Weights with their masses written on them are placed on the pans of an equal-armed balance as shown in the figure, balancing the scale.
When one of the weights given below is added to pan B of the scale and one of the weights on pan B is transferred to pan A, the scale remains balanced again.
Accordingly, how many grams is the weight added to pan B during this operation?
A) 10
B) 15
C) 30
D) 35
E) 40

When a square with side length $a$ units is divided into four regions as shown in the figure, region I represents a square with side length $b$ units.
For each $a$ and $b$ number satisfying this condition
$$a^{2} - 2ab + 2b^{2}$$
to which sum of areas of two regions is this expression equal?
A) I and II
B) I and IV
C) II and III
D) II and IV
E) III and IV

If 9 times a natural number $n$ equals a number that has the digit 3 in each of its digits, then $n$ is called a ternary number.
Accordingly, what is the sum of the digits of the smallest ternary number?
A) 7
B) 8
C) 9
D) 10
E) 11

In a project covering all 81 provinces in Turkey; first, $p$ parks are to be built in each province, and then $a$ trees are to be planted in each park built.
However, the number of parks to be built and trees to be planted in this plan was found to be insufficient, and first, one more park than the number of parks planned to be built in each province was built, and then one more tree than the number planned to be planted in each park was planted.
Accordingly, what is the difference between the total number of trees planted in the final situation and the total number of trees planned to be planted initially given correctly in which of the following?
A) 162
B) $81 \cdot a \cdot p$
C) $81 \cdot (a + p)$
D) $81 \cdot (a \cdot p + 1)$
E) $81 \cdot (a + p + 1)$

Let L be a real number. For functions f and g defined on the set of real numbers,
$$\lim _ { x \rightarrow 2 } f ( x ) = \lim _ { x \rightarrow 2 } g ( x ) = L$$
equality is satisfied.
Accordingly,
I. $f ( 2 ) = g ( 2 )$ II. $\lim _ { \mathrm { x } \rightarrow 2 } ( \mathrm { f } ( \mathrm { x } ) - \mathrm { g } ( \mathrm { x } ) ) = 0$ III. $\lim _ { x \rightarrow 2 } \frac { f ( x ) } { g ( x ) } = 1$
Which of the following statements are always true?
A) Only I B) Only II C) I and III D) II and III E) I, II and III

The unit prices used by Ali Bey, who conducts house and land buying and selling transactions in a certain region, are given in the table.

\cline{2-3} \multicolumn{1}{c|}{}	\begin{tabular}{ c } Purchase price
(TL)

&

Selling price

(TL)

\hline

House

$(1 \mathrm{~m}^{2})$

& 3000 & 3200 \hline

Land

(1 decare)

& 20000 & 25000 \hline \end{tabular}
Ali Bey bought a house for 450000 TL, and with all the money he obtained from the sale of this house, he bought a piece of land and then sold this land.
Accordingly, what is Ali Bey's profit from the sale of this land in TL?
A) 90000
B) 105000
C) 110000
D) 120000
E) 125000

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

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 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

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