Let $\mathbf { a } , \mathbf { b }$ and $\mathbf { c }$ be positive real numbers,
$$\begin{aligned} & a \cdot b + a \cdot c = 45 \\ & \frac { a } { b + c } = \frac { 4 } { 5 } \end{aligned}$$
Accordingly, what is the sum $\mathbf { a } + \mathbf { b } + \mathbf { c }$?
A) 9 B) 18 C) 27 D) $\frac { 9 } { 2 }$ E) $\frac { 27 } { 2 }$

$x$ and $y$ are positive real numbers for which
$$\frac { x - y } { x \sqrt { y } + y \sqrt { x } } = \frac { 1 } { \sqrt { x } }$$
the equality holds.
Accordingly, what is the ratio $\frac { x } { y }$?
A) 4 B) 2 C) 1 D) $\frac { 9 } { 4 }$ E) $\frac { 1 } { 2 }$

Regarding the number of elements of sets $A$ and $B$
$$\begin{aligned} & s ( A - B ) = s ( B - A ) = s ( A \cap B ) \\ & s ( A \cup B ) = 24 \end{aligned}$$
the equalities are given.
Accordingly, how many elements does set A have?
A) 9 B) 12 C) 15 D) 16 E) 18

A two-digit natural number $AB$ is greater than the two-digit natural number $BA$ by the sum of its digits.
Accordingly, what is the product of the digits of the number AB?
A) 14 B) 16 C) 18 D) 20 E) 22

If the number of elements of a set is an element of that set, then this set is called a "mysterious set".
For example; $K = \{ 3,4,5 \}$ is a mysterious set.
Accordingly, how many subsets of the set $\mathrm { A } = \{ 1,2,3,4,5,6 \}$ are mysterious sets?
A) 16 B) 24 C) 32 D) 40 E) 48

In an experiment in chemistry class, Yamac adds salt to a mixture each time; he adds as many grams of salt as the mixture weighs and uses 4 grams of the resulting mixture. After the third time, Yamac realizes that there is no mixture left and ends the experiment.
Accordingly, how many grams of salt did Yamac add throughout the experiment?
A) 7 B) 7.5 C) 8 D) 8.5 E) 9

In a store, all shirts have a 25\% discount on the tag price. Additionally, in the store, to increase sales, customers who buy two shirts receive an additional 20\% discount on the cheaper one at the discounted price.
A customer who bought two shirts with different prices from this store received an equal amount of discount on each shirt based on the tag prices.
If this customer paid a total of 90 TL to the store, what is the total discount given to the customer in TL?
A) 30 B) 35 C) 40 D) 45 E) 50

The following information is given about three vehicles moving at constant speeds in a course consisting of two sections.
- The first vehicle completed the first section at a speed of 120 kilometers per hour in 8 minutes. - The second vehicle completed the entire course at a speed of 95 kilometers per hour in 12 minutes. - The third vehicle completed the second section in 2 minutes.
Accordingly, what is the speed of the third vehicle in kilometers per hour?
A) 60 B) 80 C) 90 D) 100 E) 120

In a factory where mint and lemon candies are produced, candies are packaged with 10 pieces in each package. These packages contain only mint candies, only lemon candies, or equal numbers of mint and lemon candies.
In this factory, a total of 1200 candies were produced and packaged, of which 400 were lemon.
If the total number of packages containing only one type of candy is 70, how many packages contain only mint candies?
A) 40 B) 45 C) 50 D) 55 E) 60

Nagihan created embroidery on a fabric in a single row using beads and sequins. In one part of this embroidery, she used 4 beads, and in the others, she used 5 beads to create motifs, and placed one sequin between each pair of adjacent motifs.
Nagihan started the embroidery with a motif and ended it with a motif, creating 56 motifs using a total of 300 beads and sequins.
Accordingly, how many motifs did Nagihan create using 5 beads?
A) 15 B) 21 C) 28 D) 36 E) 40

In a classroom where two people sit in each row, $\frac { 1 } { 2 }$ of the female students share a row with a male student; $\frac { 1 } { 3 }$ of the male students share a row with a female student.
If the number of rows with two male students is 12, how many total rows are in the classroom?
A) 24 B) 28 C) 30 D) 32 E) 36

In a basket, there are 9 red balls each weighing 3 kg and 12 blue balls each weighing 6 kg. Some red and some blue balls are taken from this basket and placed in a second empty basket.
As a result of this operation; the average weight of the balls in the first basket is 5 kg, and the average weight of the balls in the second basket is 4 kg.
Accordingly, how many blue balls were placed in the second basket?
A) 2 B) 3 C) 4 D) 5 E) 6

Engin uses the following ingredients for a cake recipe: - 3 cups of flour or 2 cups of semolina - 1 cup of milk - 2 eggs
He has 6 cups of flour, 4 cups of milk, and 10 eggs. Engin made cakes according to this recipe until all his flour ran out. Then, since he had no flour left, he used a sufficient amount of semolina instead and continued making cakes according to the recipe until all his milk ran out.
Accordingly, how many eggs does Engin have left in the end?
A) 1 B) 2 C) 3 D) 4 E) 5

The times for Aslı and Banu, who work at a flower shop, to prepare a rose and a daisy bouquet are given in the table below.

