Where $a$ and $b$ are positive real numbers,
$$2ax^2 - 5bx + 8b = a$$
the roots of the equation are $a$ and $b$. Accordingly, what is the sum $a + b$?
A) 5
B) 6
C) 10
D) 12
E) 15

In a neighborhood with 95 buildings, each building is either 2 or 3 stories. Within the scope of urban renewal, 15 of these buildings are demolished and replaced with 5-story buildings each, and the total number of stories of the buildings in the neighborhood increases from 240 to 274.
Accordingly, by what percentage did the number of 3-story buildings in the neighborhood decrease as a result of urban renewal?
A) 16
B) 18
C) 20
D) 22
E) 24

Duygu, who starts running on a running course, takes a break to rest after running a certain distance.
After the break, Duygu

• if she runs 240 meters more, she will have run $\frac{7}{12}$ of the entire course,
• if she runs $\frac{1}{3}$ of the distance she ran before, she will have run $\frac{3}{5}$ of the entire course.

Accordingly, what is the length of the entire course in meters?
A) 1440
B) 1620
C) 1800
D) 1980
E) 2160

Uncle Ahmet has a rectangular field with side lengths $x + 20$ and $2x + 30$ meters. He grows sunflowers in a square-shaped part with side length $x$ meters as shown in the figure.
If the area of the remaining part of the field is 1400 square meters, what is the perimeter of the entire field in meters?
A) 148 B) 154 C) 160 D) 166 E) 172

For positive real numbers $a, x$ and $y$
$$\begin{aligned} & -2x^{2} + y^{2} = 2a \\ & 3x^{2} - 2y^{2} = -6a \end{aligned}$$
what is the ratio $\dfrac{y}{x}$?
A) 1 B) $\sqrt{2}$ C) $\sqrt{3}$ D) 2 E) 3

Let $a$ and $b$ be positive real numbers. For each of the equations
$$\begin{aligned} & ax^{2} - 2x + b = 0 \\ & bx^{2} - 3bx + a = 0 \end{aligned}$$
the sum of roots is 1 more than the product of roots.
Which of the following could be the quadratic equation whose roots are $a$ and $b$?
A) $9x^{2} + 8x + 18 = 0$ B) $9x^{2} - 14x + 8 = 0$ C) $9x^{2} - 18x + 14 = 0$ D) $9x^{2} - 8x + 14 = 0$ E) $9x^{2} - 18x + 8 = 0$