne's brother Burcu, not knowing the digits, presses the keys in the same positions as his sister pressed them in the same order on the calculator on the right.
Given that Burcu obtained a result of 95, what is the result that Defne obtained?
A) 100
B) 103
C) 105
D) 107
E) 110

Arif read in a recipe that when fresh corn is dried, its weight decreases by $\%20$, and when dried corn is popped, its weight decreases by $\%10$. Then, in accordance with these ratios, he bought enough fresh corn to obtain 720 grams of popped corn.
After drying and popping all the fresh corn he bought, Arif obtained less popped corn than he wanted, and he realized that this was due to an error in the recipe, and that the ratio written as $\%20$ should actually be $\%30$.
Accordingly, how many grams of popped corn did Arif obtain?
A) 630
B) 640
C) 660
D) 680
E) 690

For each of the 25 guests attending an opening, one glass each of mandarin juice, pomegranate juice, and orange juice was prepared and served to the guests. The following are known about these beverages served.

• All guests took at least one type of beverage.
• No guest took more than one glass of the same type of beverage.
• No guest took exactly two types of beverages.

At the end of the opening, it was determined that 7 glasses of mandarin juice, 8 glasses of pomegranate juice, and 9 glasses of orange juice were not taken.
Accordingly, how many guests at this opening took all three types of beverages?
A) 7
B) 9
C) 11
D) 13
E) 15

Below is shown the appearance of 12 pens and 9 balls that will be numbered with different digits from 1 to 9.
In the figure, the number of the ball indicated by the writing end of each pen is greater than the number of the ball indicated by the non-writing end of the pen.
For example, in the figure above, B is greater than A.
Accordingly, what is the sum $\mathrm{A} + \mathrm{E} + \mathrm{G}$?
A) 13
B) 14
C) 15
D) 16
E) 17

In a kindergarten, a child on the top step of a toy made up of four steps of yellow cubes wants to reach any of the blue cushions shown in the figure.
In the first three steps, this child will jump to any of the cubes one step below that share a common edge with the cube he is on, and in the last step, he will jump to any of the cushions that share a common edge with the cube he is on.
Accordingly, in how many different ways can this child reach the cushions?
A) 8
B) 12
C) 16
D) 18
E) 20

An electronic scale; in each measurement, weighs the weight placed on it $\%20$ probability 1 kilogram more than the actual weight, $\%30$ probability 1 kilogram less than the actual weight, and $\%50$ probability correctly.
Ali and Mehmet, whose actual weights are 80 and 81 kilograms respectively, will each be weighed once on this scale.
Accordingly, what is the probability that Ali and Mehmet's weights will be equal as a result of the measurement, as a percentage?
A) 40
B) 35
C) 30
D) 25
E) 20

Hande, who designs emblems, takes four pieces of isosceles triangle-shaped cardboard from Figure 1 and joins them on a table without leaving gaps between them so that each is completely visible, obtaining the pattern in Figure 2.
Accordingly, what is the measure of angle $x$ in degrees?
A) 15
B) 20
C) 30
D) 36
E) 48

On a straight road, there are two lamp posts of heights 3 and 5 meters with a distance of 9 meters between them, and a rod of height 1 meter located between these posts, as shown in the figure.
The lengths of the shadows created by the lamps on the posts on both sides of the rod are equal to each other.
Accordingly, what is the length of the shadow created by one of the lamps in meters?
A) 1
B) 1.2
C) 1.5
D) 1.8
E) 2

A square frame made by assembling four wires of equal length and fixed to the wall with nails at its corners as shown in Figure 1 covers an area of 100 square units on the wall.
As a result of the nails on corners A and B coming loose, one side slides down to form a rhombus shape as shown in Figure 2. In this frame, the height of corners A and B from the ground has decreased by 6 units each, while the position of the other two corners has not changed.
Accordingly, by how many square units has the area covered by the frame on the wall decreased?
A) 18 B) 20 C) 26 D) 30 E) 32

A blue electric pole 20 meters long broke exactly in the middle due to a storm, and the tip of the pole landed on a wall 8 meters away from the pole, as shown in the figure.
Accordingly, what is the height of the wall in meters?
A) 2
B) 3
C) 4
D) 5
E) 6

Below is shown a rectangular television screen and half of a square-shaped lace whose diagonal is on the top edge of the television.
When the corners of this lace that are on the screen are shifted 2 units downward in the vertical direction, it is observed that the area covered by the lace on the screen increases by 16 square units compared to the initial situation.
Accordingly, what is the area of the lace in square units?
A) 48
B) 49
C) 50
D) 56
E) 64

A rectangular piece of paper is first folded along the line AB parallel to the short side in the direction of the arrow as shown in Figure 1, then folded along the line CD parallel to the long side in the direction of the arrow as shown in Figure 2, obtaining Figure 3.
The rectangles formed in the final shape have areas $a$, $b$, $c$ and $d$ square units.
Accordingly, which of the following is the expression of the area of the paper used initially in terms of $a$, $b$, $c$ and $d$?
A) $a + 2b + 3c + 4d$
B) $a + 2b + 2c + 2d$
C) $a + 2b + 2c + 3d$
D) $a + 2b + 4c + 2d$
E) $2a + 2b + 2c + 2d$

