$$A = 13 + 26 + 39 + \cdots + 169$$
Given this, what is the sum of the prime numbers that divide A?
A) 16
B) 18
C) 20
D) 22
E) 24

The following are known about a set A.

• It consists of 6 consecutive odd natural numbers.
• The sum of the elements in the set equals 4 times the largest element.

Accordingly, what is the largest element of set $A$?
A) 21
B) 19
C) 17
D) 15
E) 13

The following information is known about the athletes participating in a race.

• The jersey numbers of male athletes are consecutive odd numbers starting from 1.
• The jersey numbers of female athletes are consecutive even numbers starting from 2.
• The number of male athletes is 3 times the number of female athletes.
• The largest jersey number given to male athletes is 83.

Given this, what is the largest jersey number given to female athletes?
A) 28
B) 30
C) 32
D) 34
E) 36

The following information is known about the monthly salaries of Ahmet and Beyza, who started work on the same day at a workplace.

• Ahmet's initial salary is 2500 TL.
• Ahmet's salary increases by 50 TL every 4 months.
• Beyza's salary increases by 100 TL every 6 months.

Given that their salaries are equal 6 years after they receive their first salaries, what is Beyza's initial salary in TL?
A) 2000
B) 2100
C) 2200
D) 2300
E) 2400

$$\sum _ { n = 5 } ^ { 14 } \frac { 1 } { 1 + 2 + \cdots + n }$$
What is the value of this sum?
A) $\frac { 1 } { 3 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 3 } { 5 }$
D) $\frac { 2 } { 15 }$
E) $\frac { 4 } { 15 }$

A school principal sends an electronic mail on Monday to some students of the school containing the note, ``Every student who receives this message should send it to two students the next day.'' The students who receive the message follow what is written in that note.
By the end of Friday of the same week, this message reaches all students in the school and each student receives this message only once.
Given that the number of students in the school is 930, how many students was this message initially sent to?
A) 6
B) 10
C) 15
D) 21
E) 30

$$\left( \sum _ { k = 1 } ^ { 9 } k \right) \cdot \left( \sum _ { n = 1 } ^ { 8 } \frac { 1 } { n ( n + 1 ) } \right)$$
What is the result of this operation?
A) 27
B) 30
C) 32
D) 36
E) 40

Let $\left( a _ { n } \right)$ be an arithmetic sequence such that $$\begin{aligned}& a _ { 10 } + a _ { 7 } = 6 \\& a _ { 9 } - a _ { 6 } = 1\end{aligned}$$ the following equalities are given.\ Accordingly, what is $a _ { 1 }$?\ A) $\frac { 7 } { 3 }$\ B) $\frac { 5 } { 2 }$\ C) $\frac { 4 } { 3 }$\ D) $\frac { 5 } { 6 }$\ E) $\frac { 1 } { 2 }$

On a circular playground, five players named Ali, Büşra, Cem, Deniz, and Ekin are playing with a ball in positions shown in the figure. In each turn of this game; the player holding the ball passes it to the third player after them in the direction of the arrow.
Initially, the ball is in Ali's hands and the game starts when Ali passes the ball to Deniz. Deniz received the ball on the 1st turn, Büşra on the 2nd turn, and the game continued in this way.
Accordingly, who received the ball on the 99th turn?
A) Ali B) Büşra C) Cem D) Deniz E) Ekin

For an arithmetic sequence $(a_n)$ with distinct terms and common difference $r$,
$$\begin{aligned} & a _ { 1 } = 3 \cdot r \\ & a _ { 6 } = a _ { 2 } \cdot a _ { 4 } \end{aligned}$$
the equalities are given.
Accordingly, what is $\mathbf { a } _ { \mathbf { 1 0 } }$?
A) 10 B) 8 C) 6 D) 4 E) 2

Filiz creates cup towers by placing identical cardboard cups inside each other. The distance between the bases of every two consecutive cups is equal in all the cup towers she creates. Then, she places these towers on a table and measures their heights.
Filiz observes that the sum of the heights of two towers with 6 and 9 cups equals the height of the tower with 18 cups.
Accordingly, to what height of a cup tower is the sum of the heights of two towers with 8 and 12 cups equal?
A) 23
B) 24
C) 26
D) 27
E) 29

