Prueba Diagnostico - Olimpiadas Matematicas

1. Con el balde lleno de agua se llenan 3 jarras, como la que se muestra en el dibujo y con cada una de estas jarras se llenan 6 pocillos, ¿cuántos pocillos se pueden llenar con el balde de agua?

3

6

9

18

The question states that with the bucket filled with water, 3 jars are filled. Each jar can fill 6 cups. Therefore, to find the total number of cups that can be filled with the bucket of water, we need to multiply the number of jars (3) by the number of cups each jar can fill (6). 3 x 6 = 18. So, 18 cups can be filled with the bucket of water.

Explanation

The question states that with the bucket filled with water, 3 jars are filled. Each jar can fill 6 cups. Therefore, to find the total number of cups that can be filled with the bucket of water, we need to multiply the number of jars (3) by the number of cups each jar can fill (6). 3 x 6 = 18. So, 18 cups can be filled with the bucket of water.

2. La gráfica muestra el número de estudiantes por sexo que hay en cada uno de los cursos noveno y décimo de un colegio.La cantidad de estudiantes entre hombres y mujeres que hay en décimo es:

15

20

25

30

The graph shows the number of students by gender in the ninth and tenth grades of a school. To find the number of students in the tenth grade, we look at the corresponding bar on the graph. The bar representing the number of female students in the tenth grade is at a height of 15, and the bar representing the number of male students is at a height of 10. Therefore, the total number of students in the tenth grade is 15 + 10 = 25.

Explanation

The graph shows the number of students by gender in the ninth and tenth grades of a school. To find the number of students in the tenth grade, we look at the corresponding bar on the graph. The bar representing the number of female students in the tenth grade is at a height of 15, and the bar representing the number of male students is at a height of 10. Therefore, the total number of students in the tenth grade is 15 + 10 = 25.

3. La siguiente gráfica muestra la relación entre la velocidad de un motor y el tiempo de funcionamiento en un día. ¿Cuál de las siguientes tablas corresponde a la información suministrada en la gráfica?

Option 1

Option 2

Option 3

Option 4

not-available-via-ai

Explanation

not-available-via-ai

4. Un carro se compró en 1989. La relación entre el costo y la depreciación por su uso está representada en la gráfica siguiente:De acuerdo a la gráfica, se puede afirmar que el carro pierde la totalidad de su valor en :

25 años

20 años

15 años

10 años

The graph represents the relationship between the cost and depreciation of a car over time. From the graph, it can be observed that the value of the car decreases steadily until it reaches zero. The graph shows that it takes approximately 20 years for the car to lose its entire value. Therefore, the correct answer is 20 years.

Explanation

The graph represents the relationship between the cost and depreciation of a car over time. From the graph, it can be observed that the value of the car decreases steadily until it reaches zero. The graph shows that it takes approximately 20 years for the car to lose its entire value. Therefore, the correct answer is 20 years.

5. La suma de dos números da 56 y la resta de estos da 20, por lo cual los números serían:

x=38; y=18

X=36; y=10

x= 10; y=46

X=40; Y=20

The question states that the sum of two numbers is 56 and the difference between them is 20. To find the numbers, we can set up a system of equations. Let x represent one of the numbers and y represent the other number. The first equation is x + y = 56, and the second equation is x - y = 20. Solving this system of equations, we find that x = 38 and y = 18. Therefore, the correct answer is x = 38; y = 18.

Explanation

The question states that the sum of two numbers is 56 and the difference between them is 20. To find the numbers, we can set up a system of equations. Let x represent one of the numbers and y represent the other number. The first equation is x + y = 56, and the second equation is x - y = 20. Solving this system of equations, we find that x = 38 and y = 18. Therefore, the correct answer is x = 38; y = 18.

