Quant. Reasoning Test #5

A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question.

100 people were surveyed on their favorite sport to watch. How many people chose football as their favorite sport to watch? 1) The number of people who like football and the number of people who like baseball are both prime numbers 2) The number of people who like baseball and football is the same A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question. B. Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. D. Each statement alone is sufficient to answer the question. E. Statements 1) and 2) together are not sufficient to answer the question.

E. 50π

A square of side length 10 is inscribed in a circle. What is the area of the circle? A. 25π B. 30π C. 35π D. 40π E. 50π

E. 39

Carla and Alvin have a total of 120 marbles. Alvin has three more than twice the number of marbles that Carla has. How many marbles does Carla have? A. 19 B. 25 C. 28 D. 33 E. 39

E. x2 - 11x + 28

If f(x) = x(x - 3) and g(x) = (x - 4), what is f(g(x))? A. x2 - 11x - 28 B. x2 - 7x + 28 C. x2 - 7x + 12 D. x2 - 7x E. x2 - 11x + 28

E. 35

Kim is in charge of picking out tennis balls for the upcoming match. How many ways can she pick 4 tennis balls from 7 tennis balls? A. 7 B. 14 C. 21 D. 28 E. 35

E. x = 2, y = 1

Solve the following system of equations for x and y: x + y = 3 3x - y = 5 A. x = -2, y = 1 B. x = 1, y = 2 C. x = 1/2, y = 1 D. x = 2, y = -1 E. x = 2, y = 1

D.

Which of the following represents the range of x for the following equation? A. B. C. D.

C. The two quantities are equal.

a, b, and c are three consecutive integers. A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

D. $2250

A TV from Brand A costs $1500 more than a TV from Brand B. A TV from Brand A is also three times as expensive as a TV from Brand B. How much does a TV from Brand A cost? A. $750 B. $1500 C. $2150 D. $2250 E. $2500

A. 58 - 83

A distribution of test scores has the follow characteristics: Mean: 70 | Median: 74 | Standard Deviation: 10 | First Quartile: 58 | Third Quartile: 83 About 50% of the people in this sample have test scores that are in the range of: A. 58 - 83 B. 60 - 80 C. 70 - 90 D. 64 - 84 E. 60 - 85

D. 750 mL

A farmer has 4 liters of liquid fertilizer. The farmer takes the fertilizer and fills 3 bottles (150 mL each), then 8 more bottles (250 mL each), and finally 4 bottles (200 mL each). How much liquid fertilizer does the farmer have left? A. 200 mL B. 350 mL C. 600 mL D. 750 mL

D. The relationship cannot be determined from the information given.

A hotel is 10 miles from a train station. The post office is 7 miles from the train station. All three buildings are situated 100m above sea level. A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

E. 0.60

A newspaper has 1,400,000 daily readers. There are 600,000 male readers, and 800,000 female readers. 40% of the men and three-quarters of the women read the advertisements in the newspaper. What is the probability that a randomly selected reader reads the advertisements? A. 0.45 B. 0.50 C. 0.52 D. 0.55 E. 0.60

D. 216

A rectangular metal prism with a base area of 27 and a height of 8 was melted down. The molten metal was re-solidified as a cube. What is the total surface area of the cube? A. 128 B. 156 C. 200 D. 216 E. 320

C. 224/3π

A smaller concentric sphere of radius 2 is located within the center of a larger concentric sphere with a radius of 4. What is the volume of the region between the larger and smaller sphere? A. 56π B. 56 C. 224/3π D. 224/3 E. 32/2

A. Quantity A is greater.

A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

B. Quantity B is greater.

A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

B. 48 minutes

Danny takes 80 minutes to trim a hedge. Together, Danny and William can trim a hedge in only 30 minutes. How long does it take for William to trim the hedge alone? A. 40 minutes B. 48 minutes C. 60 minutes D. 72 minutes E. 80 minutes

D.

Factor the following expression: A. B. C. D.