When all of the numbers 1, 2, 3, 4, 5, 6, and 7 are placed in 7 boxes with addition or subtraction symbols between them, with one number in each box, the result of the operation obtained is 4.
$$\square + \square + \square + \square + \square - \mathrm { A } - \mathrm { B } = 4$$
Accordingly, what is the product A · B?
A) 15
B) 24
C) 28
D) 30
E) 35

Ceyda plans to take an equal number of steps each day for a week. The graph below shows the difference between the number of steps Ceyda took daily and the number of steps she planned to take during this week.
For example, Ceyda took 50 more steps than planned on Monday and 100 fewer steps than planned on Tuesday.
On Friday, Ceyda took 165 more steps than on Thursday and 10 fewer steps than on Saturday, and after 7 days, the total number of steps she took was equal to the number of steps she initially planned to take.
Accordingly, how many more steps did Ceyda take on Friday than the number of steps she planned to take daily?
A) 85
B) 90
C) 95
D) 100
E) 105

For an arithmetic sequence $(a_n)$:
$$\begin{gathered} a _ { 2 } = 2 a _ { 1 } + 1 \\ a _ { 6 } + a _ { 22 } = 34 \end{gathered}$$
equalities are given.
Accordingly, what is $a _ { 7 }$?
A) $61^3$
B) 7
C) 8
D) 9
E) 10

The table below shows some musical note symbols and the duration lengths of these note symbols.
Accordingly, what is the sum of the duration lengths of the musical note symbols given above?
A) $\frac{3}{2}$ B) $\frac{7}{4}$ C) $\frac{5}{4}$ D) $\frac{13}{8}$ E) $\frac{15}{8}$

A flower bed with a height of 1.2 meters has five shelves at equal intervals in its left compartment and six shelves at equal intervals in its right compartment. The shelves at the bottom and top of these two compartments are at equal heights. A flower has been placed on the 4th shelf in the left compartment and on the 3rd shelf in the right compartment of the flower bed as shown in the figure.
Accordingly, what is the sum of the heights from the ground of the shelves where the flowers are located in meters?
A) 1.38 B) 1.36 C) 1.34 D) 1.32 E) 1.30

Two balloons are hung on a string stretched between two walls as shown in the figure. Between these two balloons, 2 white balloons or 4 yellow balloons are to be hung such that the distance between the points where any two adjacent balloons are attached to the string is equal.
The distance between the points where any two adjacent balloons are attached to the string is 18 cm more when white balloons are hung compared to when yellow balloons are hung.
Accordingly, what is the distance in cm between the points where the two initially hung balloons are attached to the string?
A) 135 B) 144 C) 153 D) 162 E) 171

A geometric sequence $(b_n)$ with first two terms $b_{1} = \frac{4}{3}$ and $b_{2} = 2$ and an arithmetic sequence $(a_n)$ whose common difference equals the common ratio of this geometric sequence are given.
If $b_{7} = a_{11}$, what is $a_{1}$?
A) $\frac{1}{4}$ B) $\frac{1}{8}$ C) $\frac{3}{8}$ D) $\frac{3}{16}$ E) $\frac{5}{16}$

For an arithmetic sequence $(a_{n})$ with common difference $r$
$$\begin{aligned} & a_{30} - a_{25} < 53 \\ & a_{25} - a_{8} > 53 \end{aligned}$$
the inequalities are given.
What is the sum of the integer values that $r$ can take?
A) 49 B) 56 C) 64 D) 72 E) 84

Merve plans a 30-day walking program. On the first day, she walks for a certain duration, and plans to walk 1 minute longer each subsequent day than the previous day. Following this plan for the first 15 days, Merve began to struggle and reduced her walking time by 1 minute each day for the remaining days compared to the previous day.
After 30 days, Merve calculated her total walking time to be 1395 minutes.
Accordingly, how many minutes did Merve's first day walk last?
A) 30
B) 35
C) 40
D) 45
E) 50

For an arithmetic sequence $(a_{n})$,
$$\begin{aligned} & a_{1} \cdot a_{2} \cdot a_{3} = 2 \\ & a_{2} \cdot a_{3} \cdot a_{4} = 14 \end{aligned}$$
are given. Accordingly, what is the product $a_{3} \cdot a_{4} \cdot a_{5}$?
A) 28 B) 35 C) 42 D) 49 E) 56