Let $n$ be a positive integer such that the remainder when 33 is divided by $n$ is 5.
Given this, what is the sum of the values that $n$ can take?
A) 42
B) 44
C) 45
D) 48
E) 49

Let $X , Y$ and $Z$ be sets. The following proposition is given:
$$\text { " If } ( X \subseteq Y \text { and } X \subseteq Z ) \text { then } Y \subseteq Z \text {." }$$
Which of the following is a counterexample that shows this proposition is false?

A function $f$ defined on the set of integers satisfies the following equalities for every integer $n$:
$$\begin{aligned} & f ( n + 2 ) = f ( n ) + 4 \\ & f ( n + 3 ) = f ( n ) + 6 \end{aligned}$$
Given that $f ( 4 ) = 5$, what is the value of $f ( 11 )$?
A) 15
B) 17
C) 19
D) 21
E) 23

Sets $A = \{ 1,2,3 \}$ and $B = \{ 2,3,4,5 \}$ are given.
Given this, how many functions $\mathbf { f } : \mathbf { A } \rightarrow \mathbf { B }$ can be defined such that for every $a \in A$
$$a + f ( a ) \leq 6$$
A) 12
B) 18
C) 20
D) 24
E) 27

All three-element subsets of a four-element set A whose elements are integers are written out. When the arithmetic mean of the elements of each of these subsets is calculated, the values 8, 9, 10, and 11 are found.
Given this, which of the following is not an element of set A?
A) 5
B) 8
C) 11
D) 14
E) 17

If the difference between two prime numbers $p$ and $q$ is 4, then the pair $(p , q)$ is called a "cousin prime pair."
Given this, which of the following cannot be the sum of a cousin prime pair?
A) 18
B) 30
C) 42
D) 66
E) 78

Let $x , y$ be integers such that
$$\begin{aligned} & 0 < x < 100 \\ & 0 < y < 100 \end{aligned}$$
Given this, for how many ordered pairs $(x , y)$ is the sum $x + y$ a three-digit number?
A) 1980
B) 2500
C) 4500
D) 4950
E) 5050

In a bakery, 40 sesame rings and 50 pastries are sold for a total of 100 TL. A sesame ring vendor gives 100 TL to the baker for 30 sesame rings and 50 pastries and receives A TL in change.
What is the total price of 1 sesame ring and 1 pastry in terms of A in TL?
A) $\frac { A + 20 } { 10 }$
B) $\frac { \mathrm { A } + 50 } { 10 }$
C) $\frac { A + 100 } { 50 }$
D) $\frac { 100 - A } { 50 }$
E) $\frac { 100 - A } { 50 - A }$

Fresh grapes with a water content of 36% by weight are left to dry. After some time, the water content in these grapes becomes 8% by weight.
What is the weight of the grapes after this time in kg?
A) 12
B) 13
C) 14
D) 15
E) 16

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