Quant. Reasoning Test #10

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

x2 + x - 6 = 0 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. 33.3%

If 5 liters of 20% alcohol solution are mixed with 10 liters of 40% alcohol solution, what is the percentage of alcohol in the mixture? A. 18.5% B. 22.5% C. 30% D. 33.3% E. 35%

B. 11

If 5x + 3y = 15 and 3x + y = 4, what is the value of 2x + 2y? A. 10 B. 11 C. 12 D. 13 E. 16

A. 62 mph

If Garry drives 50 kilometers in 30 minutes, approximately what is his speed in miles per hour? (1 km = 0.62 miles) A. 62 mph B. 74 mph C. 80 mph D. 100 mph E. 120 mph

A. 7/8

If a coin is flipped 3 times, what is the probability of obtaining at least one tail? A. 7/8 B. 1/8 C. 15/16 D. 1/2 E. 1/16

C. 17.8 minutes

A 200-gallon tank has a pipe at the top that fills it with water at a rate of 15 gallons per minute. However, it also has a leak at the bottom that drains water at a rate of 6 gallons per minute. Assuming the tank is initially empty, how long would it take to fill the tank to 80% of its capacity? A. 14.4 minutes B. 15.3 minutes C. 17.8 minutes D. 19.2 minutes E. 20.2 minutes

C. The two quantities are equal.

A bag contains 4 red marbles, 6 green marbles, and 2 white marbles. The probability of picking a red marble and a white marble with replacement 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.

A. 1/2

A fair coin is flipped 5 times, what is the probability of getting a tail in the fifth flip? A. 1/2 B. 1/4 C. 1/6 D. 1/8 E. 1/16

C. 8 days

Albert signed a contract to work 30 days under the following conditions: for each day he worked he was to receive 50 dollars. For each day he did not work he was to forfeit 15 dollars. At the end of 30 days, Albert received 980 dollars. How many days was Albert not working? A. 5 days B. 6 days C. 8 days D. 12 days E. 14 days

B. Quantity B is greater.

An unknown amount of a 20% saline solution (1) is mixed with an unknown amount of a 60% saline solution (2) to produce an 80-liter solution that is 50% saline. 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. 55

Approximately, how many yards are there in 5,000 centimeters? (1 m = 1.1 yd) A. 50 B. 55 C. 110 D. 500 E. 5500

E. 30 liters

How many liters of a 10% acid solution must be mixed with 10 liters of a 30% acid solution to produce a solution that is 15% acid solution? A. 10 liters B. 15 liters C. 20 liters D. 25 liters E. 30 liters

B. 7/5

If 2x + 3y = 7x - 4y, what is x/y? A. 5/7 B. 7/5 C. 3/5 D. -5/3 E. -7/5

C. a2 > 48

If 2x2 - ax + 6 = 0 has two distinct real roots, which of the following must be true? A. a2 < 48 B. a2 = 48 C. a2 > 48 D. a2 = 12 E. a2 = 24

B. 36

Dana is 20 years younger than her mother. In 4 years, the mother will be twice as old as Dana. How old is the mother now? A. 30 B. 36 C. 40 D. 44 E. 60

D. 96.0

Dana's test scores on the first four exams are 80, 78, 70, and 60. If Dana wants to increase her test average by 8 points, what is the minimum average she needs on her last 2 exams to accomplish her goal? A. 98.5 B. 97.5 C. 96.8 D. 96.0 E. 94.0

D. 15

Dennis has $4.00 in nickels, dimes and quarters. If he has four more quarters than nickels, and 3 times as many dimes as nickels, how many dimes does he have? A. 9 B. 10 C. 11 D. 15 E. 17

D. 1,200

For a company that manufactures air conditioners, the fixed costs for the company amount to $60,000 regardless of how many air conditioners they sell. If the company produces air conditioners for $49 a unit and sells them for $99 a unit, what is the least amount of air conditioners the company must sell to break even? A. 750 B. 908 C. 1,104 D. 1,200 E. 1,350

B. Quantity B is greater.

For questions 36 through 39 refer to the chart below. The chart above shows the average monthly rainfall in millimeters for region R for 6 months. Percent increase of rainfall fromJanuary to February Percent increase of rainfall fromMarch to April 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. 100%

For questions 36 through 39 refer to the chart below. The chart above shows the average monthly rainfall in millimeters for region R for 6 months. The amount of rainfall in May is what percent of the amount of rainfall in January and June combined? A. 75% B. 100% C. 150% D. 175% E. 200%

C. 52.5mm

For questions 36 through 39 refer to the chart below. The chart above shows the average monthly rainfall in millimeters for region R for 6 months. What is the median rainfall in millimeters for the six months? A. 46.0mm B. 48.5mm C. 52.5mm D. 60.0mm E. 62.5mm

