brazil-enem

brazil-enem

2025 enem__day2

Papers (12)

Q139 Probability Definitions Finite Equally-Likely Probability Computation View

Four candidates presented themselves to take the exam of a competition. Before starting the exam, the cell phones of the four candidates were collected by the proctor, who stored them, each one, inside a black envelope. At the end of the exam, the proctor returned the four envelopes with the cell phones to the four candidates, in a random manner, since he had not identified the envelopes.
The probability that all candidates received back the envelopes with their respective cell phones is
(A) $\dfrac{1}{2}$
(B) $\dfrac{1}{10}$
(C) $\dfrac{1}{16}$
(D) $\dfrac{1}{24}$
(E) $\dfrac{1}{256}$

Q141 Probability Definitions Finite Equally-Likely Probability Computation View

A magazine report addressed the use of social networks by Brazilian internet users. Some of the data collected by the report are presented in the infographic.
According to the infographic data, when randomly selecting a Brazilian internet user in the period to which the report refers, the probability that he is a man who accesses some social network is
(A) $\dfrac{30}{90}$
(B) $\dfrac{36}{100}$
(C) $\dfrac{40}{100}$
(D) $\dfrac{40}{90}$
(E) $\dfrac{46}{90}$

Q150 Measures of Location and Spread View

A technology company will standardize the internet connection speed it offers to its customers in ten cities. The company's management decides that its new reference speed standard will be the median of the reference speed values of connections in these ten cities. These values, in megabytes per second (MB/s), are presented in the table.

Cities	Reference speed (MB/s)
C1	390
C2	380
C3	320
C4	390
C5	340
C6	380
C7	390
C8	400
C9	350
C10	360

The reference speed, in megabytes per second, to be adopted by this company is
(A) 360.
(B) 370.
(C) 380.
(D) 390.
(E) 400.

Q151 Circles Line Equation and Parametric Representation View

In a digital game, there are three characters: one hero and two villains. The programming is done in such a way that the hero will always be attacked by the villain closest to him. One way to ``confuse'' the villains is to move the hero along trajectories that keep him equidistant from the villains, creating uncertainty between them, and thus preventing him from being attacked.
For the programming of one of the stages of this game, the programmer considered, in the Cartesian plane, the square STUV as the region of movement of the characters, where V and $T$ represent the fixed positions of the villains, and $S$, the initial position of the hero, as shown in the figure.
What is the equation of the trajectory along which the hero can move without being attacked?
(A) $y = -3x + 20$
(B) $y = -3x + 16$
(C) $y = -3x - 20$
(D) $y = 3x + 16$
(E) $y = 3x - 16$

Q152 Data representation View

A bookstore sells books of the following literary genres: science fiction, self-help, romance, and biography. The graph presents the inventory of books that this bookstore has, by literary genre and by author's nationality, as well as the demand by literary genre, obtained through a survey conducted with its regular customers.
The bookstore manager will place an order for new copies only of the genre whose quantity in stock is insufficient to meet the demand identified by the survey.
The genre of book from which the manager should order more copies is
(A) science fiction, because it is the one with the highest demand.
(B) biography, because it is the genre with the lowest demand.
(C) self-help, because the quantity in stock is less than the demand.
(D) biography, because it is the genre with the smallest quantity of books in stock.
(E) romance, because it is the one with the smallest inventory of books by Brazilian authors.

Q153 Data representation View

A language school offers courses in English, Spanish, French, and German. The graphs present the percentage distribution of enrollments, by language, in 2023, and the distribution of the number of enrollments, by language, in 2024.
To plan the activities for 2025, the school manager estimated that the total number of enrollments will be the same as in 2024, and the percentage distribution of enrollments, by language, will be equal to that recorded in 2023.
According to this estimate, the number of enrollments in the French course for the year 2025 will be
(A) 2.
(B) 12.
(C) 20.
(D) 22.
(E) 40.

