A formica factory produces square plates with sides measuring $y$ centimetres. These plates are sold in boxes with $N$ units and, on the box, the maximum area $S$ that can be covered by the $N$ plates is specified.
Due to market demand for larger plates, the factory tripled the measurement of the sides of its plates and managed to gather them in a new box, in such a way that the covered area $S$ was not altered.
The quantity $X$, of plates of the new model, in each new box will be equal to:
(A) $\frac{N}{9}$ (B) $\frac{N}{6}$ (C) $\frac{N}{3}$ (D) $3N$ (E) $9N$

In a water park there is a children's pool in the shape of a right circular cylinder, 1 m deep and with a volume equal to $12 \mathrm{~m}^{3}$, whose base has radius $\mathbf{R}$ and centre $\mathbf{O}$. It is desired to build a dry leisure island inside this pool, also in the shape of a right circular cylinder, whose base will be at the bottom of the pool and with the centre of the base coinciding with the centre of the bottom of the pool, as shown in the figure. The radius of the leisure island will be $r$. It is desired that after the construction of this island, the space intended for water in the pool has a volume of at least $4 \mathrm{~m}^{3}$.
Consider 3 as an approximate value for $\pi$.
To satisfy the given conditions, the maximum radius of the leisure island $\mathbf{r}$, in metres, will be closest to
(A) 1.6. (B) 1.7. (C) 2.0. (D) 3.0. (E) 3.8.

The taxpayer who sells more than $\mathrm{R}\$ 20$ thousand of shares on the Stock Exchange in a month must pay Income Tax. Payment to the Federal Revenue Service will consist of 15\% of the profit obtained from the sale of shares.
A taxpayer who sells for $\mathrm{R}\$ 34$ thousand a batch of shares that cost $\mathrm{R}\$ 26$ thousand will have to pay Income Tax to the Federal Revenue Service in the amount of
(A) $\mathrm{R}\$ 900{,}00$. (B) $\mathrm{R}\$ 1\,200{,}00$. (C) $\mathrm{R}\$ 2\,100{,}00$. (D) $\mathrm{R}\$ 3\,900{,}00$. (E) $\mathrm{R}\$ 5\,100{,}00$.

To build a screed, it is common, in the composition of concrete, to use cement, sand and gravel in the following proportion: 1 part cement, 4 parts sand and 2 parts gravel. To build the screed for a garage, a construction company ordered a concrete mixer truck with $14 \mathrm{~m}^{3}$ of concrete.
What is the volume of cement, in $\mathrm{m}^{3}$, in the load of concrete brought by the mixer?
(A) 1.75 (B) 2.00 (C) 2.33 (D) 4.00 (E) 8.00

It is desired to mail non-commercial letters, being two of 100 g, three of 200 g and one of 350 g. The graph shows the cost to send a non-commercial letter by the Postal Service.
The total amount spent, in reais, to mail these letters is
(A) 8.35. (B) 12.50. (C) 14.40. (D) 15.35. (E) 18.05.

To increase sales at the beginning of the year, a department store remarked the prices of its products 20\% below the original price. When they reach the checkout, customers who have the store's loyalty card are entitled to an additional discount of 10\% on the total value of their purchases.
A customer wishes to buy a product that cost $\mathrm{R}\$ 50{,}00$ before the price remarking. He does not have the store's loyalty card.
If this customer had the store's loyalty card, the additional savings he would obtain when making the purchase, in reais, would be
(A) 15.00. (B) 14.00. (C) 10.00. (D) 5.00. (E) 4.00.

An image editing program makes it possible to transform figures into more complex ones. It is desired to construct a new figure from the original. The new figure must present symmetry with respect to point $O$.
The image that represents the new figure is:
(A), (B), (C), (D), (E) [as shown in the figures]

Ceramics constitute an artefact quite present in the history of humanity. One of its various properties is shrinkage (contraction), which consists of the evaporation of water existing in a ceramic set or block when subjected to a certain elevated temperature. This elevation of temperature, which occurs during the firing process, causes a reduction of up to 20\% in the linear dimensions of a piece.
Suppose that a piece, when moulded in clay, had a rectangular base whose sides measured 30 cm and 15 cm. After firing, these sides were reduced by 20\%.
In relation to the original area, the area of the base of this piece, after firing, was reduced by
(A) $4\%$. (B) $20\%$. (C) $36\%$. (D) $64\%$. (E) $96\%$.

