Aysel Hanım exchanged 45 grams of gold on Monday and 30 grams of gold on Tuesday. If she had exchanged 30 grams on Monday and 45 grams on Tuesday, she would have received 60 TL less compared to the first situation.
According to this, by how many TL did the price per gram of gold decrease on Tuesday compared to Monday?
A) 4
B) 5
C) 6
D) 9
E) 15

A pattern is created by painting some squares on a $4 \times 100$ grid paper. In this pattern, the squares in columns corresponding to integer multiples of 2 in row A, integer multiples of 3 in row B, integer multiples of 4 in row C, and integer multiples of 5 in row D are painted.
According to this, in how many of the columns in this pattern are the squares in rows A and D painted, while the others are unpainted?
A) 3
B) 4
C) 5
D) 6
E) 7

The types of vehicles produced at an automotive factory are shown in the diagram. A total of 120 vehicles are produced per day at this factory. Of the passenger vehicles, 15 are diesel and 12 are electric.
Given that the total number of diesel vehicles produced per day is 2 times the total number of gasoline vehicles, how many commercial diesel vehicles are produced?
A) 50
B) 52
C) 55
D) 57
E) 60

10 boxes are placed at equal intervals on a pallet consisting of two semicircles and two parallel line segments, moving in the direction of the arrow, as shown in the figure.
According to this, when the boxes at points A and E are first vertically aligned, where will the box at point K be?
A) Between points A and B
B) At point B
C) Between points B and C
D) At point C
E) Between points C and D

A wooden block in the shape of a square prism with a base area of 16 square units and height of 3 units has all its surfaces painted. Then, this wooden block is cut to obtain 48 unit cubes.
Of the unit cubes obtained this way, how many have exactly two faces painted?
A) 10
B) 12
C) 14
D) 18
E) 20

Teacher Cemal conducted the following activity step by step with his students in a geometry lesson and asked them a question at the end of the activity.

• Let us draw a line segment AB of length 8 cm.
• Let us open our compass to 5 cm.
• By placing the sharp point of the compass first at point A and then at point B, let us draw two circles.
• Let us name the intersection points of these two circles as C and D.
• Let us form the quadrilateral ACBD with vertices at points A, B, C, and D.

• What is the area of the quadrilateral region ACBD in $\mathrm { cm } ^ { 2 }$?

According to this, what is the answer to the question asked by Teacher Cemal?
A) 20
B) 24
C) 25
D) 26
E) 32

A decoration as shown in dark color has been made on a floor covered with tiles in the shape of regular hexagons.
Given that the area of each hexagon is 1 square unit, what is the area covered by this decoration in square units?
A) 8
B) 9
C) 10
D) 11
E) 12

According to the given information, what is the area of the shaded region in $\mathbf { cm } ^ { \mathbf { 2 } }$?
A) $4 ( 3 \pi + 4 \sqrt { 3 } )$
B) $6 ( \pi + 4 \sqrt { 3 } )$
C) $6 ( 2 \pi + 3 \sqrt { 3 } )$
D) $12 ( \pi + 2 \sqrt { 3 } )$
E) $12 ( 2 \pi + \sqrt { 3 } )$

In the coordinate plane, the following regular hexagon ABCDEF with center at point O is given.
This hexagon is rotated $120 ^ { \circ }$ around its center in the direction of the arrow. After the rotation, the symmetry of the resulting hexagon with respect to the y-axis is taken.
According to this, which point arrives at the position where point F was located initially?
A) A
B) B
C) C
D) D
E) E

$$\begin{array} { r } A B D \\ - \quad B B C \\ \hline 294 \end{array} \quad \begin{array} { r } A C \\ - B D \\ \hline ? \end{array}$$
According to the subtraction operation given on the left, what is the result of the subtraction operation on the right?
A) 44
B) 36
C) 34
D) 26
E) 24

Let A, B and C be sets. I. If $A \cup B = A \cup C$ then $B = C ^ { \prime }$. II. If $\mathrm { A } \cap \mathrm { B } = \varnothing$ then $\mathrm { A } \backslash \mathrm { B } = \mathrm { A } ^ { \prime }$. III. If $A \cup B = A$ then $B \backslash A = \varnothing$. Which of these propositions are always true?
A) Only I
B) Only II
C) Only III
D) I and II
E) II and III

An operation $\Theta$ is defined on the set of integers for every integers a and b as
$$a \ominus b = a - b + 1$$
Regarding the $\Theta$ operation, I. The identity element is 1. II. It has the commutative property. III. It has the associative property. Which of these statements are true?
A) Only I
B) I and II
C) I and III
D) II and III
E) I, II and III

$\mathrm { p } : \sqrt { 3 } + \sqrt { 5 } = \sqrt { 8 }$ q: $\sqrt { 5 } - \sqrt { 3 } = \sqrt { 2 }$ r: $\sqrt { 3 } \cdot \sqrt { 5 } = \sqrt { 15 }$ The following propositions are given. Accordingly, which of the following compound propositions is true?
A) $p \wedge ( r \vee q )$
B) $( p \vee q ) \wedge r$
C) $r \Rightarrow ( p \wedge q )$
D) $p \vee ( r \Rightarrow q )$
E) $p \Rightarrow ( q \wedge r )$

When the distinct positive integers $a , 2 , b , 9$ and 6 are arranged from smallest to largest, the middle number is a.
Accordingly, which of the following cannot $b$ be?
A) 1
B) 3
C) 5
D) 8
E) 10

