ASTB Mathematics Preparation Quiz

1) If a= 4b and 8b= 30c, then a=

ANSWER- Da= 4b2a= 8b= 30c2a=30ca= 15c

B- 9c

C- 12c

A- 6c

To find the value of a, we start with a= 4b and then substitute 4b from the first equation into the second equation, which gives us 2a= 30c. Solving for a, we get a= 15c.

Explanation

To find the value of a, we start with a= 4b and then substitute 4b from the first equation into the second equation, which gives us 2a= 30c. Solving for a, we get a= 15c.

2) What is the third root of 64?

2

8

ANSWER- C4*4*4= 64

3

To find the third root of a number, you need to find a number that when multiplied by itself three times equals the original number. In this case, 4 * 4 * 4 = 64.

Explanation

To find the third root of a number, you need to find a number that when multiplied by itself three times equals the original number. In this case, 4 * 4 * 4 = 64.

3) A bridge crosses a river that is 1,400 feet wide. One bank of the river holds 1/5 of the bridge, while the other holds 1/10 of it. How long is the bridge?

A. 1,700 feet

B. 1,800 feet

D. 2,100 feet

By solving for the length of the bridge using the given fractions and the width of the river, it is determined that the bridge is 2,000 feet long.

Explanation

By solving for the length of the bridge using the given fractions and the width of the river, it is determined that the bridge is 2,000 feet long.

4) Successive discounts of 20 percent and 10 percent are equivalent to a single discount of

B. 29 percent.

C. 30 percent.

D. 31 percent.

To find the equivalent single discount, we start with 100 (original price). With a 20% discount, the price becomes 80. Then, with a 10% discount, the price becomes 80 * 0.90 = 72. So, the equivalent single discount would be 100 - 72 = 28 percent.

Explanation

To find the equivalent single discount, we start with 100 (original price). With a 20% discount, the price becomes 80. Then, with a 10% discount, the price becomes 80 * 0.90 = 72. So, the equivalent single discount would be 100 - 72 = 28 percent.

5) Two ships are 2,000 miles apart and sailing toward each other. One sails at the rate of 80 miles per day and the other at the rate of 100 miles per day. How far apart will they be at the end of 9 days?

C. 440 miles

D. 500 miles

A. 364 miles

80 x 9 days = 720 miles; 100 x 9 days = 900 miles; 720 + 900 = 1620 miles; 2000 - 1620 = 380 miles.

Explanation

80 x 9 days = 720 miles; 100 x 9 days = 900 miles; 720 + 900 = 1620 miles; 2000 - 1620 = 380 miles.

6) Angle E is 40° smaller than its complement. The number of degrees in angle E is

B. 45°

D. 90°

C. 60°

ANSWER- ALet x equal the number of degrees in angle E.

Since angle E is 40° smaller than its complement, we can set up the equation x + (x + 40) = 90 where x represents angle E. Solving this equation gives us x = 25°, so the correct answer is a. 25°.

Explanation

Since angle E is 40° smaller than its complement, we can set up the equation x + (x + 40) = 90 where x represents angle E. Solving this equation gives us x = 25°, so the correct answer is a. 25°.

7) If a driver completes a trip of 240 miles at the rate of 30 mph, at what rate would the driver have to travel on the return trip in order to average 40 mph for the round trip?

A. 50 mph

D. 65 mph

B. 55 mph

Traveling at 30 mph for 8 hours, the driver travels 240 miles; the round trip was 480 miles. Coming back, 480 miles at 40 mph would take 12 hours. If the first 240 miles took 8 hours, the return 240 miles must be covered in 4 hours, which equals a speed of 60 mph.

Explanation

Traveling at 30 mph for 8 hours, the driver travels 240 miles; the round trip was 480 miles. Coming back, 480 miles at 40 mph would take 12 hours. If the first 240 miles took 8 hours, the return 240 miles must be covered in 4 hours, which equals a speed of 60 mph.

8) A class of 216 recruits consists of three racial and ethnic groups. If 72 are black, 54 are Hispanic, and the remaining recruits are white, how many of the recruits in the class are white?