C. 52.5mm

For questions 36 through 39 refer to the chart below. The chart above shows the average monthly rainfall in millimeters for region R for 6 months. What is the average amount of rainfall in millimeters for the six months? A. 46.0mm B. 48.5mm C. 52.5mm D. 60.0mm E. 62.5mm

D. 58%

If the price of a concert ticket increases by 20%, then increases by another 20%, and then increases again by 10%, what is approximately the overall percent increase of the ticket? A. 40% B. 48.5% C. 50% D. 58% E. 60%

B. 5/36

If two fair dice are rolled, what is the probability of getting a sum of 8? A. 3/36 B. 5/36 C. 1/4 D. 5/12 E. 21/36

E. 60

In a cookie bag, the ratio of almond cookies to raisin cookies to peanut butter cookies is 4:3:7. If there are 280 cookies in the bag, how many raisin cookies are there? A. 25 B. 30 C. 45 D. 50 E. 60

E. 20

In a summer camp of 220 students, 150 have blond hair, 80 are left-handed, and 30 have blond hair and are left-handed. How many students in the camp are neither blond nor left-handed? A. 8 B. 10 C. 13 D. 15 E. 20

D. 720

In how many ways can 3 different algebra books and 3 different physics books be arranged on a shelf? A. 9 B. 20 C. 90 D. 720 E. 780

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

Is x < 0 ? 1) xy < 0 2) x|y| < 0 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. 700

James drives from City A to City B at a speed of 70 mph. Three hours later, Grant also starts driving from City A to City B, but at a speed of 100 mph. If they continue driving at their respective speeds, how many miles away from City A will they meet? A. 443 B. 550 C. 675 D. 700 E. 815

C. 28

Lily and Nada share silver coins in the ratio 7:3. If Lily gives 3 silver coins to Nada, the ratio becomes 5:3. How many silver coins did Lily have initially? A. 14 B. 22 C. 28 D. 30 E. 36

B. 50

Questions 27 through 30 refer to the two box-and-whisker plots below. The two-box-and whisker plots above show how many hours seniors study for a final exam at Glendale high school and Riverdale high school. If 200 seniors we surveyed at Riverdale high school, how many seniors study between 2.5 hours and 6 hours for the final? A. 45 B. 50 C. 55 D. 60 E. Cannot be determined

C. 75

Questions 27 through 30 refer to the two box-and-whisker plots below. The two-box-and whisker plots above show how many hours seniors study for a final exam at Glendale high school and Riverdale high school. If 300 seniors were surveyed at Glendale high school, how many seniors' studies between 10 hours and 12 hours for the final? A. 25 B. 65 C. 75 D. 125 E. Cannot be determined

B. Quantity B is greater.

Questions 27 through 30 refer to the two box-and-whisker plots below. The two-box-and whisker plots above show how many hours seniors study for a final exam at Glendale high school and Riverdale high school. Quantity AQuantity B The interquartile range (IQR) of hours spentstudying at Glendale high school The interquartile range (IQR) of hours spentstudying at Riverdale high school 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.

Questions 27 through 30 refer to the two box-and-whisker plots below. The two-box-and whisker plots above show how many hours seniors study for a final exam at Glendale high school and Riverdale high school. Quantity AQuantity B The range of hours spent studying for thefinal at Glendale high school. The range of hours spent studying for thefinal at Riverdale high school. 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.

Simplify: A. B. C. D. E.

D.

Simplify: A. B. C. D. E.

B. 58

The scores on a math exam worth 100 points are normally distributed with a mean of 70 and a standard deviation of 8. If Allen's z-score on the exam is -1.5, what grade did he receive on the exam? A. 48 B. 58 C. 62 D. 72.5 E. 78

A. 5, 5.5, 6, 8

What is the mean, median, mode, and range of the following set, in that order? {1, 2, 4, 5, 6, 6, 7, 9} A. 5, 5.5, 6, 8 B. 5.5, 5, 6, 9 C. 5.5, 5.5, 6, 9 D. 5, 5.5, 2, 8 E. 5, 6, 2, 8

A. -13 ≤ x ≤ 7

What is the solution set of: |x + 3| ≤ 10 A. -13 ≤ x ≤ 7 B. 7 ≤ x ≤ 13 C. -13 < x < 7 D. x ≤ -13 or x ≥ 7 E. 3 ≤ x ≤ 10

C. x = -4

Which of the following lines is perpendicular to the x-axis? A. y + 3x - 2 = 0 B. y = 5x C. x = -4 D. y = 4 E. y = x