Question 161
A equação $x^2 - 5x + 6 = 0$ tem como raízes
(A) $x = 1$ e $x = 6$ (B) $x = 2$ e $x = 3$ (C) $x = -2$ e $x = -3$ (D) $x = 1$ e $x = -6$ (E) $x = -1$ e $x = 6$

Question 173
Um número inteiro positivo de dois algarismos é tal que a soma de seus algarismos é 9 e o produto de seus algarismos é 18. Esse número é
(A) 27 (B) 36 (C) 45 (D) 63 (E) 72

Uma função $f: \mathbb{R} \to \mathbb{R}$ é definida por $f(x) = 2x^2 - 3x + 1$. O valor de $f(2)$ é
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Um retângulo tem perímetro de 36 cm e área de 80 cm$^2$. As dimensões do retângulo são
(A) 8 cm e 10 cm (B) 9 cm e 9 cm (C) 6 cm e 12 cm (D) 5 cm e 16 cm (E) 4 cm e 20 cm

The temperature $T$ of an oven (in degrees Celsius) is reduced by a system from the moment it is turned off ($t = 0$) and varies according to the expression $T(t) = -\frac{t^{2}}{4} + 400$, with $t$ in minutes. For safety reasons, the oven lock is only released for opening when the oven reaches a temperature of $39^{\circ}C$.
What is the minimum waiting time, in minutes, after turning off the oven, for the door to be opened?
(A) 19.0 (B) 19.8 (C) 20.0 (D) 38.0 (E) 39.0

QUESTION 136
A person, when buying a property, paid $20\%$ of the total value as a down payment and financed the rest in 48 equal monthly installments of R\$ 1,500.00. The total value of the property is
(A) R\$ 72,000.00
(B) R\$ 86,400.00
(C) R\$ 90,000.00
(D) R\$ 96,000.00
(E) R\$ 100,000.00

QUESTION 137
A company has 60 employees. Of these, $\frac{1}{3}$ work in the administrative sector, $\frac{1}{4}$ work in the production sector, and the rest work in the commercial sector. The number of employees in the commercial sector is
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35

QUESTION 145
A store offers a $15\%$ discount on a product that costs R\$ 200.00. The price of the product after the discount is
(A) R\$ 160.00
(B) R\$ 165.00
(C) R\$ 170.00
(D) R\$ 175.00
(E) R\$ 180.00

QUESTION 146
The function $f(x) = 2x^2 - 3x + 1$ has roots
(A) $x = 1$ and $x = \frac{1}{2}$
(B) $x = -1$ and $x = \frac{1}{2}$
(C) $x = 1$ and $x = -\frac{1}{2}$
(D) $x = -1$ and $x = -\frac{1}{2}$
(E) $x = 2$ and $x = \frac{1}{2}$

QUESTION 168
The equation $x^2 - 5x + 6 = 0$ has roots
(A) $x = 1$ and $x = 6$
(B) $x = 2$ and $x = 3$
(C) $x = -2$ and $x = -3$
(D) $x = 1$ and $x = -6$
(E) $x = -1$ and $x = 6$

To prevent an epidemic, the Health Department of a city disinfected all neighborhoods to prevent the spread of the dengue mosquito. It is known that the number $f$ of infected people is given by the function $f(t) = -2t^{2} + 120t$ (where $t$ is expressed in days and $t = 0$ is the day before the first infection) and that this expression is valid for the first 60 days of the epidemic.
The Health Department decided that a second disinfection should be done on the day when the number of infected people reached 1600 people, and a second disinfection had to take place.
The second disinfection began on
(A) the $19^{\text{th}}$ day.
(B) the $20^{\text{th}}$ day.
(C) the $29^{\text{th}}$ day.
(D) the $30^{\text{th}}$ day.
(E) the $60^{\text{th}}$ day.

A company produces cylindrical cans to store food. The technical standard requires that the ratio between the height and the diameter of the base of the can must be equal to 2. A can that meets this standard has a volume of $V = 500\pi \text{ cm}^3$.
What is the height, in centimeters, of this can?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25

A person invests R\$\,2{,}000.00 in a savings account that yields 0.5\% per month in simple interest. After 12 months, this person withdraws all the money.
What is the total amount withdrawn, in reais?
(A) R\$\,2{,}100.00
(B) R\$\,2{,}110.00
(C) R\$\,2{,}120.00
(D) R\$\,2{,}130.00
(E) R\$\,2{,}140.00