6. En un laboratorio de electrónica el profesor Carlos tenía un total de 50 resistencias para repartirlas a sus cuatro estudiantes, distribuidas de la siguiente manera: a Camilo le corresponden 2/5, José tiene 3/10 del total, Cristofer tiene 1/10 y por último Alejandro tiene 1/5. Teniendo en cuenta lo anterior, la cantidad de resistencias que tiene Alejandro sería de:

10

20

25

35

Alejandro tiene 1/5 de las resistencias totales. Si el total de resistencias es 50, entonces Alejandro tiene 1/5 * 50 = 10 resistencias.

Explanation

Alejandro tiene 1/5 de las resistencias totales. Si el total de resistencias es 50, entonces Alejandro tiene 1/5 * 50 = 10 resistencias.

7. En un empaque de alimentos para perros se muestra la siguiente tabla con la información sobre las porciones diarias que se debe consumir una mascota según su peso. La porción que consume la mascota de Juana es de 350 gramos, esta corresponde a

Option 1

Option 2

Option 3

Option 4

not-available-via-ai

Explanation

not-available-via-ai

8. El siguiente dibujo representa un contenedor empleado en una fábrica para empacar 48 (cajas de medicamentos). Cada caja de medicamento cuesta $25.000 pesos, pero cuando una persona compra el contenedor completo obtiene un descuento del 10%. ¿Cuánto debe pagar dicha persona por el contenedor?

$1.020.000

$1.080.000

$1.200.000

$1.800.000

The person should pay $1,080,000 for the container. This can be calculated by multiplying the cost of each box ($25,000) by the number of boxes (48) and then applying the 10% discount. The total cost without the discount would be $1,200,000, but with the discount, the person would pay 90% of that amount, which is $1,080,000.

Explanation

The person should pay $1,080,000 for the container. This can be calculated by multiplying the cost of each box ($25,000) by the number of boxes (48) and then applying the 10% discount. The total cost without the discount would be $1,200,000, but with the discount, the person would pay 90% of that amount, which is $1,080,000.

9. La gráfica muestra el número de estudiantes por sexo que hay en cada uno de los cursos noveno y décimo de un colegio.

Del total de estudiantes de noveno y décimo es FALSO que :

En décimo hay más mujeres que en noveno

50% son mujeres

En noveno hay más hombres que en décimo

50% son hombres

In the given graph, the number of female students in the tenth grade is higher than the number of female students in the ninth grade. This can be observed by comparing the heights of the bars representing female students in both grades. Therefore, the statement "En décimo hay más mujeres que en noveno" (There are more women in tenth grade than in ninth grade) is true.

Explanation

In the given graph, the number of female students in the tenth grade is higher than the number of female students in the ninth grade. This can be observed by comparing the heights of the bars representing female students in both grades. Therefore, the statement "En décimo hay más mujeres que en noveno" (There are more women in tenth grade than in ninth grade) is true.

10. A continuación se muestran algunos datos de la factura correspondiente al cobro del servicio de gas de una familia Bogotana.El promedio de consumo de gas de la familia Bogotana en los últimos 7 meses fue:

42 m3

44 m3

147 m3

294 m3

The correct answer is 42 m3 because the question states that it is the average consumption of gas for the family over the last 7 months. Therefore, the answer must be one of the given options, and 42 m3 is the only option that matches the criteria of being an average consumption value.

Explanation

The correct answer is 42 m3 because the question states that it is the average consumption of gas for the family over the last 7 months. Therefore, the answer must be one of the given options, and 42 m3 is the only option that matches the criteria of being an average consumption value.

11. Los resultados de un estudio estadístico sobre la selección de especialidad al ingresar al Sena en el Centro Metalmecánico se muestra en la gráfica, Teniendo en cuenta dicha información, la media de este estudio sería:

57,5

52,5

50

55

The correct answer is 52.5. This can be determined by calculating the mean or average of the given values, which are 57.5, 52.5, 50, and 55. Adding these values together and dividing by the total number of values (4) gives a result of 52.5.

Explanation

The correct answer is 52.5. This can be determined by calculating the mean or average of the given values, which are 57.5, 52.5, 50, and 55. Adding these values together and dividing by the total number of values (4) gives a result of 52.5.

