# Curso

**¿Cómo funciona?**

En esta página encontrarás los módulos ordenados por temas. La mayoría tiene un video con la materia, un fichero PDF con material y/o varios ejercicios y un video con las explicaciones de los ejercicios.

Empieza por la parte de las "operaciones" si necesitas recordar cómo hacer operaciones sin una calculadora.

**Escoge uno de los temas siguientes.**

Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 120 sandwiches were made, how many bologna sandwiches were made?

A. 15

B. 30

C. 38

D. 42

E. 48

If Lisa walks t blocks in 3 minutes, how many minutes will it take her to walk s blocks at the same rate?

A. s/3t

B. 3s/t

C. 3/st

D. 3t/s

E. t/3s

At a certain photography store, it costs Pete $1.65 for the first print and $0.85 for each additional print. How many prints of a particular photography can Pete get for $20.00?

A. 19

B. 20

C. 21

D. 22

E. 24

The sum of three consecutive integers is 312. What is the sum of the next three consecutive integers?

A. 315

B. 321

C. 330

D. 415

E. 424

What is the selling price of a radio after its original price is reduced by 20 percent?

(1) The price before the reduction was $120

(2) The price after the reduction is $24 less than the price before the reduction

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D. If either statement BY ITSELF is sufficient to answer the question

E. If statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

In a state lottery, 40 percent of the money collected goes towards education. If during a certain week 6.4 million dollars were obtained for education, how much money was collected in the lottery during that week, in millions of dollars?

A. 25.6

B. 16.0

C. 8.96

D. 8.0

E. 2.56

A man bought 10 crates of oranges for $80 total. If he lost 2 of the crates, at what price would he have to sell each of the remaining crates in order to earn a total profit of 25 percent of the total cost?

A. $10.00

B. $12.50

C. $15.00

D. $100.00

E. $120.00

A supply of sugar lasts for 30 days. If its use is increased by 50%, how many days would the same amount of sugar last?

A. 15

B. 20

C. 25

D. 30

E. 45

Medical analysts predict that one-third of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?

A. 16/81

B. 8/27

C. 2/3

D. 19/27

E. 1/27

A box with water has two leaks. The first leak by itself makes the box empty in 9 minutes. The second leak by itself would make the box empty in 6 minutes. How long will it take for both leaks together to make the box empty?

A. 2.2 minutes

B. 3.6 minutes

C. 4.4 minutes

D. 5.5 minutes

E. 10 minutes

Is ∆ABC a right triangle?

(1) The degree measure of angle A is equal to the sum of the degree measures of angles B and C

(2) The degree measure of angle C is 45º

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D. If either statement BY ITSELF is sufficient to answer the question.

E. If statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A. -25

B. -3

C. -1

D. 1

E. 25

A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

A 3

B 4

C 6

D 8

E 9

If 3M / 2N = 0.125, what is the value of N in terms of M?

A. M / 8

B. 8 / M

C. 4 M

D. 8 M

E. 12 M

A car travels from City A to City B, a distance of 120km, at the average rate of 96 km per hour. The car then travels back to City A. The total traveling time of the car is 2 hours and 45 minutes. What was the average rate of speed of the car on the return trip to City A?

A. 115 km/h

B. 100 km/h

C. 96 km/h

D. 80 km/h

E. 75 km/h

A box with water has two leaks. The first leak by itself makes the box empty in 9 minutes. The second leak by itself would make the box empty in 6 minutes. How long will it take for both leaks together to make the box empty?

A. 2.2 minutes

B. 3.6 minutes

C. 4.4 minutes

D. 5.5 minutes

E. 10 minutes

A chemist has 10 liters of a solution that is 10 percent nitric acid by volume. He wants to dilute the solution to 4 percent strength by adding water. How many liters of water must he add?

A. 15

B. 18

C. 20

D. 25

E. 26

During the past week, a local medical clinic tested N individuals for two infections. If 1/3 of those tested had infection A and, of those with infection A, 1/5 also had infection B, how many individuals did not have both infection A and B?

A. N/15

B. 4N/15

C. N/5

D. 14N/15

E. 4N/5

Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?

A. y + 3z

B. (y +z) / 4

C. 2y + 3z

D. 3y + z

E. 3y + 4.5z

A farm has only ducks and horses. When the owner counted the heads of the stock in the farm, the number totaled up to 200. However, when the number of legs was counted, the number totaled up to 540. How many ducks were there in the farm?

A. 60

B. 70

C. 80

D. 120

E. 130

During the past week, a local medical clinic tested N individuals for two infections. If 1/3 of those tested had infection A and, of those with infection A, 1/5 also had infection B, how many individuals did not have both infection A and B?

A. N/15

B. 4N/15

C. N/5

D. 14N/15

E. 4N/5

Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?