ANSWER- B1/3 * 216= 72 blacks1/4 * 216= 54 hispanics72+54= 126216- 126= 90 whites

94

75

68

To find the number of white recruits, subtract the total of black and Hispanic recruits from the total recruits in the class. 72 + 54 = 126. 216 - 126 = 90.

Explanation

To find the number of white recruits, subtract the total of black and Hispanic recruits from the total recruits in the class. 72 + 54 = 126. 216 - 126 = 90.

9) A tank that holds 500 gallons of water can be filled by one pipe in 25 minutes and emptied by another in 50 minutes. How long would it take to fill the tank if both pipes are open?

C. 55 minutes

D. 56 minutes

B. 52 minutes

The filling rate is 20 gallons/minute. The emptying rate is 10 gallons/minute. The difference, 20 - 10 = 10, is how many gallons are added per minute with both pipes open, so it takes 50 minutes to fill the tank.

Explanation

The filling rate is 20 gallons/minute. The emptying rate is 10 gallons/minute. The difference, 20 - 10 = 10, is how many gallons are added per minute with both pipes open, so it takes 50 minutes to fill the tank.

10) An island is defended by a battery of coastal guns with a maximum range of 5 miles. A ship sailing due north at 24 mph will be within 4 miles of these guns on a straight course. How long will the ship be within range of the coastal guns?

C- 25 min

D- 30 min

B- 20 min

The ship will be within range of the coastal guns from point A to point C based on the provided diagram and calculations.

Explanation

The ship will be within range of the coastal guns from point A to point C based on the provided diagram and calculations.

11) If x^2 varies directly as y and if x=2 when y=10, what is the value of y when x=8?

B- 130

A- 32

ANSWER- C4:10= 64:y 4y= 64 *10 y= 640/4 y=160

D- 168

When x=2, y=10. To find y when x=8, use the direct variation formula. (2^2):10 = (8^2):y. Simplifying gives 4:10 = 64:y, hence y = 160.

Explanation

When x=2, y=10. To find y when x=8, use the direct variation formula. (2^2):10 = (8^2):y. Simplifying gives 4:10 = 64:y, hence y = 160.

12) A closed rectangular box with a square base is 3 inches high. If the volume of the box is 48 cubic inches, what is the surface area of the box in square inches?

90

66

81

To find the surface area, determine the dimensions of the square base using the volume provided. Once the base side length is found to be 4 inches, calculate the total surface area using the formula. The correct answer is 80 square inches.

Explanation

To find the surface area, determine the dimensions of the square base using the volume provided. Once the base side length is found to be 4 inches, calculate the total surface area using the formula. The correct answer is 80 square inches.

13) A CD system originally priced at $1000 is first discounted by 20%, then later by another 10%. If a 5% tax is added to the purchase price, how would a customer buying the system at its lowest price pay for it to the nearest dollar, including tax?

D- $800

A- $720

B- $750

The correct calculation is: after the 20% discount= $800 (1000 * .20= 200, 1000- 200= 800). After 10% off $800= $720 (800* .10= 80, 800-80=720). After 5% tax= $756 (720*.05= 36, 720+36=756).

Explanation

The correct calculation is: after the 20% discount= $800 (1000 * .20= 200, 1000- 200= 800). After 10% off $800= $720 (800* .10= 80, 800-80=720). After 5% tax= $756 (720*.05= 36, 720+36=756).

14) A cash box contains a certain number of coins, of which 63 are dimes and 33 are nickels. The rest of the coins in the box are quarters. If the probability of selecting a quarter from this bank is one in five, how many quarters does the bank contain?

27

35

30

To solve this problem, we set up the equation: 1/5 = x / (x+96), where x is the number of quarters. By solving for x, we find that x = 24. Therefore, there are 24 quarters in the bank.

Explanation

To solve this problem, we set up the equation: 1/5 = x / (x+96), where x is the number of quarters. By solving for x, we find that x = 24. Therefore, there are 24 quarters in the bank.

15) Two trains running in the same direction on the same track travel at the rate of 40 and 45 mph. If the slower train starts out an hour earlier, how long will it take the faster one to catch up with it?