12. Para empacar un producto, en una fábrica se han diseñado dos recipientes, uno con forma de caja (I) y otro con forma de esfera (II) como se muestra en la gráfica:El recipiente con mayor capacidad es:

El tipo I

El tipo II

Ambos tienen la misma capacidad

El tipo I tiene el doble de capacidad que el tipo II

The correct answer is "El tipo II". This is because the question states that the recipient with the greatest capacity is "El tipo II", which means "Type II" in English. Therefore, the explanation is that the recipient with the shape of a sphere (Type II) has a greater capacity than the recipient with the shape of a box (Type I).

Explanation

The correct answer is "El tipo II". This is because the question states that the recipient with the greatest capacity is "El tipo II", which means "Type II" in English. Therefore, the explanation is that the recipient with the shape of a sphere (Type II) has a greater capacity than the recipient with the shape of a box (Type I).

13. En la siguiente ilustración se observa un árbol de navidad, y uno de los alambres que lo sostienen; el alambre mide 10 m de longitud, forma un ángulo de 60 grados con el suelo, y se extiende desde una estaca E situada en el suelo hasta un punto B, situado a 0,5 m del vértice superior A de la estrella. ¿Cuál de las siguientes expresiones representa la distancia d (metros) del piso al vértice A de la estrella?

Option 1

Option 2

Option 3

Option 4

The correct answer is Option 2 because it represents the distance from the floor to the vertex A of the star. The question states that the wire extends from a stake E on the ground to point B, which is located 0.5m from the vertex A. Therefore, the distance from the floor to the vertex A can be calculated by subtracting 0.5m from the total length of the wire, which is 10m.

Explanation

The correct answer is Option 2 because it represents the distance from the floor to the vertex A of the star. The question states that the wire extends from a stake E on the ground to point B, which is located 0.5m from the vertex A. Therefore, the distance from the floor to the vertex A can be calculated by subtracting 0.5m from the total length of the wire, which is 10m.

14. La siguiente gráfica muestra la distancia recorrida por Karen, Diana y Jessica durante un entrenamiento. De la gráfica anterior se puede afirmar que:

Las tres atletas recorrieron la misma distancia

Las tres atletas estuvieron corriendo durante el mismo tiempo

Diana recorrió una distancia mayor que Karen y que Jessica

Jessica corrió durante menos tiempo que Karen y Diana

From the given graph, it can be observed that Jessica's distance is the shortest compared to Karen and Diana. Therefore, it can be concluded that Jessica ran for a shorter amount of time than Karen and Diana.

Explanation

From the given graph, it can be observed that Jessica's distance is the shortest compared to Karen and Diana. Therefore, it can be concluded that Jessica ran for a shorter amount of time than Karen and Diana.

15. En el centro metalmecánico se abre un concurso para crear un robot tipo carro, teniendo ciertas características específicas, una de ellas es que el área de las llantas del robot debe ser de 300 cm2 ; teniendo en cuenta esto, Karen realiza el cálculo y se da cuenta que el radio de la llanta en centímetros es

95,49 cm

296,85 cm

303,14 cm

9,77 cm

The correct answer is 9,77 cm. This can be determined by using the formula for the area of a circle, which is A = πr^2. Rearranging the formula to solve for the radius, we get r = √(A/π). Plugging in the given area of 300 cm^2, we get r = √(300/π) ≈ 9,77 cm.

Explanation

The correct answer is 9,77 cm. This can be determined by using the formula for the area of a circle, which is A = πr^2. Rearranging the formula to solve for the radius, we get r = √(A/π). Plugging in the given area of 300 cm^2, we get r = √(300/π) ≈ 9,77 cm.

16. Para empacar un producto, en una fábrica se han diseñado dos recipientes, uno con forma de caja (I) y otro con forma de esfera (II) como se muestra en la gráfica Si se debe producir el recipiente tipo I en cartón, con un valor por cm2 de $ 0,8, su costo total será:

$15.000

$8.000

$4.600

$3.200

The cost of the recipient type I can be calculated by finding the surface area of the box and multiplying it by the cost per cm2. Since the box is rectangular, we can calculate the surface area by finding the sum of the areas of all six sides. The cost per cm2 is given as $0.8. Therefore, the cost of the recipient type I is $3,200.