Defined on the set of real numbers R,
$$\begin{aligned} & \beta _ { 1 } = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } = 1 \right\} \\ & \beta _ { 2 } = \left\{ ( x , y ) : x ^ { 2 } + y = 2 \right\} \\ & \beta _ { 3 } = \left\{ ( x , y ) : x - y ^ { 2 } = 3 \right\} \end{aligned}$$
Which of these relations define a function of the form $\mathbf { y } = \mathbf { f } ( \mathbf { x } )$ on $R$?
A) Only $\beta _ { 1 }$
B) Only $\beta _ { 2 }$
C) $\beta _ { 1 }$ and $\beta _ { 3 }$
D) $\beta _ { 2 }$ and $\beta _ { 3 }$
E) $\beta _ { 1 } , \beta _ { 2 }$ and $\beta _ { 3 }$

Let $d$ be the greatest common divisor of positive integers $a$ and $b$. I. The number $d ^ { 2 }$ divides the number $a ^ { 2 }$. II. The number $d ^ { 2 }$ divides the number $a ^ { 2 } + b$. III. The number $\mathrm { d } ^ { 2 }$ divides the number $\mathrm { a } ^ { 2 } + \mathrm { b } ^ { 2 }$. 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

Let $A = \{ 1,2,3,4,5,6 \}$ and $f : A \rightarrow A$ is a one-to-one function.
Accordingly, $$f ( 1 ) + f ( 2 ) + f ( 3 ) + f ( 4 )$$
What is the difference between the maximum and minimum values that this sum can take?
A) 6
B) 7
C) 8
D) 9
E) 10

The table of an operation $\Delta$ defined on the set $A = \{ 1,2,3,4,5 \}$ is given below.

$\Delta$	1	2	3	4	5
1	5	1	3	2	4
2	3	2	1	4	5
3	2	3	4	5	1
4	5	4	1	3	2
5	1	5	4	2	3

Also, for $\mathrm { a } \in \mathrm { A }$, the set $\mathrm { M } ( \mathrm { a } ) = \{ \mathrm { b } \in \mathrm { A } \mid \mathrm { a } \Delta \mathrm { b } = \mathrm { b } \Delta \mathrm { a } \}$ is defined.
Accordingly, which of the following is the set $\mathbf { M } ( \mathbf { 4 } )$?
A) $\{ 1,2,4 \}$
B) $\{ 1,3,5 \}$
C) $\{ 2,3,4 \}$
D) $\{ 2,4,5 \}$
E) $\{ 3,4,5 \}$

Let x and y be two-digit natural numbers such that
$$x - y = 65$$
How many x numbers satisfy this equation?
A) 20
B) 25
C) 30
D) 35
E) 40

Let p be a prime number. If the number $\mathrm { p } + 2$ is prime or if the number $\mathrm { p } + 2$ can be written as the product of two prime numbers, then p is called a Chen prime.
Accordingly, which of the following is not a Chen prime?
A) 37
B) 59
C) 67
D) 73
E) 83

The average of the profits obtained by a company in 2009, 2010 and 2011 is 4 million TL. In 2012, the company obtained 25\% more profit than in 2011, and the average profit obtained in these four years became 4.5 million TL.
Accordingly, how much profit did the company obtain in 2011?
A) 4.8
B) 5
C) 5.2
D) 5.4
E) 5.6

In the calendar of an ancient civilization,
1 month has 36 days
1 year has 10 months exist. In this civilization, dates given in the order day-month-year in the form AB-CD-ABCD are called ``symmetric days.''
According to this calendar, how many days after the date 20-08-2008 will the next symmetric day occur?
A) 360
B) 396
C) 480
D) 720
E) 756

A teacher conducted the following activity in class with four of her students named Ali, Banu, Can, and Do\u011fa.

• These students each think of a number. Let these numbers be $\mathrm { A } , \mathrm { B } , \mathrm { C }$ and D respectively.
• Each student writes their own number on a piece of paper and gives it to the teacher.
• The teacher calculates the result of the following addition operations written on the board and fills in the right side of the equations.

$$\begin{aligned} & A + B = \\ & B + D = \\ & A + B + C = \end{aligned}$$
Based on what is written on the board, which students alone have sufficient information to find all four numbers A, B, C, and D?
A) Ali, Banu, and Do\u011fa
B) Ali, Can, and Do\u011fa
C) Ali and Banu
D) Banu and Can
E) Can and Do\u011fa

Below is an abacus consisting of five sufficiently long rods. On the abacus; 1 bead is placed on the 1st rod, 2 beads on the 2nd rod, and similarly, as many beads as its number are placed on the other rods. Thus the first round is completed as shown in the figure.
Then we start over and 6 beads are placed on the 1st rod, 7 beads on the 2nd rod, and similarly, one more bead than was placed on the previous rod is placed on the other rods. After each round, the number of beads on the 5th rod plus one is placed on the 1st rod, and the rounds continue.
Accordingly, on which rod will the 220th bead to be placed be located?
A) I.
B) II.
C) III.
D) IV.
E) V.

Below is a running park consisting of an isosceles right triangle and a semicircle with the hypotenuse of this triangle as its diameter. There are three running paths in this park. Ay\c{c}a, Bar\i\c{s}, and Cem start running from the starting point at the same time using paths A, B, and C respectively and reach the finish point.
Given that the speeds of Ay\c{c}a, Bar\i\c{s}, and Cem are 4 km, $\mathbf { 2 ~ km }$, and $\mathbf { 3 ~ km }$ per hour respectively, what is the order of arrival at the finish point?
A) Ay\c{c}a, Bar\i\c{s}, Cem
B) Ay\c{c}a, Cem, Bar\i\c{s}
C) Bar\i\c{s}, Cem, Ay\c{c}a
D) Bar\i\c{s}, Ay\c{c}a, Cem
E) Cem, Ay\c{c}a, Bar\i\c{s}