In a competition, a jury consisting of three people votes yes or no to the contestants. In this competition with 20 participants, a contestant must receive at least two yes votes to be successful.
In this competition where the jury members gave a total of 30 yes votes, 8 contestants were successful and no contestant received three no votes.
Accordingly, how many contestants received three yes votes?
A) 1 B) 2 C) 3 D) 4 E) 5

The weight of three of the balls $A, B, C$ and $D$ is the same. On a balance scale with equal arms:
- when balls $A$ and $B$ are placed on the left pan and balls $C$ and $D$ are placed on the right pan, the left pan is heavier, - when balls A and C are placed on the left pan and balls B and D are placed on the right pan, the left pan is again heavier.
Accordingly,
I. Balls A and B have equal weight. II. Balls B and C have equal weight. III. Ball A is heavier than ball D.
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

Passengers traveling on an airplane took at most one of the tea and coffee offered. From these passengers:
- the number of passengers who took tea is 3 times the number of passengers who took coffee, - the number of passengers who took neither of the tea and coffee refreshments is one-third of the total number of passengers.
Given that the number of passengers who did not take tea is 72, how many passengers did not take coffee?
A) 90 B) 96 C) 100 D) 108 E) 120

In an egg production farm, Ayhan and Burcu perform the work of arranging eggs in crates and packaging these crates.
- Ayhan arranges 3 crates per minute, while Burcu arranges 4 crates per minute. - Ayhan packages 6 crates per minute, while Burcu packages 5 crates per minute.
Ayhan arranged eggs in some crates and packaged these crates. During this time, Burcu arranged 60 crates of eggs and packaged these crates.
Accordingly, how many crates of eggs did Ayhan arrange?
A) 48 B) 50 C) 54 D) 60 E) 66

Alper will attend a meeting at his workplace that will be held at 08.00 in the morning. Leaving home one hour before the meeting time, Alper adjusts his walking speed so that he will arrive at the workplace in 1 hour.
When he reaches the midpoint of the road, Alper realizes he forgot his file at home, retrieves his file at a constant speed by running, and arrives at the workplace exactly on time by running at the same speed without stopping.
Given that Alper used the same route between home and workplace throughout his entire movement, at what time did he retrieve his file from home?
A) 07.36 B) 07.40 C) 07.42 D) 07.45 E) 07.48

Below is a moving device consisting of two small and large disks with the same centers and symbols placed at equal intervals on them. A rectangular fixed indicator is placed on top of this device.
These two disks moving at constant speeds in the direction of the arrow: the small disk rotates $90 ^ { \circ }$ per second. When the small disk completes one full rotation, the large disk rotates $90 ^ { \circ }$.
For example; 10 seconds after the beginning, the following view is obtained in the device and the indicator appears as $\square$.
What is the appearance of the indicator 100 seconds after the beginning?
(See answer choices A)–E) with figures in original paper.)

$A B C D E F$ regular hexagon
ABGH square
$[ \mathrm { AG } ] \cap [ \mathrm { BE } ] = \{ \mathrm { K } \}$
$\mathrm { m } ( \widehat { \mathrm { AKE } } ) = \mathrm { x }$
According to the given information above, what is $x$ in degrees?
A) 85 B) 90 C) 95 D) 100 E) 105

ABCD is a square
$\mathrm { AE } \perp \mathrm { EB }$
$| \mathrm { AB } | = 25 \mathrm {~cm}$
$| \mathrm { BE } | = 20 \mathrm {~cm}$
$| \mathrm { DE } | = \mathrm { x }$
According to the given information above, what is x in cm?
A) $8 \sqrt { 6 }$ B) $12 \sqrt { 2 }$ C) $6 \sqrt { 5 }$ D) $5 \sqrt { 10 }$ E) $10 \sqrt { 3 }$

The paper in the shape of an isosceles right triangle ABC shown in the figure is folded along [AD] so that side $AB$ falls onto side $AC$.
Accordingly, what is the ratio $\frac { | C D | } { | A B | }$?
A) $\frac { 1 } { 2 }$ B) $\frac { 2 } { 3 }$ C) $\frac { \sqrt { 2 } } { 2 }$ D) $2 - \sqrt { 2 }$ E) $3 - 2 \sqrt { 2 }$

A right circular cylinder with height 7 cm and completely filled with water and an empty right cone with the same base and height h cm are combined as shown in Figure 1.
When this solid is inverted as shown in Figure 2, the height of water inside the solid is 11 cm. What is h in cm?
A) 5 B) 5.5 C) 6 D) 6.5 E) 7