On a map consisting of unit squares where each unit square has an area of $1 \mathrm{~km}^{2}$, the locations of villages $\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}$, $\mathrm{D}$ and $\mathrm{E}$ are shown as in the figure.
A helicopter located at point O has enough fuel to fly 4 kilometers.
Which of the following is the farthest village that this helicopter can reach?
A) A
B) B
C) C
D) D
E) E

The area of a circle with radius $r$ is calculated using the formula $A = \pi r^{2}$.
A car has a wiper on its semicircular rear window that can rotate around point O. This wiper cleans points on the window that are at least 1 unit and at most 5 units away from point O. When this wiper is operated and rotates $120^{\circ}$ as shown in the figure, the area cleaned by the wiper is half the area of the window.
Accordingly, what is the radius of the window in units?
A) $4\sqrt{2}$
B) $5\sqrt{2}$
C) $6\sqrt{2}$
D) $4\sqrt{3}$
E) $5\sqrt{3}$

The measure of an interior angle of a regular $n$-sided polygon is calculated as $$\frac{(n-2) \cdot 180^{\circ}}{n}.$$
In the figure, a regular nonagon and a regular pentagon sharing one side are given, along with a blue line segment connecting one vertex of each polygon.
Accordingly, what is the measure of angle $x$ in degrees?
A) 64
B) 66
C) 68
D) 70
E) 72

In the rectangular coordinate plane, the distance between points $\mathrm{A}(\mathrm{a}, \mathrm{b})$ and $\mathrm{B}(\mathrm{c}, \mathrm{d})$ is calculated using the formula
$$|AB| = \sqrt{(c-a)^{2} + (d-b)^{2}}$$
On the scaled map below; the coordinates of points $\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$ in the rectangular coordinate plane are given according to a certain unit of length.
A map program that calculates the distance between two points calculates the distance shown by the blue line between points $\mathrm{A}(2,8)$ and $\mathrm{B}(10,14)$ as 6 kilometers.
Accordingly, what distance in kilometers does this map program calculate for the blue line distance between points A and C?
A) 7.8
B) 8.1
C) 9.6
D) 10.4
E) 11.7

Three cubes, each with edge length 1 unit, are glued together such that at least one face of each cube completely overlaps with a face of another cube.
Accordingly, which of the following cannot be the distance between two selected vertices of the solid obtained in this way, in units?
A) $\sqrt { 7 }$ B) $\sqrt { 8 }$ C) $\sqrt { 9 }$ D) $\sqrt { 10 }$ E) $\sqrt { 11 }$

Initially, all faces of a rectangular prism are white. When one face is painted red, one face is painted blue, and one face is painted yellow:

• the sum of the areas of the faces other than the red painted face is 82 square units,
• the sum of the areas of the faces other than the blue painted face is 79 square units,
• the sum of the areas of the faces other than the yellow painted face is 74 square units.

Accordingly, what is the surface area of this rectangular prism in square units?
A) 90
B) 92
C) 94
D) 96
E) 98

In space, a plane E is given with points A and B on it, and a point P at a distance of 4 units from this plane.
The perpendicular projections of line segments PA and PB onto plane E, together with line segment AB, form an equilateral triangle with side length 2 units.
Accordingly, what is the product $| \mathbf { P A } | \cdot | \mathbf { P B } |$?
A) 8 B) 12 C) 16 D) 18 E) 20

The volume of a right circular cylinder with radius $r$ and height $h$ is calculated using the formula $\mathrm{V} = \pi r^{2} \mathrm{~h}$.
Two right circular cylinders with equal heights, empty interiors, and parallel bases are nested inside each other, with two faucets on top. One of these faucets fills the inner cylinder, while the other fills the region between the cylinders, with the same amount of water per unit time.
The faucets are opened simultaneously and closed when the inner cylinder is completely filled. In the final state, the height of the water in the inner cylinder is 4 times the height of the water in the region between the cylinders.
Accordingly, what is the ratio of the radius of the outer cylinder to the radius of the inner cylinder?
A) $\sqrt{3}$
B) $\sqrt{5}$
C) $\sqrt{7}$
D) 2
E) 3

Emel is able to calculate the amount of water she drinks by first dividing the 2-liter cylindrical section of the water bottle shown in the figure into 4 equal parts, and then dividing each part into 5 equal parts to create a scale. After Emel drinks some of the water in her bottle containing 2 liters of water, the appearance created in the bottle is given below.
Accordingly, how many liters of water did Emel drink from this bottle?
A) $\frac{1}{4}$
B) $\frac{3}{4}$
C) $\frac{2}{5}$
D) $\frac{3}{5}$
E) $\frac{4}{5}$