The rhombus represented in Figure 1 was formed by the union of the centers of four tangent circles, with radii of the same measure.
By doubling the radius of two of the circles centered at opposite vertices of the rhombus and still maintaining the tangency configuration, a situation is obtained as illustrated by Figure 2.
The perimeter of the rhombus in Figure 2, when compared to the perimeter of the rhombus in Figure 1, had an increase of
(A) 300\%.
(B) $200\%$.
(C) 150\%.
(D) 100\%.
(E) $50\%$.

José, Carlos and Paulo must transport a certain quantity of oranges on their bicycles. They decided to divide the route to be traveled into two parts, and at the end of the first part they would redistribute the quantity of oranges that each one carried depending on each one's fatigue. In the first part of the route José, Carlos and Paulo divided the oranges in the proportion 6:5:4, respectively. In the second part of the route José, Carlos and Paulo divided the oranges in the proportion $4:4:2$, respectively.
Knowing that one of them carried 50 more oranges in the second route, what is the quantity of oranges that José, Carlos and Paulo, in that order, transported in the second part of the route?
(A) 600, 550, 350
(B) 300, 300, 150
(C) 300, 250, 200
(D) 200, 200, 100
(E) $100, 100, 50$

On a blog of miscellaneous content, music, mantras and diverse information, ``Halloween Tales'' were posted. After reading, visitors could give their opinion by marking their reactions as: ``Fun'', ``Scary'' or ``Boring''. At the end of one week, the blog recorded that 500 distinct visitors accessed this post.
The following graph presents the result of the survey.
The blog administrator will draw a book among the visitors who gave their opinion on the ``Halloween Tales'' post.
Knowing that no visitor voted more than once, the probability that a person chosen at random among those who voted marked that the ``Halloween Tales'' story is ``Boring'' is most closely approximated by
(A) 0.09.
(B) 0.12.
(C) 0.14.
(D) 0.15.
(E) 0.18.

Arthur wishes to buy a piece of land from Cléber, who offers him the following payment options:

• Option 1: Pay in full, for $\mathrm{R}\$ 55000.00$;
• Option 2: Pay in installments, giving a down payment of $\mathrm{R}\$ 30000.00$, and another installment of $\mathrm{R}\$ 26000.00$ six months from now.
• Option 3: Pay in installments, giving a down payment of $\mathrm{R}\$ 20000.00$, plus an installment of $\mathrm{R}\$ 20000.00$, six months from now and another of $\mathrm{R}\$ 18000.00$ twelve months from the purchase date.
• Option 4: Pay in installments giving a down payment of R\$15000.00 and the remainder in 1 year from the purchase date, paying $\mathrm{R}\$ 39000.00$.
• Option 5: Pay in installments, one year from now, the amount of $\mathrm{R}\$ 60000.00$.

Arthur has the money to pay in full, but evaluates whether it would not be better to invest the money from the full payment amount (or even a smaller amount) in an investment, with a return of 10\% per semester, withdrawing the amounts as the installments of the chosen option became due.
After evaluating the situation from a financial point of view and the conditions presented, Arthur concluded that it was more financially advantageous to choose option
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.

A rectangular fabric lining brings on its label the information that it will shrink after the first wash while maintaining, however, its shape. The following figure shows the original measurements of the lining and the size of the shrinkage (x) in length and (y) in width. The algebraic expression that represents the area of the lining after being washed is $(5-x)(3-y)$.
Under these conditions, the area lost from the lining after the first wash will be expressed by
(A) $2xy$
(B) $15 - 3x$
(C) $15 - 5y$
(D) $-5y - 3x$
(E) $5y + 3x - xy$

The minimum capacity, in BTU/h, of an air conditioning unit for environments without sun exposure, can be determined as follows:

• $600 \mathrm{BTU}/\mathrm{h}$ per $\mathrm{m}^{2}$, considering up to two people in the environment;
• for each additional person in this environment, add 600 BTU/h;
• add another 600 BTU/h for each electrical appliance in operation in the environment.