A. y + 3z

B. (y +z) / 4

C. 2y + 3z

D. 3y + z

E. 3y + 4.5z

Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6

B. 8

C. 10

D. 12

E. 15

Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many of the animals are cows?

(1) The farm has more than twice as many cows as pigs

(2) The farm has more than 12 pigs

A. If you can get the answer from (1) ALONE but not from (2) alone

B. If you can get the answer from (2) ALONE but not from (1) alone

C. If you can get the answer from BOTH (1) and (2) TOGETHER but not from (1) alone or (2) alone

D. If EITHER statement (1) ALONE OR statement (2) ALONE suffices

E. If you CANNOT get the answer from statements (1) and (2) TOGETHER but need even more data

If the average (arithmetic mean) of four different numbers is 30, how many of the numbers are greater than 30?

(1) None of the four numbers is greater than 60.

(2) Two of the four numbers are 9 and 10, respectively.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D. If either statement BY ITSELF is sufficient to answer the question

E. If statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

If an item which ordinarily costs $90 is discounted by 25%, what is the new selling price?

A. $22.50

B. $25.00

C. $45.00

D. $67.50

E. $112.50

James’s library contains only reference, biography, and fiction books in the ratio of 1:2:7, respectively. If James’s library contains 30 books, how many biographies does he own?

A. 2

B. 3

C. 4

D. 6

E. 10

After installing a powerful pump onto a large gasoline tank, John pumped gasoline out of the tank. Each time John ran the pump, it removed 1/3 of the gas remaining in the tank. Assuming the gas tank was full when John began, what fraction of the total gas in the tank at the beginning was removed if John ran the pump three times?

A. 8/27

B. 1/27

C. 2/3

D. 19/27

E. 27/28

Pumps A, B, and C operate at their respective constant rates. Pumps A & B, operating simultaneously, can fill a certain tank in 6/5 hours; Pumps A & C, operating simultaneously, can fill the tank in 3/2 hours, and pumps B & C, operating simultaneously can fill the tank in 2 hours. How many hours does it take pumps A, B, & C, operating simultaneously, to fill the tank?

A. 1/3

B. 1/2

C. 1/4

D. 1

E. 5/6

A sink contains exactly 12 liters of water. If water is drained from the sink until it holds exactly 6 liters of water less than the quantity drained away, how many liters of water were drained away?

A. 2

B. 3

C. 4.5

D. 6

E. 9

Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 50% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?

A. 60%

B. 50%

C. 25%

D. 15%

E. 10%

If Lisa walks t blocks in 3 minutes, how many minutes will it take her to walk s blocks at the same rate?

A. s / (3t)

B. 3s / t

C. 3 / st

D. 3t / s

E. t / 3s

If z is an integer, is z prime?

(1) z is greater than 15!

(2) 17! + 2 ≤ z ≤ 17! + 17

A. If you can get the answer from (1) ALONE but not from (2) alone

B. If you can get the answer from (2) ALONE but not from (1) alone

C. If you can get the answer from BOTH (1) and (2) TOGETHER but not from (1) alone or (2) alone

D. If EITHER statement (1) ALONE OR statement (2) ALONE suffices

E. If you CANNOT get the answer from statements (1) and (2) TOGETHER but need even more data

When travelling in a foreign country, one should always «keep their passport with them at all times».

(A) their passport with them at all times

(B) one's passport with them at all times

(C) one's passport close by at all times

(D) one's passport constantly with them

(E) his passport with him constantly

What fraction of the boys and girls at a school are girls?

(1) The ratio of boys to girls in school is 4:5.

(2) The number of girls is 25% larger than the number of boys in school.

Since its invention in the 1940s, radiocarbon dating, which helps scientists in calculating the age of organic material, revolutionized archaeology and geology.

A) Since its invention in the 1940s, radiocarbon dating, which helps scientists in calculating the age of organic material, revolutionized archaeology and geology.

B) Radiocarbon dating, since its invention in the 1940s, helps scientists in calculating the age of organic material, revolutionizing archaeology and geology.

C) Revolutionizing archaeology and geology since its invention in the 1940s, radiocarbon dating, which helps scientists in calculating the age of organic material.

D) Since its invention in the 1940s, radiocarbon dating has revolutionized archaeology and geology, helping scientists in calculating the age of organic material.

E) Radiocarbon dating, from its invention in the 1940s, has helped scientists in calculating the age of organic material, and in revolutionizing archaeology and geology.

A and B form 1/2 of the square, while C and D form the other 1/2 of the square. The area of A is 1/2 the area of B, while the area of C is 2/5 the area of D. What fraction of the square is the area of C?

A. 1/9

B. 1/8

C. 1/7

D. 1/6

E. 1/5

Team A played 3 matches against team B and scored an average of 42 points per match. Then team A played 5 matches against team C with an average of 38 points scored per match. What will be Team A’s average points scored per match for all 8 matches?

A. 38.5

B. 39

C. 39.5

D. 40

E. 40.5