Quant. Reasoning Test #8

A. 2:1

A bag contains 300 marbles that are green, blue, and red. The ratio of green marbles to blue marbles to red marbles is 3:2:1. We then remove 20 blue marbles and 10 red marbles. What is the new ratio of blue marbles to red marbles? A. 2:1 B. 3:2 C. 1:1 D. 4:3 E. 1:2

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

A class has honor students and non-honor students. How many honor students are there? 1) One-third of the class are honor students. 2) There are a total of 36 students in the class. 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. 1000 - 125π cubic inches

A cube of side length 10 inches is filled with water. If a solid cylinder of height 5 inches and radius of 5 inches is placed inside the cube, what volume of water will remain inside the cube? A. 1000 cubic inches B. 125π cubic inches C. 875π cubic inches D. 1000 - 125π cubic inches E. 1000 + 125π

E. 880

A fathom is an old unit used in the United States to measure the depth of water. One fathom is equivalent to 6 feet. If a well is 1 mile deep, what is the equivalent depth in fathoms? A. 650 B. 675 C. 700 D. 790 E. 880

C. 8

A line intersects a circle with radius 4 at two points: A and B. What is the greatest possible straight distance between A and B? A. 4 B. 4π C. 8 D. 8π E. Cannot be determined

B. 424 m2

A rectangular tank is 15 meters long, 4 meters wide, and 8 meters high. What is the total surface area of the tank? A. 212 m2 B. 424 m2 C. 480 m2 D. 544 m2 E. 600 m2

A. 75

A sea turtle laid eggs on a beach. 4/5 of the eggs hatched, and 7/10 of the hatched eggs survived the first week. If 42 baby turtles survived the first week, how many eggs were laid at the beach? A. 75 B. 88 C. 95 D. 110 E. 125

B. 16

A vat that contains 40 liters of water is to be poured completely into two vats with capacities of 20 liters and 30 liters, respectively, such that both vats will be filled to the same percent of their respective capacities. How many liters should be poured into the 20-liter vat? A. 15 B. 16 C. 24 D. 27.6 E. 30

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.

E. 3/4

Both the small and large circles have center O. The small circle has a radius of r and the large circle has double the radius of the small circle. What proportion of the area of the large circle is shaded? A. 1/2 B. 1/4 C. 7/8 D. 3/8 E. 3/4

B. 0.01

Evaluate: A. 0.1 B. 0.01 C. 0.001 D. 0.0001

E. 50 minutes

Five workers from team A working at the same constant rate can lay 1000 bricks in one hour. Three workers from team B working at the same constant rate can lay 800 bricks in 40 minutes. How long it would take 6 workers from each team to lay 3000 bricks? A. 25 minutes B. 30 minutes C. 40 minutes D. 45 minutes E. 50 minutes

C. (-2, 3), r = 5

Given the following equation of a circle, what are the coordinates of the center of the circle, and what is the radius of the circle? x2 + y2 + 4x - 6y + 2 = 14 A. (2, -3), r = 5 B. (2, 3), r = 4 C. (-2, 3), r = 5 D. (5, 2), r = 2 E. (-2, 5), r = 3

E. 45 - n

If Jana will be 52 years old in 7 years, how old was she n years ago? A. 52 - n B. n - 52 C. 59 - n D. 45 + n E. 45 - n

A. 1/2

If a - b = 13/15 and a + b = 15/26, what is the value of a2 - b2? A. 1/2 B. 2 C. 2/3 D. 3 E. 2/5

C. 40%

If a five-digit number is formed from the digits {2, 3, 5, 8, 9} and each digit is only used once, what is the probability that it is an even number? A. 20% B. 30% C. 40% D. 45% E. 52.5%

C. 8

If a2 - 2ab + b2 = 2 then (a - b)6 = ? A. 4 B. 6 C. 8 D. 12 E. 16

D. $2000

If nation X has a population of 26 million people and a Gross Domestic Product (GDP) of 52 billion dollars, what is the per capita GDP (Gross Domestic Product per person) of the nation in dollars? A. $750 B. $1135 C. $1875 D. $2000 E. $2100

D. 1/4

If two fair dice are rolled, what is the probability that both numbers shown on the dice are odd? A. 1 B. 1/2 C. 3/4 D. 1/4 E. 1/8

A.