B- 6 hours

A- 5 hours

C- 7 hours

The slower train is 40 miles ahead in one hour. The difference in rate of change is 5 mph, and 40/5= 8 hours.

Explanation

The slower train is 40 miles ahead in one hour. The difference in rate of change is 5 mph, and 40/5= 8 hours.

16) In a 4-hour exam of 420 questions, there are 60 math problems. If twice as much time should be allowed for each math problem as for each of the other questions, how many minutes should be spent on the math problems?

D

B

C

The correct answer is calculated based on providing twice as much time for math problems compared to others. By solving the equation provided, it is determined that 60 minutes should be spent on the 60 math problems.

Explanation

The correct answer is calculated based on providing twice as much time for math problems compared to others. By solving the equation provided, it is determined that 60 minutes should be spent on the 60 math problems.

17) A family drove from New York to San Francisco, a distance of 3000 miles. They drove 1/8 of the distance the first day and 1/7 of the remaining distance the second day. How many miles were left to be driven?

ANSWER- B1/8 of 3000= 3753000- 375= 26251/7 of 2625= 3752625- 375= 2250 miles still to be driven

2400 miles

2200 miles

2500 miles

1/8 of 3000 is 375 miles driven on the first day. Remaining distance is 2625 miles. 1/7 of 2625 is 375 miles driven the second day. Therefore, 2625 - 375 = 2250 miles still to be driven.

Explanation

1/8 of 3000 is 375 miles driven on the first day. Remaining distance is 2625 miles. 1/7 of 2625 is 375 miles driven the second day. Therefore, 2625 - 375 = 2250 miles still to be driven.

18) Jane's grades on three tests were: 93, 82, and 72. What must she get on her next test so her average for the four tests is 85?

ANSWER- Dtotal score of all 3= 247to get an average of 85 then- 85*4= 340so.. 340-247= 93

B- 89

C- 90

A- 88

Total score of all 3 tests = 247. To get an average of 85 on 4 tests, the total score needed is 340. Therefore, Jane must score 93 on her next test to achieve an average of 85.

Explanation

Total score of all 3 tests = 247. To get an average of 85 on 4 tests, the total score needed is 340. Therefore, Jane must score 93 on her next test to achieve an average of 85.

19) If (x - y)^2 = 60 and x^2 + y^2 = 40, then xy = ?

C. -12

A. -40

B. -20

The correct way to solve this problem is by expanding (x - y)^2 to get x^2 - 2xy + y^2. By substituting this expression into the first equation and simplifying, we find that xy = -10.

Explanation

The correct way to solve this problem is by expanding (x - y)^2 to get x^2 - 2xy + y^2. By substituting this expression into the first equation and simplifying, we find that xy = -10.

20) A farmer who is 6 feet tall wants to determine the height of his barn, he notices that his shadow is 14 feet long and that his barn casts a shadow of 70 feet long. How high is the barn?

D- 45 feet

C- 40 feet

B- 35 feet

To determine the height of the barn, set up a proportion: 6 : 14 = x : 70. Solve for x to find the height of the barn, which is 30 feet.

Explanation

To determine the height of the barn, set up a proportion: 6 : 14 = x : 70. Solve for x to find the height of the barn, which is 30 feet.

21) How much pure acid must be added to 10 ounces of a 55% acid solution in order to produce a 75% acid solution?

C- 7 ounces

A- 5 ounces

B- 6 ounces

By setting up the equation with the given information of pure acid and the two different solutions, solving for x gives us the correct answer of 8 ounces.

Explanation

By setting up the equation with the given information of pure acid and the two different solutions, solving for x gives us the correct answer of 8 ounces.

22) What is the perimeter of a right triangle whose legs are 3 and 4 feet?

ANSWER- BUsing the Pythagorean theorm, the hypotenuse of the right triangle = 5: 3′ + 4′ + 5′ = 12

A. 10 feet

D. 16 feet

C. 14 feet

Using the Pythagorean theorem, the hypotenuse of the right triangle = 5. Therefore, the perimeter would be 3 + 4 + 5 = 12 feet.

Explanation

Using the Pythagorean theorem, the hypotenuse of the right triangle = 5. Therefore, the perimeter would be 3 + 4 + 5 = 12 feet.