In a right triangle, the hypotenuse measures 10 cm and one of the legs measures 6 cm. What is the area, in square centimeters, of this triangle?
(A) 20
(B) 24
(C) 30
(D) 36
(E) 48

The sum of three consecutive even integers is 78. What is the largest of these integers?
(A) 24
(B) 26
(C) 28
(D) 30
(E) 32

A rectangle has a perimeter of 36 cm and its length is twice its width. What is the area, in square centimeters, of this rectangle?
(A) 48
(B) 72
(C) 96
(D) 108
(E) 144

A store is offering a 20\% discount on all products. After the discount, a product costs R\$\,80.00. What was the original price of the product, in reais?
(A) R\$\,96.00
(B) R\$\,100.00
(C) R\$\,104.00
(D) R\$\,108.00
(E) R\$\,112.00

A map uses a scale of 1:50,000. On the map, the distance between two cities is 8 cm. What is the real distance between the two cities, in kilometers?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

In a laboratory, a container holds 10 liters of a solution composed only of substances $\mathrm{S}_1$ and $\mathrm{S}_2$. Of this solution, 99.95\% is $\mathrm{S}_1$. An amount of $\mathrm{S}_1$ will be removed from this solution, maintaining the initial amount of $\mathrm{S}_2$, so that 99.90\% of the new solution is $S_1$.
What is the amount of $\mathrm{S}_1$, in liters, that will be removed?
(A) 0.0050
(B) 0.0100
(C) 0.5000
(D) 4.9775
(E) 5.0000

A fuel distributor owns tanker trucks with a capacity of 30,000 liters each. In any transport carried out by these trucks, the same volume of fuel is discarded because it contains many impurities. This discarded volume is independent of the quantity transported.
A gas station ordered 10,000 liters of gasoline from this distributor, which sent 10,200 liters, considering the volume discarded in transport. Nevertheless, the amount of gasoline delivered to the gas station was 9,900 liters.
In a new order, this gas station requested that exactly double the volume of gasoline ordered in the previous order be delivered.
Using the same truck from the previous delivery, what is the minimum volume of gasoline, in liters, that the distributor should send to guarantee delivery of the ordered quantity in this new order?
(A) 20,100
(B) 20,200
(C) 20,300
(D) 20,400
(E) 20,600

A parking lot has 120 spaces for vehicles, and all these spaces are occupied. Each customer pays a monthly fee to use a space, which is calculated based on the parking lot's monthly expenses and the desired profit. The parking lot's monthly expenses are: R\$14,240.00 for maintenance plus R\$36.00 insurance per vehicle. The parking lot's profit is determined by the difference between the amount collected from monthly fees and the expenses incurred. Starting the following month, the insurance value per vehicle will increase by 20\%, and maintenance expenses will remain unchanged. With this, the parking lot owner will adjust the monthly fees to obtain a monthly profit of R\$10,000.00. Despite this adjustment, all spaces will remain occupied.
The value, in reais, of the adjusted monthly fee will be
(A) 185.60.
(B) 226.09.
(C) 245.20.
(D) 268.93.
(E) 285.60.

A company produced, in a given month, 110 tons of plastic from petroleum derivatives and 80 tons from recycled plastics. The cost to recycle one ton of plastic is R\$ 500.00, which equals 5\% of the cost to produce the same amount of plastic from petroleum derivatives. For the following month, this company's goal is to produce the same amount of plastic that was produced in this month, but with a reduction of at least 50\% in production cost.
For the company to achieve its goal in the following month, the minimum amount of tons of plastic that must be produced from recycling should be
(A) 135.
(B) 140.
(C) 155.
(D) 160.
(E) 175.

A car that costs 60 thousand reais is sold by a dealership that offers two payment options, both without down payment and without interest:

• option 1: payment in $n$ equal installments;
• option 2: payment in 6 more installments than in option 1 and, with this, the value of each installment becomes R\$ 500.00 less than the value of the installment in option 1. In both payment options, the total value to be paid for the car is the same.

What is the quantity $n$ of installments contained in payment option 1?
(A) 18
(B) 24
(C) 30
(D) 42
(E) 48

Find the product of all real roots of the irrational equation $x ^ { 2 } + 7 x + 10 + \sqrt { x ^ { 2 } + 7 x + 12 } = 0$. [3 points]

What is the sum of all real roots of the equation $\sqrt { x ^ { 2 } - 2 x + 1 } - \sqrt { x ^ { 2 } - 2 x } = \frac { 1 } { 2 }$? [3 points]
(1) 5
(2) 4
(3) 3
(4) 2
(5) 1