An air conditioning unit will be installed in a room, without sun exposure, with dimensions $4\mathrm{~m} \times 5\mathrm{~m}$, in which four people remain and which has a television set in operation.
The minimum capacity, in BTU/h, of this air conditioning unit should be
(A) 12000.
(B) 12600.
(C) 13200.
(D) 13800.
(E) 15000.

The mechanical resistance $S$ of a wooden beam, in the form of a rectangular parallelepiped, is directly proportional to its width (b) and to the square of its height (d) and inversely proportional to the square of the distance between the beam's supports, which coincides with its length ($x$), as illustrated in the figure. The constant of proportionality k is called the resistance of the beam.
The expression that translates the resistance S of this wooden beam is
(A) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}^{2}}{\mathrm{x}^{2}}$
(B) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}}{\mathrm{x}^{2}}$
(C) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}^{2}}{\mathrm{x}}$
(D) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b}^{2} \cdot \mathrm{d}}{\mathrm{x}}$
(E) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot 2\mathrm{d}}{2\mathrm{x}}$

The principal of a school invited the 280 third-year students to participate in a game. Suppose there are 5 objects and 6 characters in a house with 9 rooms; one of the characters hides one of the objects in one of the rooms of the house. The objective of the game is to guess which object was hidden by which character and in which room of the house the object was hidden.
All students decided to participate. Each time a student is drawn and gives their answer. The answers must always be different from the previous ones, and the same student cannot be drawn more than once. If the student's answer is correct, they are declared the winner and the game is ended.
The principal knows that some student will get the answer right because there are
(A) 10 more students than possible distinct answers.
(B) 20 more students than possible distinct answers.
(C) 119 more students than possible distinct answers.
(D) 260 more students than possible distinct answers.
(E) 270 more students than possible distinct answers.

A biologist measured the height of five different trees and represented them on the same grid, using different scales, as indicated in the figure below.

I	II	III	IV	V
1:100	2:100	2:300	1:300	2:300

Which tree has the greatest actual height?
(A) I
(B) II
(C) III
(D) IV
(E) V

In a game there are two urns with 10 balls of the same size in each urn. The table below indicates the quantities of balls of each color in each urn.

Color	Urn 1	Urn 2
Yellow	4	0
Blue	3	1
White	2	2
Green	1	3
Red	0	4

A turn consists of: $1^{\circ}$) the player makes a guess about the color of the ball that will be drawn by them from urn 2; $2^{\circ}$) they randomly draw a ball from urn 1 and place it in urn 2, mixing it with those already there; $3^{\circ}$) then they also randomly draw a ball from urn 2; $4^{\circ}$) if the color of the last ball drawn is the same as the initial guess, they win the game.
Which color should be chosen by the player so that they have the greatest probability of winning?
(A) Blue.
(B) Yellow.
(C) White.
(D) Green.
(E) Red.

Water meters are markers of water consumption in residences and commercial establishments. There are several models of water meter displays, some of which have a combination of a display and two pointer clocks. The number formed by the first four digits of the display gives the consumption in $\mathrm{m}^{3}$, and the last two digits represent, respectively, the hundreds and tens of liters of water consumed. One of the pointer clocks indicates the quantity in liters, and the other in tenths of liters, as illustrated in the figure below.
Considering the information indicated in the figure, the total water consumption recorded on this water meter, in liters, is equal to
(A) 3534.85.
(B) 3544.20.
(C) 3534850.00.
(D) 3534859.35.
(E) 3534850.39.

The owner of a pharmacy decided to display the following graph, which shows the evolution of total sales (in Reais) of a certain medication throughout the year 2011.
According to the graph, the months in which the greatest and least absolute sales occurred in 2011 were, respectively,
(A) March and April.
(B) March and August.
(C) August and September.
(D) June and September.
(E) June and August.

Maria wants to innovate in her packaging store and decided to sell boxes with different formats. In the images presented are the unfoldings of these boxes.
What geometric solids will Maria obtain from these unfoldings?
(A) Cylinder, pentagonal prism and pyramid.
(B) Cone, pentagonal prism and pyramid.
(C) Cone, truncated pyramid and pyramid.
(D) Cylinder, truncated pyramid and prism.
(E) Cylinder, prism and truncated cone.