A rectangular prism made of unit cubes with edge lengths 2 units, 3 units, and 4 units has all its faces painted. Then, this prism is separated into 24 unit cubes.
In the final state, what is the total number of unpainted faces of these unit cubes?
A) 78 B) 82 C) 86 D) 90 E) 92

$$\left( \frac { 8 } { 3 } - \frac { 9 } { 4 } \right) \left( 4 + \frac { 4 } { 5 } \right)$$
What is the result of this operation?
A) $\frac { 1 } { 2 }$
B) $\frac { 3 } { 2 }$
C) $\frac { 4 } { 3 }$
D) 1
E) 2

$$\frac { 8 ! - 7 ! - 6 ! } { 8 ! }$$
What is the result of this operation?
A) $\frac { 4 } { 5 }$
B) $\frac { 5 } { 6 }$
C) $\frac { 6 } { 7 }$
D) $\frac { 7 } { 8 }$
E) $\frac { 8 } { 9 }$

The greatest common divisor of positive integers a and b is odd, and their least common multiple is even.
Accordingly, I. $a \cdot b$ II. $a + b$ III. $a ^ { b }$ Which of the following expressions always equals an odd number?
A) Only I
B) Only II
C) Only III
D) I and III
E) II and III

$$\begin{array} { r } A C B \\ + \quad A C \\ \hline 3 B C \end{array}$$
According to this operation, what is the product $A \cdot C$?
A) 12
B) 14
C) 15
D) 16
E) 21

In the following table consisting of 100 unit squares numbered from 1 to 100, some squares will be painted.

1	2	3	$\ldots$	10
11	12	13	$\ldots$	20
.	.	.		.
.	.	.		.
.	.	.		.
91	92	93	..	100

Squares with even numbers are painted yellow, squares that are multiples of 3 are painted red, and squares that are multiples of 5 are painted blue.
For a square to be orange, it must be painted only yellow and red.
Accordingly, how many unit squares in the table are orange?
A) 8
B) 12
C) 13
D) 15
E) 18

$$\begin{aligned} & \frac { a + c } { b } = \frac { 3 } { 2 } \\ & \frac { b } { c } = \frac { 3 } { 4 } \end{aligned}$$
Given this, what is the ratio $\frac { a } { b }$?
A) $\frac { 1 } { 3 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 6 }$
E) $\frac { 5 } { 6 }$

Let $p$ be a prime number and $n$ be a natural number such that
$$p \cdot n = 3 ^ { p }$$
Given this equality, what is the sum $p + n$?
A) 10
B) 12
C) 15
D) 16
E) 18

An operation is defined on the set of positive real numbers as
$$a \bullet b = \frac { a \cdot b } { a + b }$$
Given that
$$\frac { 1 } { 2 } \bullet \frac { 3 } { 4 } = 3 \bullet \frac { 1 } { x }$$
what is $x$?
A) $\frac { 3 } { 2 }$
B) $\frac { 9 } { 4 }$
C) 2
D) 3
E) 5

Let $x$, $y$, and $z$ be integers such that

• The product $x \cdot y$ is an even number
• The sum $x + z$ is an odd number
• The sum $y + z$ is an odd number

Given this; I. $x$ is an odd number. II. $y$ is an even number. III. $z$ is an odd number. Which of these statements are true?
A) Only I
B) Only III
C) I and II
D) II and III
E) I, II and III

When a number is multiplied by $\frac { 1 } { 3 }$, it equals the two-digit natural number $AB$, and when multiplied by $\frac { 1 } { 8 }$, it equals the two-digit natural number $BA$.
Given this, what is the sum $A + B$?
A) 7
B) 8
C) 9
D) 10
E) 11

Numbers that equal the sum of the squares of two or three consecutive positive integers are called consecutive numbers.
Example: $13 = 2 ^ { 2 } + 3 ^ { 2 }$
$$14 = 1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 }$$
Since 13 and 14 are consecutive numbers. Given this, which of the following is not a consecutive number?
A) 29
B) 35
C) 41
D) 50
E) 61

$$A = \{ - 3 , - 2 , - 1,0,1,2,3 \}$$
All 2-element subsets of the set are written. The sum of the elements of each of these subsets is calculated separately and set B is formed with these numbers.
Accordingly, how many elements does set B have?
A) 9
B) 11
C) 13
D) 15
E) 17

In a workplace, a color printer prints 2 pages per second, and a black-and-white printer prints 3 pages per second.
When Ahmet starts printing documents on these printers at the same time, when the color printer has printed the first 50 pages, he sees that the black-and-white printer still needs to print 60 more pages.
How many pages in total have these printers printed when they complete the printing task at the same time?
A) 175
B) 200
C) 225
D) 240
E) 250

A fisherman caught 16 kg of horse mackerel, 20 kg of whiting, and 50 kg of mackerel. Later, he determined the kg selling prices of these fish as follows:

• horse mackerel is 25\% more expensive than whiting, and whiting is 25\% more expensive than mackerel

The fisherman sold all of these fish at the prices he determined and earned 1600 TL in revenue.
Accordingly, what is the kg selling price of whiting in TL?
A) 15
B) 20
C) 24
D) 30
E) 32