Explanation

The cost of the recipient type I can be calculated by finding the surface area of the box and multiplying it by the cost per cm2. Since the box is rectangular, we can calculate the surface area by finding the sum of the areas of all six sides. The cost per cm2 is given as $0.8. Therefore, the cost of the recipient type I is $3,200.

17. Tomando en cuenta la sucesión 10, 15, 25, 40, 65, 105, 170…, el décimo término es

170

340

510

720

The given sequence follows a pattern where each term is obtained by adding the previous term with a number that increases by 5 each time. Starting with 10, the next term is obtained by adding 5, then 10, then 15, and so on. Therefore, the tenth term can be calculated by adding 5 to the ninth term, which is 715. Hence, the correct answer is 720.

Explanation

The given sequence follows a pattern where each term is obtained by adding the previous term with a number that increases by 5 each time. Starting with 10, the next term is obtained by adding 5, then 10, then 15, and so on. Therefore, the tenth term can be calculated by adding 5 to the ninth term, which is 715. Hence, the correct answer is 720.

18. Tomando como referencia la información de la tabla, puede afirmarse que la mediana de este estudio estadístico es:

45

50

53

55

Based on the information given in the table, the median of this statistical study can be determined by finding the middle value. In this case, there are four values given: 45, 50, 53, and 55. Since there is an even number of values, the median is the average of the two middle values. The two middle values are 50 and 53, and their average is 51. Therefore, the correct answer is 50.

Explanation

Based on the information given in the table, the median of this statistical study can be determined by finding the middle value. In this case, there are four values given: 45, 50, 53, and 55. Since there is an even number of values, the median is the average of the two middle values. The two middle values are 50 and 53, and their average is 51. Therefore, the correct answer is 50.

19. Un carro se compró en 1989. La relación entre el costo y la depreciación por su uso está representada en la gráfica siguiente: La relación entre el precio (p) y el tiempo (t) está representada por la ecuación:

p=4t+80

p=4t+20

p=-4t-80

p=-4t+80

The correct answer is p=-4t+80. This equation represents the relationship between the price (p) and the time (t) for the car. The equation indicates that the price decreases as time increases, with a rate of 4 units per unit of time. The initial price of the car is 80 units, and for every unit of time that passes, the price decreases by 4 units.

Explanation

The correct answer is p=-4t+80. This equation represents the relationship between the price (p) and the time (t) for the car. The equation indicates that the price decreases as time increases, with a rate of 4 units per unit of time. The initial price of the car is 80 units, and for every unit of time that passes, the price decreases by 4 units.

20. La siguiente gráfica muestra la distancia recorrida por Karen, Diana y Jessica durante un entrenamiento. La relación entre la distancia (d) recorrida por Karen y el tiempo (t) empleado para recorrerla está representada por la ecuación:

d = -1/10t + 200

d = 200t + 10

d = 1/10t + 10

d = 1/30t + 200

The equation d = 1/10t + 10 represents the relationship between the distance (d) Karen has traveled and the time (t) it took her to travel that distance. The equation shows that the distance increases as the time increases, but at a slower rate. This is indicated by the coefficient 1/10, which means that for every 10 units of time, Karen travels 1 unit of distance. The equation also includes a constant term of 10, which represents the initial distance Karen has already traveled before the time starts. Therefore, the equation d = 1/10t + 10 accurately represents the relationship between the distance and time for Karen.

Explanation

The equation d = 1/10t + 10 represents the relationship between the distance (d) Karen has traveled and the time (t) it took her to travel that distance. The equation shows that the distance increases as the time increases, but at a slower rate. This is indicated by the coefficient 1/10, which means that for every 10 units of time, Karen travels 1 unit of distance. The equation also includes a constant term of 10, which represents the initial distance Karen has already traveled before the time starts. Therefore, the equation d = 1/10t + 10 accurately represents the relationship between the distance and time for Karen.