Playing cards is an activity that stimulates reasoning. A traditional game is Solitaire, which uses 52 cards. Initially seven columns are formed with the cards. The first column has one card, the second has two cards, the third has three cards, the fourth has four cards, and so on until the seventh column, which has seven cards, and what remains forms the stock, which are the cards not used in the columns.
The number of cards that forms the stock is
(A) 21.
(B) 24.
(C) 26.
(D) 28.
(E) 31.

The graph shows the variation in the average extent of sea ice, in millions of square kilometers, comparing data from the years 1995, 1998, 2000, 2005 and 2007. The data correspond to the months of June to September. The Arctic begins to recover ice when summer ends, in mid-September. Sea ice acts as Earth's cooling system, reflecting almost all sunlight back into space. Dark ocean waters, in turn, absorb sunlight and reinforce Arctic warming, causing increasing melting of ice.
Based on the graph and the information in the text, it is possible to infer that there was greater global warming in
(A) 1995.
(B) 1998.
(C) 2000.
(D) 2005.
(E) 2007.

In plastic arts exhibitions, it is common for statues to be displayed on rotating platforms. A safety measure is that the base of the sculpture is fully supported on the platform. To provide the appropriate equipment, in the case of a square base that will be fixed on a circular platform, the technical assistant of the event must estimate the measure $R$ of the appropriate radius for the platform in terms of the measure $L$ of the side of the statue's base.
What relationship between $R$ and $L$ should the technical assistant present so that the safety requirement is met?
(A) $\mathrm{R} \geq L/\sqrt{2}$
(B) $\mathrm{R} \geq 2L/\pi$
(C) $\mathrm{R} \geq L/\sqrt{\pi}$
(D) $\mathrm{R} \geq L/2$
(E) $\mathrm{R} \geq L/(2\sqrt{2})$

The globe of death is an attraction widely used in circuses. It consists of a kind of cage in the shape of a spherical surface made of steel, where motorcyclists ride their motorcycles inside.
In Figure 2, point A is on the ground plane where the globe of death is placed and segment AB passes through the center of the sphere and is perpendicular to the ground plane. Suppose there is a light source directed at the ground placed at point B and that a motorcyclist makes a path inside the sphere, traveling a circle that passes through points A and B.
The image of the path made by the motorcyclist on the ground plane is best represented by
(A) [figure A]
(B) [figure B]
(C) [figure C]
(D) [figure D]
(E) [figure E]

In a project for the electrical part of a residential building to be constructed, it states that outlets should be placed at $0.20\mathrm{~m}$ above the floor, while light switches should be placed at $1.47\mathrm{~m}$ above the floor. A wheelchair user, a potential buyer of an apartment in this building, upon seeing such measurements, alerts to the fact that they will not meet their needs. The reference heights (in meters) for activities that do not require the use of force are shown in the following figure.
A substitute proposal, regarding the heights of outlets and switches, respectively, that will meet that potential buyer is
(A) $0.20\mathrm{~m}$ and $1.45\mathrm{~m}$.
(B) $0.20\mathrm{~m}$ and $1.40\mathrm{~m}$.
(C) $0.25\mathrm{~m}$ and $1.35\mathrm{~m}$.
(D) $0.25\mathrm{~m}$ and $1.30\mathrm{~m}$.
(E) $0.45\mathrm{~m}$ and $1.20\mathrm{~m}$.

A survey conducted by students from the Faculty of Statistics shows, in hours per day, how young people between 12 and 18 years old spend their time, both during the week (Monday to Friday) and on weekends (Saturday and Sunday). The following table illustrates the results of the survey.