Q155 Measures of Location and Spread View

In a clinical study, 55 women were randomly distributed into 5 groups of 11 people. To test a new medication, a group will be chosen in which the majority of women are between 20 and 30 years old. The other groups will take placebo or medications already on the market. The table, partially filled, provides some data related to the ages of women in these groups.

Even with the incomplete table, it was possible to select one of these groups because, with only the data presented in the table, a group was identified that certainly met the selection criterion.
The group chosen was
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.

Q156 Measures of Location and Spread View

Pace is a term used by a runner to denote his average rhythm in a race. It represents the average time, in seconds, that this runner takes to cover 1 km.
The diagram presents the time, in seconds, that a runner took to cross the marks that define the first four 1 km sections in a 5 km race, and the time spent to cover each 1 km section.
The best pace that this runner achieved in 5 km races was $281\,\mathrm{s/km}$. For him to repeat his best pace in 5 km races in this race, his time in the $5^{\text{th}}$ section should be how many seconds less than what he spent to cover the $4^{\text{th}}$ section?
(A) 1
(B) 2
(C) 8
(D) 9
(E) 15

Q157 Permutations & Arrangements Selection and Task Assignment View

Ten couples founded a dance group and decided to establish a board of directors with three positions: president, secretary, and treasurer. For greater representation, it was decided that at most one person per couple could hold a position on this board.
How many different boards can be formed by these 10 couples?
(A) $10 \times 9 \times 8$
(B) $20 \times 18 \times 16$
(C) $20 \times 19 \times 18$
(D) $10 \times 9 \times 8 \times 2$
(E) $20 \times 18 \times 16 \times 2$

Q169 Combinations & Selection Distribution of Objects into Bins/Groups View

A father bought eight different gifts (among which, a bicycle and a cell phone) to give to his three children. He intends to distribute the gifts so that the oldest and youngest children receive three gifts each, and the middle one receives the two remaining gifts. The oldest will receive, among his gifts, either a bicycle or a cell phone, but not both.
In how many distinct ways can the distribution of gifts be made?
(A) 36
(B) 53
(C) 300
(D) 360
(E) 560

Q179 Laws of Logarithms Logarithmic Formula Application (Modeling) View

An entrepreneur uses machines whose internal pressure $P$, in atmosphere, depends on the continuous time of use $t$, in hour, and on a positive parameter $K$, which defines the model of the machine, according to the expression: $$P = 4 \cdot \log[-K \cdot (t + 1) \cdot (t - 19)]$$
The manufacturer of these machines recommends to the user that the internal pressure of this type of machine does not exceed 10 atmospheres during its operation.
The entrepreneur intends to buy new machines of this type that should operate, daily, for a continuous period of 10 hours. For this, he needs to define the model of machine to be acquired by choosing the largest possible value of the parameter $K$, in accordance with the manufacturer's recommendation. The largest value to be chosen for $K$ is
(A) $10^{0.5}$
(B) $10^{8}$
(C) $\dfrac{10^{2.5}}{84}$
(D) $\dfrac{10^{2.5}}{99}$
(E) $25 \times 10^{-2}$

Q180 Measures of Location and Spread View

The productivity of soybeans in a cultivated area is the average quantity of 50-kilogram sacks that are produced per hectare. The table presents the cultivated area and soybean productivity on a certain property, over five harvests, with periods of one year, from 2011 to 2016.

Harvest	$\mathbf{11\text{-}12}$	$\mathbf{12\text{-}13}$	$\mathbf{13\text{-}14}$	$\mathbf{14\text{-}15}$	$\mathbf{15\text{-}16}$
Cultivated area (hectare)	200	220	250	250	200
Productivity (sacks of $50\,\mathrm{kg}$ per hectare)	40	30	45	45	50

The line graph that represents the soybean production of this property, in tons, in these five harvests is
(A), (B), (C), (D), or (E) as indicated in the figures.

Minimum age

Maximum age

Standard deviation