In the United States the unit of volume measurement most used in soft drink cans is the fluid ounce (fl oz), which is equivalent to approximately 2.95 centiliters (cL).
It is known that the centiliter is one hundredth of a liter and that the soft drink can usually sold in Brazil has a capacity of 355 mL.
Thus, the volume measurement of the 355 mL soft drink can, in fluid ounces (fl oz), is closest to
(A) 0.83. (B) 1.20. (C) 12.03. (D) 104.73. (E) 120.34.

The figure presents two maps, in which the state of Rio de Janeiro is seen at different scales.
There is interest in estimating the number of times the area corresponding to this state was enlarged in the Brazil map.
This number is
(A) less than 10. (B) greater than 10 and less than 20. (C) greater than 20 and less than 30. (D) greater than 30 and less than 40. (E) greater than 40.

A baker, specialist in making cakes, uses a mold in the format represented in the figure.
In it one can identify the representation of two three-dimensional geometric figures.
These figures are
(A) a truncated cone and a cylinder. (B) a cone and a cylinder. (C) a truncated pyramid and a cylinder. (D) two truncated cones. (E) two cylinders.

The crossing of the quantity of hours studied with performance in the International Student Assessment Program (Pisa) shows that more time in school is not a guarantee of above-average grades.
Among countries with grades below the average in this exam, the one that presents the greatest quantity of study hours is
(A) Finland. (B) Netherlands. (C) Israel. (D) Mexico. (E) Russia.

A restaurant uses, to serve beverages, trays with square bases. All glasses in this restaurant have the format represented in the figure.
Consider that $\overline{AC} = \frac{7}{5}\overline{BD}$ and that $l$ is the measure of one of the sides of the base of the tray.
What should be the smallest value of the ratio $\frac{l}{d}$ for a tray to have the capacity to carry exactly four glasses at once?
(A) 2 (B) $\frac{14}{5}$ (C) 4 (D) $\frac{24}{5}$ (E) $\frac{28}{5}$

The owner of a property intends to place a support rod to better secure two posts of equal lengths of 6 m and 4 m. The figure represents the real situation in which the posts are described by segments $AC$ and $BD$ and the rod is represented by segment $EF$, all perpendicular to the ground, which is indicated by the line segment $AB$. The segments $AD$ and $BC$ represent steel cables that will be installed.
What should be the value of the length of the rod $EF$?
(A) 1 m (B) 2 m (C) $2.4 \text{ m}$ (D) 3 m (E) $2\sqrt{6} \text{ m}$

A seesaw is a toy that consists of a long and narrow board balanced and fixed at its central point (pivot). In this toy, two people sit at the ends and, alternately, push themselves upward, causing the opposite end to descend, thus performing the seesaw movement.
Consider the seesaw represented in the figure, in which points $A$ and $B$ are equidistant from the pivot.
The orthogonal projection of the trajectory of points $A$ and $B$, on the plane of the seesaw ground, when it is in motion, is:
(A), (B), (C), (D), (E) [as shown in the figures]

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 138
A survey was conducted with 200 people about their preference for a type of music. The results are shown in the table below:

Type of music	Number of people
Rock	80
Pop	60
Samba	40
Other	20

The percentage of people who prefer Rock is
(A) $20\%$
(B) $30\%$
(C) $40\%$
(D) $50\%$
(E) $60\%$

QUESTION 139
A rectangular piece of land has dimensions 30 m by 20 m. The owner wants to build a fence around the entire perimeter of the land. If the fence costs R\$ 15.00 per meter, the total cost of the fence will be
(A) R\$ 900.00
(B) R\$ 1,200.00
(C) R\$ 1,500.00
(D) R\$ 1,800.00
(E) R\$ 2,100.00

QUESTION 140
The graph below shows the evolution of the price of a product over 5 months.
[Figure]
Based on the graph, the percentage increase in the price of the product from the first to the fifth month is
(A) $20\%$
(B) $25\%$
(C) $40\%$
(D) $50\%$
(E) $60\%$

QUESTION 141
A cylindrical tank has a base radius of 2 m and a height of 5 m. The volume of this tank, in cubic meters, is
(A) $10\pi$
(B) $15\pi$
(C) $20\pi$
(D) $25\pi$
(E) $30\pi$

QUESTION 143
A car travels at a constant speed of 90 km/h. The time, in hours, for this car to travel 270 km is
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

QUESTION 144
The sum of the interior angles of a hexagon is
(A) $540^\circ$
(B) $600^\circ$
(C) $660^\circ$
(D) $720^\circ$
(E) $780^\circ$

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 150
In a right triangle, one leg measures 6 cm and the hypotenuse measures 10 cm. The other leg measures
(A) 4 cm
(B) 6 cm
(C) 7 cm
(D) 8 cm
(E) 9 cm