Youth Routine	During the week	On weekends
Watching television	3	3
Household activities	1	1
School activities	5	1
Leisure activities	2	4
Rest, hygiene and eating	10	12
Other activities	3	3

According to this survey, how many hours of their time does a young person between 12 and 18 years old spend in the entire week (Monday to Sunday) on school activities?
(A) 20
(B) 21
(C) 24
(D) 25
(E) 27

A certain salesman has their monthly salary calculated as follows: they earn a fixed amount of $\mathrm{R}\$ 750.00$, plus a commission of $\mathrm{R}\$ 3.00$ for each product sold. If they sell more than 100 products, their commission becomes $\mathrm{R}\$ 9.00$ for each product sold, starting from the $101^{\circ}$ product sold.
With this information, the graph that best represents the relationship between salary and the number of products sold is
(A) [graph A]
(B) [graph B]
(C) [graph C]
(D) [graph D]
(E) [graph E]

A train driver earns $\mathrm{R}\$ 100.00$ per trip and can only travel every 4 days. They only earn if they make the trip and know that they will be on vacation from June $1^{\circ}$ to 10, when they cannot travel. Their first trip took place on January first. Consider that the year has 365 days.
If the train driver wants to earn the maximum possible, how many trips will they need to make?
(A) 37
(B) 51
(C) 88
(D) 89
(E) 91

Some objects, during their manufacture, need to go through a cooling process. For this to occur, a factory uses a cooling tank, as shown in the figure.
What would happen to the water level if we placed an object in the tank whose volume was $2400\mathrm{~cm}^{3}$?
(A) The level would rise $0.2\mathrm{~cm}$, making the water $20.2\mathrm{~cm}$ high.
(B) The level would rise 1 cm, making the water 21 cm high.
(C) The level would rise 2 cm, making the water 22 cm high.
(D) The level would rise 8 cm, causing the water to overflow.
(E) The level would rise 20 cm, causing the water to overflow.

Jorge wants to install heaters in his beauty salon to improve the comfort of his clients in winter. He studies the purchase of units of two types of heaters: model A, which consumes $600\mathrm{~g}/\mathrm{h}$ (grams per hour) of propane gas and covers $35\mathrm{~m}^{2}$ of area, or model B, which consumes $750\mathrm{~g}/\mathrm{h}$ of propane gas and covers $45\mathrm{~m}^{2}$ of area. The manufacturer indicates that the heater should be installed in an environment with an area smaller than its coverage area. Jorge will install one unit per environment and wants to spend the minimum possible on gas. The area of the salon that should be climatized is found in the following plan (environments represented by three rectangles and a trapezoid).
Evaluating all the information, it will be necessary
(A) four units of type A and no units of type B.
(B) three units of type A and one unit of type B.
(C) two units of type A and two units of type B.
(D) one unit of type A and three units of type B.
(E) no units of type A and four units of type B.

To decorate the facade of a building, an architect designed the placement of stained glass windows composed of squares with side measuring 1 m, as shown in the following figure.
In this figure, points A, B, C and D are midpoints of the sides of the square and segments AP and QC measure $1/4$ of the side length of the square. To make a stained glass window, two types of materials are used: one for the shaded part of the figure, which costs $\mathrm{R}\$ 30.00$ per $\mathrm{m}^{2}$, and another for the lighter part (regions ABPDA and BCDQB), which costs $\mathrm{R}\$ 50.00$ per $\mathrm{m}^{2}$.
According to these data, what is the cost of materials used in the manufacture of a stained glass window?
(A) $\mathrm{R}\$ 22.50$
(B) $\mathrm{R}\$ 35.00$
(C) $\mathrm{R}\$ 40.00$
(D) $\mathrm{R}\$ 42.50$
(E) $\mathrm{R}\$ 45.00$

João decided to hire the services of a company by phone through the SAC (Customer Service). The attendant dictated the call protocol number to João and asked him to write it down. However, João did not understand one of the digits dictated by the attendant and wrote down the number $\underline{1}\underline{3}\,\_\,\underline{9}\underline{2}\underline{0}\underline{7}$, with the empty space being the digit that João did not understand.
According to this information, the position occupied by the missing digit in the protocol number is that of
(A) hundreds.
(B) tens of thousands.
(C) hundreds of thousands.
(D) millions.
(E) hundreds of millions.