Two vehicles start moving from city A towards city B at the same time. When the faster vehicle has traveled half the distance, the slower vehicle has traveled 40 km. When the slower vehicle has traveled half the distance, the faster vehicle has traveled 90 km.
Given this, what is the distance between cities A and B in km?
A) 120
B) 130
C) 140
D) 150
E) 160

In a measurement operation; one of two measuring devices shows 3% more than the actual length, while the second shows 5% less than the actual length.
A rod with an actual length of 72 units is divided into two parts. When the longer part is measured with the first device and the shorter part with the second device, the sum of the displayed values is 72 units.
Given this, what is the actual length of the shorter part in units?
A) 24
B) 27
C) 28
D) 30
E) 32

Ayşe, Bora, and Can have a total of 72 marbles.

• Ayşe sets aside half of her marbles for Bora,
• Bora sets aside one-third of his marbles for Can,
• Can sets aside one-quarter of his marbles for Ayşe and they give these set-aside marbles to each other at the same time.

Given that no one's number of marbles changes in the end, how many marbles does Ayşe have?
A) 12
B) 16
C) 18
D) 20
E) 24

In an airline company, the price of a one-way ticket is 150 TL, and the price of a round-trip ticket is 200 TL. The table below provides some information about the number of tickets purchased by Ali and Buket from this airline.

	Ali	Buket
Number of one-way tickets	x+4
Number of round-trip tickets		x
Total number of tickets	17	16

Given that these people paid equal amounts for their tickets, what is $x$?
A) 6
B) 7
C) 8
D) 9
E) 10

The distribution of grains produced in a village by type is given in the pie chart below.
Given that the amount of barley produced in this village is 25 tons more than the amount of oats, how many tons of wheat were produced?
A) 225
B) 250
C) 270
D) 275
E) 300

Below is a wall clock with an hour hand 1 unit long and a minute hand 2 units long.
Given this, what is the total area swept by the hour hand and minute hand from 9:00 to 9:30 in square units?
A) $\frac { 97 \pi } { 48 }$
B) $\frac { 49 \pi } { 24 }$
C) $\frac { 25 \pi } { 12 }$
D) $\frac { 13 \pi } { 6 }$
E) $\frac { 7 \pi } { 3 }$

A piece is removed from a rectangular prism with edge lengths 4, 5, and 7 units such that all intersecting edges are perpendicular to each other, and the resulting solid is shown in the figure.
Given this, what is the volume of this resulting solid in cubic units?
A) 122
B) 124
C) 126
D) 128
E) 130

On the paper with unit squares shown in the figure, a circular arc with center at one of the points A, B, C, D, or E is drawn such that it is tangent to line PQ at point Q.
Given this, which point is the center of the drawn circular arc?
A) A
B) B
C) C
D) D
E) E

$\left( \frac { 9 } { 2 } - \frac { 10 } { 3 } \right) \left( 6 + \frac { 6 } { 7 } \right)$
What is the result of this operation?
A) 5 B) 6 C) 7 D) 8 E) 9

$\frac { 0,6 } { ( 0,2 ) ^ { 2 } } + \frac { 0,8 } { ( 0,4 ) ^ { 2 } }$
What is the result of this operation?
A) 20 B) 24 C) 25 D) 27 E) 30

Three-fourths of a number equals 5.
Accordingly, what is 6 times this number?
A) 30 B) 40 C) 45 D) 50 E) 60

Where n is an integer, the expression $\frac { 120 } { \mathrm { n } }$ equals a prime number.
Accordingly, what is the sum of the values that n can take?
A) 104 B) 108 C) 112 D) 116 E) 124

$$\begin{aligned} & 2 a - 3 b + 2 c = 0 \\ & a \cdot b + b \cdot c = 9 \end{aligned}$$
Given that, what is $\mathbf { b } ^ { \mathbf { 2 } }$?
A) 6 B) 8 C) 9 D) 12 E) 16

The four-digit natural number $A B A B$ equals 404 times the sum of its digits.
Accordingly, what is the product A$\bullet$B?
A) 14 B) 16 C) 18 D) 20 E) 24