\cline { 2 - 3 } \multicolumn{1}{c|}{}	Aslı's preparation time	Banu's preparation time
Rose bouquet	2 minutes	3 minutes
Daisy bouquet	3 minutes	4 minutes

After the flower shop receives an order consisting of 40 rose and 55 daisy bouquets; Aslı starts preparing the rose bouquets and Banu starts preparing the daisy bouquets. The person who reaches the number in the order first immediately helps the other person prepare the remaining bouquets.
Accordingly, how many minutes does it take to prepare all the orders at the flower shop?
A) 100 B) 120 C) 140 D) 160 E) 180

A factory produced a total of 1800 vehicles of models A, B, and C in 2016, and the distribution of production quantities is shown in the circular graph. A total of 800 vehicles of these three models were sold in 2016. For each vehicle model, the ratio of the number of vehicles sold in 2016 to the number of the same model vehicles produced that year is given as a percentage in the bar graph.
Accordingly, what is the sales percentage of model C vehicles?
A) 54 B) 57 C) 60 D) 63 E) 66

Pelin finds the following menu from a cafeteria at home, with only the hot beverages section torn.
MENU
FOOD: Gözleme: Minced meat, Spinach, Eggplant; Poğaça: Cheese, Potato
BEVERAGES: Cold Beverages: Water, Ayran, Lemonade, Orange juice; Hot Beverages: (torn)
Pelin wants to call this cafeteria and place an order for either "one type of gözleme and one type of cold beverage" or "one type of poğaça and one type of hot beverage". The cafeteria employee says this order can be given in 22 different ways.
Accordingly, how many different types of hot beverages are available at this cafeteria?
A) 1 B) 2 C) 3 D) 4 E) 5

In a game of tag played by Arda, Berk, and Can, the person who is "it" catches one of the others, and the person caught becomes the new "it". Then the game continues in a similar way for the new "it". The following information is given about the probabilities of these three people catching each other.
- If Arda is "it", he catches Berk with 60\% probability and Can with 40\% probability. - If Berk is "it", he catches Arda with 80\% probability and Can with 20\% probability. - If Can is "it", he catches Arda with 40\% probability and Berk with 60\% probability.
If Arda is the first "it" in this game, what is the probability that the 3rd "it" is Arda again, as a percentage?
A) 50 B) 54 C) 58 D) 64 E) 70

Aslı has divided her birthday cake into four equal slices as shown below.
Then, she shared one slice of this cake equally among Burcu, Cem, and Deniz.
Accordingly, what is the ratio of the amount that falls to Cem's share to the whole cake?
A) $\frac{1}{4}$
B) $\frac{1}{6}$
C) $\frac{1}{9}$
D) $\frac{1}{12}$
E) $\frac{1}{16}$

Melis, holding a piece of modeling clay, divides each piece of modeling clay she has into 2 pieces at each step, and after the 3rd step she has 8 pieces of modeling clay.
If Melis had divided each piece of modeling clay she had into 3 pieces instead of 2 at each step from the beginning, how many pieces of modeling clay would she have after the 4th step?
A) 12
B) 36
C) 51
D) 72
E) 81

A two-compartment rectangular prism-shaped refrigerator has a lower compartment height of 1.5 meters and an upper compartment height of 0.5 meters. A decoration is attached to the top of the refrigerator's upper compartment as shown below.
Accordingly, the height of this attached decoration from the ground in meters could be which of the following?
A) $\sqrt{2}$
B) $\sqrt{3}$
C) $\sqrt{5}$
D) $\sqrt{6}$
E) $\sqrt{7}$

I. $-2 \square 25$ II. $2 \square \square -2$ III. $-2 \square -2$ In what order should the symbols for addition (+), subtraction (-), and multiplication (×) be placed in the empty boxes in the expressions so that the result of all three operations equals the same number?

	I	II	III
\cline{2-2} A)	+		$\times$
B)	-		+	-
C)	-		$\times$	+
D)	$\times$		+	-
E)	$\times$		-	+

A natural number $a$ written inside an $n$-sided regular polygon is represented by a symbol that denotes the number $n \cdot a^{n}$.
For example, the symbol represents the number $3 \cdot 2^{3} = 24$.
Accordingly, which of the following symbols represents the value of the product?
A) [symbol A]
B) [symbol B]
C) [symbol C]
D) [symbol D]
E) $\square 4$

Let $a$, $b$, and $c$ be digits different from zero and from each other. Three numbers with decimal notations are given as:
$$\begin{aligned} K &= a,b \\ L &= b,c \\ M &= c,a \end{aligned}$$
Alican, who learned the ordering of numbers with decimal notation incorrectly, thought that the ordering of these three numbers should be done according to the magnitude of the value in the tenths place instead of the ones place, and obtained the ordering $\mathrm{K} < \mathrm{L} < \mathrm{M}$.
Accordingly, what is the correct ordering of these numbers?
A) $\mathrm{K} < \mathrm{M} < \mathrm{L}$
B) $\mathrm{L} < \mathrm{K} < \mathrm{M}$
C) $\mathrm{L} < \mathrm{M} < \mathrm{K}$
D) $\mathrm{M} < \mathrm{K} < \mathrm{L}$
E) $\mathrm{M} < \mathrm{L} < \mathrm{K}$

Below a 10 cm ruler with 0.8 cm distance on both sides, two identical 6 cm rulers with 0.2 cm distance on both sides are joined end to end without leaving a gap and aligned from the left as shown in the figure.
Accordingly, with which point on the 6 cm ruler is the right edge of the 10 cm ruler aligned?
A) 4
B) 4.5
C) 4.8
D) 5
E) 5.2

For positive integers $a$, $b$, and $c$,
$$a(b + c)$$
the expression equals an odd number.
Accordingly,
I. $a^{b} + c$ II. $b^{c} + a$ III. $c^{a} + b$
Which of these expressions always equals an odd number?
A) Only II
B) Only III
C) I and II
D) II and III
E) I, II, and III