C. 360

How many 4-digit PINS can be made from the digits 4, 5, 6, 7, 8, and 9 if each digit is to be used only once? A. 120 B. 240 C. 360 D. 720 E. 1296

D. 3

How many roots are greater than -1 in the following equation: x3 - 3x2 + 2x = 0 A. 0 B. 1 C. 2 D. 3 E. 4

B. $8.92

If $1 US dollar is equivalent to $1.30 Canadian dollars and $1 US dollar is equivalent to $1.45 Australian dollars, how many Australian dollars are equivalent to $8 Canadian dollars? (Answers are given in Australian dollars) A. $7.17 B. $8.92 C. $9.45 D. $14.00 E. $15.08

D. 1:10,000

If all the lengths of the sides of a rectangular prism are scaled up 22 times to create a new rectangular prism, approximately, what is the ratio of the volume of the original prism to the volume of the new prism? A. 1:10 B. 1:100 C. 1:1,000 D. 1:10,000

D. 7

In a basket, there are 8 oranges, 6 apples, and an unknown number of pears. If the probability of picking a pear is one-third, how many pears are in the basket? A. 3 B. 5 C. 6 D. 7

B. 34%

In a survey conducted by a major clothing retailer, its consumers own a mean number of 5 pairs of jeans, with a standard deviation of 1 pairs of jeans. The data is normally distributed. What percentage of the consumers own between 4 and 5 pairs of jeans? A. 25% B. 34% C. 50% D. 68% E. Answer cannot be determined

B. 420

In how many unique ways can the seven letters in the word MINIMUM be arranged, if all the letters are used each time? A. 210 B. 420 C. 840 D. 1008 E. 5040

C. 5:00 pm

John drives from City A to City B at a speed of 90 mph. Two hours later, at 11:00 am, Tom also starts driving from City A to City B, but at a speed of 120 mph. If John and Tom both arrive at the same time, what time do they arrive? A. 3:00 pm B. 4:00 pm C. 5:00 pm D. 6:00 pm E. 7:00 pm

D. 62.5%

Question 18 and 19 refer to the chart below. The graph below shows the total number of Seniors by major in four different colleges. The number of Seniors in all three majors in College B is what percent of Seniors in all three majors in College A? A. 33.3% B. 40% C. 55% D. 62.5%

D. 62

Question 18 and 19 refer to the chart below. The graph below shows the total number of Seniors by major in four different colleges. What is the total number of Seniors majoring in Pre-Health in all four colleges? A. 60 B. 55 C. 70 D. 62

E. 64

Rockwell High offers two electives. 42 students are enrolled in chemistry, 30 are enrolled in biology, and 8 are enrolled in both electives. How many students at Rockwell High are currently taking electives? A. 100 B. 72 C. 82 D. 80 E. 64

C. -1/32

Solve for f(-3/5). A. 19/18 B. -19/18 C. -1/32 D. 1/32 E. -5/3

B. -2/3

Solve for x A. -5/3 B. -2/3 C. -2 D. 2 E. 3/2

B. 2

Solve for x: 3logx = log8 A. 8/3 B. 2 C. 8 D. log (8/3) E. 10(8/3)

B. 40.0%

The following bar chart tells us how Sophomores, Juniors, and Seniors from a high school scored on a diagnostic math exam. What percent of the students who scored between 80-100 on the exam were Seniors? A. 33.3% B. 40.0% C. 50.0% D. 63.3%

C. 3

The height of a cylinder is twice the radius of its base. If the volume of the cylinder is 54π, what is the radius of its base? A. 2 B. 3π C. 3 D. 6 E. 9

C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone.

The roles at company X are recorded and divided into the five following sub-categories. 35 employees work in the sales department. How many employees are in the marketing department? 1) One out of every five employees works in marketing 2) The sales department is half of all the employees A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question. B. Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. D. Each statement alone is sufficient to answer the question. E. Statements 1) and 2) together are not sufficient to answer the question.

D. +7%

The stock XYZ increased 20% during the first day, fell 15% on the second day and then increased 5% on the last day. What is the net percentage change of the stock XYZ? A. -5% B. 0% C. +5% D. +7% E. +10%

D. 17/4

What is the y-intercept of the line that passes through the two points whose coordinates are (5, -2) and (1, 3)? A. 10/3 B. 11/4 C. 14/3 D. 17/4 E. 21/4

B. (2x5 - 5y3)(2x5 + 5y3)

Which of the following are correct factors of the expression 4x10 - 25y6? A. (2x5 - 5y3)2 B. (2x5 - 5y3)(2x5 + 5y3) C. (2x5 + 5y3)(2x10 + 5y6) D. (2x5 + 5y3)2 E. (4x10 - 5y3)(4x5 + 5y6)