Where n is an integer greater than 2; $\mathrm { A } ( \mathrm { n } )$ is defined as the product of the prime divisors of the number n.
Accordingly, what is the sum of the digits of the smallest three-digit number n that satisfies the equation $\mathbf { A } ( \mathbf { n } ) = \mathbf { 6 }$?
A) 8 B) 9 C) 10 D) 12 E) 15

$$2 ^ { 20 } \cdot 3 ^ { 25 }$$
What is the remainder when this product is divided by 5?
A) 0 B) 1 C) 2 D) 3 E) 4

$$\begin{aligned} & a = 5 ! \cdot 9 ! \\ & b = 6 ! \cdot 8 ! \\ & c = 7 ! \cdot 7 ! \end{aligned}$$
Given that, which of the following orderings is correct?
A) $a < b < c$ B) $a < c < b$ C) $b < c < a$ D) $c < a < b$ E) $c < b < a$

Let $A , B$ be two sets, $B \backslash A \neq \emptyset$ and the Cartesian product set $( A \backslash B ) \times A$ has 14 elements.
Accordingly, what is the minimum number of elements in set B?
A) 1
B) 3
C) 4
D) 6
E) 8

Below is a regular pentagon with vertex points A1, A2, A3, A4, and A5.
The $\otimes$ operation on the vertices of this pentagon is defined as
- for each vertex A: $\mathrm { A } \otimes \mathrm { A } = \mathrm { A }$ - for different vertices $A$ and $B$: $A \otimes B$ is the vertex point located on the perpendicular bisector of the line segment connecting points $A$ and $B$.
Given that $\left( A _ { 1 } \otimes A _ { 3 } \right) \otimes X = A _ { 5 }$, which of the following is vertex $X$?
A) $\mathrm { A } _ { 1 }$ B) $A_2$ C) $A_3$ D) $A_4$ E) $A_5$

$$\begin{array} { l l } p : & x = 0 \\ q : & y = 0 \end{array}$$
The following propositions are given.
Accordingly, for real numbers x and y
I. $x \cdot y = 0$ II. $x + y = 0$ III. $x ^ { 2 } + y ^ { 2 } = 0$
Which of the following propositions are equivalent to the proposition $\mathbf { p } \wedge \mathbf { q }$?
A) Only II B) Only III C) I and II D) I and III E) II and III

For every subsets $A$ and $B$ of a non-empty set $X$, the operation $\odot$ is defined as
$$\mathrm { A } \odot \mathrm { B} = \mathrm { X } \backslash ( \mathrm { A} \cup \mathrm { B} )$$
For every subsets $K$ and $L$ of X satisfying the condition $K \subseteq L$, what is the result of the operation $$( \mathbf { X } \backslash \mathbf { L } ) \odot ( \mathbf { L } \backslash \mathbf { K } )$$
A) $X$
B) K
C) L
D) $X \backslash K$
E) $X \backslash L$

If a three-digit natural number with non-zero digits is divisible without remainder by each digit in each of its places, this number is called a "proper number."
If the number 3A4 is a proper number, what is the sum of the values that A can take?
A) 7 B) 8 C) 10 D) 13 E) 15

80\% of the students in a class can play guitar.
Given that 80\% of the students in the class are male, what is the minimum percentage of students who can play guitar that are male?
A) 64 B) 70 C) 72 D) 75 E) 80

Eight balls numbered 1 to 8 will be placed in two boxes with four balls in each box according to the following rules.
- The sum of the numbers of the balls in the boxes is equal to each other. - Each box contains one ball whose number is divisible by 3.
Accordingly, what is the product of the numbers of the balls in the box containing ball number 2?
A) 120 B) 192 C) 240 D) 360 E) 384

A vehicle starting with a full tank uses two-thirds of the gasoline in its tank when it stops at a gas station and adds half a tank of gasoline and continues its journey.
When the vehicle has traveled 900 km from the beginning, its gasoline runs out.
Given that the vehicle's gasoline consumption is constant throughout the journey, how many km is the distance the vehicle traveled between the starting point and the gas station?
A) 300 B) 360 C) 400 D) 450 E) 480