In the Cartesian coordinate plane, the graphs of functions $f$, $g$ and $h$ whose domains consist of real numbers are given in the figure.
Accordingly, for $x \in [ - 2,2 ]$,
$$\begin{aligned} & f ( x ) \cdot g ( x ) > 0 \\ & g ( x ) \cdot h ( x ) < 0 \end{aligned}$$
the solution set of the system of inequalities is which of the following?
A) $( - 2 , - 1 )$ B) $( - 1,0 )$ C) $( 1,2 )$ D) $( - 2 , - 1 ) \cup ( 1,2 )$

A weather forecaster made the following statement during a live broadcast on Sunday evening.
"In our city where the temperature has been 5 degrees throughout this week, the weather will suddenly warm up starting tomorrow and winter will give way to spring-like weather. On Monday afternoon, the air temperature throughout the city will have increased by 6 to 10 degrees compared to the previous day."
Based on this information, which of the following inequalities expresses the range of values that the temperature in the city could take on Monday afternoon?
A) $|x - 13| \leq 2$
B) $|x - 10| \leq 6$
C) $|x - 6| \leq 5$
D) $|x - 1| \leq 6$
E) $|x - 11| \leq 2$

A positive number A is shown on the number line as in the figure.
Then, on this number line; numbers whose distance from 0 is equal to half the distance of number A from 0 are marked.
If the distance from one of the marked numbers to number A is 6 units, what is the sum of the possible values of number A?
A) 15
B) 16
C) 18
D) 20
E) 21

Let a be a real number. Regarding the inequality $x + 1 \leq a$, the following are known.

• $\mathrm { x } = 0$ satisfies this inequality.
• $x = 4$ does not satisfy this inequality.

Accordingly, what is the widest interval expressing the values that the number a can take?
A) $( 0,4 ]$
B) $[ 0,4 )$
C) $[ 1,4 ]$
D) $( 1,5 ]$
E) $[ 1,5 )$

For distinct real numbers $a , b$ and $c$,
$$\begin{aligned} & a + b = | a | \\ & b + c = | b | \end{aligned}$$
equalities are given. Accordingly; what is the correct ordering of the numbers $\mathbf { a , b }$ and c?
A) a < b < c
B) a $<$ c $<$ b
C) b $<$ a $<$ c
D) b $<$ c $<$ a
E) c $<$ a $<$ b

For real numbers $a$, $b$, and $c$
$$a - b < 0 < c < c - b$$
the inequality is given.
Accordingly, I. $a \cdot b \cdot c > 0$ II. $( a + c ) \cdot b > 0$ III. $b - a + c > 0$ which of these statements are always true?
A) Only I
B) Only II
C) I and II
D) I and III
E) II and III

Where $a$ and $b$ are positive real numbers different from 1,
$$\log_a 2 < 0 < \log_2 b$$
the inequality is satisfied. Accordingly, I. $a + b > 1$ II. $b - a > a$ III. $a \cdot b > 1$ Which of the following statements are always true?
A) Only I
B) Only II
C) I and II
D) I and III
E) II and III

Let $a$, $b$, $c$, and $d$ be real numbers such that
$$\begin{aligned} & a x ^ { 2 } + b x + 12 \geq 0 \\ & c x ^ { 2 } + d x + 24 \leq 0 \end{aligned}$$
To find the solution set of this system of inequalities, the following table is constructed and the solution set is found to be $[ - 2 , - 1 ] \cup [ 4,6 ]$.
What is the sum $a + b + c + d$?
A) 15
B) 16
C) 17
D) 18
E) 19

An instructor at a parachute jumping course gives the following explanation to the trainees:
"When jumping from an airplane at a height of 800 meters from the ground, you need to open your parachute 400 to 500 meters after jumping from the airplane in order to land safely on the ground."
Accordingly, which of the following inequalities expresses the values that the height from the ground when the parachute opens can take in order to land safely?
A) $|x - 350| \leq 50$ B) $|x - 300| \leq 100$ C) $|x - 250| \leq 150$ D) $|x - 200| \leq 200$ E) $|x - 150| \leq 250$

Let $a, b, c$ and $d$ be real numbers such that
$$x + ay \leq b$$ $$x + cy \geq d$$
The solution set of the system of inequalities is shown in green on the coordinate plane below.
Accordingly, what are the signs of the numbers $a, b, c$ and $d$ in order?
A) $+, -, -, -$ B) $+, +, +, -$ C) $+, -, +, -$

Let $x$ and $y$ be real numbers,
$$x^{2} \cdot y^{2} < x \cdot y < x^{2} \cdot y$$
Given this inequality.
Accordingly,
I. $x < 1$ II. $y < 1$ III. $x \cdot y < 1$
Which of these statements are true?
A) Only I B) Only II C) I and III D) II and III E) I, II and III

For real numbers $a, b$ and $c$,
$$a > a \cdot b > 2 \cdot a > a \cdot c$$
is known to hold.
Accordingly, which of the following could be the representation of the numbers $\mathbf{a, b}$ and $\mathbf{c}$ on the number line?
A) [number line A] B) [number line B] C) [number line C] D) [number line D] E) [number line E]

Let $a$ and $b$ be positive integers,
$$\begin{aligned} & (x - a)(x + 2a) < 0 \\ & (x - b)(x + 2b) > 0 \end{aligned}$$
Given this system of inequalities.
If $a + b = 8$ and the solution set of this system of inequalities contains 16 integers, what is the product $a \cdot b$?
A) 7 B) 10 C) 12 D) 15 E) 16

Let $a$ be an integer. There are exactly 4 integer values of $x$ satisfying
$$0 < \left| x^{2} - 2x + 2 \right| - x^{2} - x < a$$
What is the sum of the different integer values that $a$ can take?
A) 33 B) 36 C) 39 D) 42 E) 45

In a store, the cost prices of a dishwasher, a washing machine, and a refrigerator are 18 thousand, 22 thousand, and $b$ TL, respectively. These products are sold together as a triple white goods package. This package is sold at twice the cost price of a refrigerator plus 30 thousand TL, the store makes a profit; when sold at three times the cost price of a refrigerator minus 20 thousand TL, the store makes a loss.
Accordingly, which of the following inequalities expresses all possible values of the cost price of a refrigerator?
A) $|b - 20000| < 10000$
B) $|b - 15000| < 5000$
C) $|2b - 15000| < 12000$
D) $|2b - 24000| < 17000$
E) $|3b - 16000| < 8000$