If x kilograms of almonds cost a dollars per kilogram, and y kilograms of walnuts cost b dollars per kilogram, what is the cost, in dollars, per kilogram of the entire mixture? A. B. C. D. E.

D. $141,666

In Fix-Tooth dental clinic, 2 orthodontists earn $300,000 per year, 4 periodontists earn $200,000 per year, and 6 dental assistants earn $50,000 per year. What is the average annual salary of all employees in the clinic? A. $91,666 B. $108,333 C. $125,000 D. $141,666 E. $150,000

C. 1/12

In a roll of two fair dice, what is the probability of getting a sum equal to ten? A. 5/36 B. 1/4 C. 1/12 D. 5/12 E. 7/36

A. Quantity A is greater.

Questions 23 through 26 refer to the chart below: The bar graph above shows the sales turnover for 3 companies specializing in producing dental equipment in hundreds of thousands of dollars in 2005 and 2006. 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. 3.45%

Questions 23 through 26 refer to the chart below: The bar graph above shows the sales turnover for 3 companies specializing in producing dental equipment in hundreds of thousands of dollars in 2005 and 2006. By what percent should the sales turnover for Company C increase from 2006 to 2007, so that the total sales for the company in 2007 will be the same as the sales from 2005? A. 25% B. 15% C. 12.5% D. 5% E. 3.45%

D. 55%

Questions 23 through 26 refer to the chart below: The bar graph above shows the sales turnover for 3 companies specializing in producing dental equipment in hundreds of thousands of dollars in 2005 and 2006. The total sales of Company A in 2005 were what percent of the total sales of Companies B and C combined for the same year? A. 33.3% B. 42.5% C. 50% D. 55% E. 57.5%

D. $75,000,000

Questions 23 through 26 refer to the chart below: The bar graph above shows the sales turnover for 3 companies specializing in producing dental equipment in hundreds of thousands of dollars in 2005 and 2006. What were the total sales of company B in the year 2005? Give the answer in dollars. A. $750 B. $750,000 C. $7,500,000 D. $75,000,000

A. 2

Simplify logb(b)+ logb(b) A. 2 B. b C. b2 D. 2b E. 2b

C.

Simplify the following expression: A. B. C. D. E.

A. 4

The cost to manufacture x toys is 75x + 100. The selling price of x toys is 25x2. If the manufacturer needs to break even, what is the least number of toys, the manufacturer needs to sell? A. 4 B. 40 C. 200 D. 400 E. 500

A. Quantity A is greater.

The diagram below describes the dimensions of a rectangular box. Then, the height of the box is increased by 50% and the length and width are both decreased by 25%. 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. $500.00

The figure below shows a floor plan for a kitchen. The owner wants to tile the entire floor. If each tile is a square with a side of 20 cm and costs $0.25, how much would it cost the owner to tile the entire floor? A. $350.00 B. $375.25 C. $452.50 D. $500.00 E. $520.00

C. The two quantities are equal.

The following line chart describes the average number of daylight hours per day for Taipei and Seoul throughout the year, separated by month. 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.

C. (x - 2)2 + 1

The graph of a function f is given below. Which of the following could be the equation of f? A. x2 + 1 B. (x + 2)3 + 1 C. (x - 2)2 + 1 D. (x + 2)2 + 1 E. (x - 2)2 - 1

C. 8

The number 3 * 2-4 is how many times the number 6 * 4-4? A. 2 B. 4 C. 8 D. 20 E. 30

B. $2,160

The price of a new bike is $10,000. Every year, the value of the bike diminishes by 40%. Approximately, what is the value of the bike after 3 years? A. $1,800 B. $2,160 C. $3,600 D. $6,000

B. 9

There are 15 girls and 25 boys at a certain elementary school. 60% of the students wear white shirts, and 40% of the students wear blue shirts. If all the girls wear white shirts, how many boys wear white shirts? A. 7 B. 9 C. 11 D. 15 E. 18

C. 3/2

What is the value of x? A. 3/4 B. 2/3 C. 3/2 D. -3/2 E. -1/2

B.

Which of the option choices is equivalent to the following expression: A. B. C. D. E.