23) If the sum of the edges of a cube is 36 inches, what is the volume of the cube?

24 cubic inches

ANSWER- Ba cube has 12 edges, so each edge is 24/12= 2volume= L*W*Hv= 2*2*2v=8

12 cubic inches

64 cubic inches

A cube has 12 edges, so each edge is 36/12 = 3. Volume = L * W * H = 3 * 3 * 3 = 27 cubic inches.

Explanation

A cube has 12 edges, so each edge is 36/12 = 3. Volume = L * W * H = 3 * 3 * 3 = 27 cubic inches.

24) If 3^ (n-2)= 27, what does n equal?

B- 7

C- 8

D- 12

The correct answer is obtained by solving for n as n=5 in the given equation 3^ (n-2)= 27. Thus, n equals 5 which corresponds to option a.

Explanation

The correct answer is obtained by solving for n as n=5 in the given equation 3^ (n-2)= 27. Thus, n equals 5 which corresponds to option a.

25) What is the square root of 4 raised to the 5th power?

D- 64

A- 8

ANSWER- CSQR of 4=22^5= 2*2*2*2*2 =32

B- 16

The square root of 4 is 2. When 2 is raised to the 5th power, it equals 32.

Explanation

The square root of 4 is 2. When 2 is raised to the 5th power, it equals 32.

26) If a field can be plowed by 12 machines in 7 hours, but 4 machines are broken and cannot be used, how many hours will it take to plow the field with the remaining machines?

C- 9.5 hours

B- 8.5 hours

A- 7.5 hours

The correct answer can be calculated by setting up the proportion: 12 * 7 = 8 * x, where x is the number of hours it will take with 8 machines. Solving for x gives x = 10.5 hours.

Explanation

The correct answer can be calculated by setting up the proportion: 12 * 7 = 8 * x, where x is the number of hours it will take with 8 machines. Solving for x gives x = 10.5 hours.

27) A naval detachment has enough rations to feed 15 people for 8 days. If 5 more people join, how many fewer days will the rations last?

A- 1

D- 4

C- 3

Let x be the number of ration days for 20 people. Using the formula 15 * 8 = 20 * x, we find that x = 6 ration days for 20 persons. Therefore, the rations will last 2 days fewer for the increased group size.

Explanation

Let x be the number of ration days for 20 people. Using the formula 15 * 8 = 20 * x, we find that x = 6 ration days for 20 persons. Therefore, the rations will last 2 days fewer for the increased group size.

28) Which of the following represents 1,000,000?

10^7

ANSWER- C

10^4

10^5

In mathematics, the notation 10^6 represents 1,000,000 as it means 10 multiplied by itself 6 times, which equals 1,000,000.

Explanation

In mathematics, the notation 10^6 represents 1,000,000 as it means 10 multiplied by itself 6 times, which equals 1,000,000.

29) What is the measure of angle x?

B- 45 degree

A- 35 degree

D- 70 degree

arc AB= 80 degrees therefore, AOB = 80 degrees, the two radii are equal. angle x= (180 - 80)/2 = 50 degrees.

Explanation

arc AB= 80 degrees therefore, AOB = 80 degrees, the two radii are equal. angle x= (180 - 80)/2 = 50 degrees.

30) If x is less than 0 and y is greater than 0, then

D. xy is greater than 0.

A. x is greater than y.

B. y is greater than x.

ANSWER- CWhen a negative number and a positive number are multiplied, the product is negative.

When a negative number and a positive number are multiplied, the product is negative.

Explanation

When a negative number and a positive number are multiplied, the product is negative.

ASTB Mathematics Preparation Quiz

1) If a= 4b and 8b= 30c, then a=

2)

What first name or nickname would you like us to use?

2) What is the third root of 64?

3) A bridge crosses a river that is 1,400 feet wide. One bank of the river holds 1/5 of the bridge, while the other holds 1/10 of it. How long is the bridge?

4) Successive discounts of 20 percent and 10 percent are equivalent to a single discount of

5) Two ships are 2,000 miles apart and sailing toward each other. One sails at the rate of 80 miles per day and the other at the rate of 100 miles per day. How far apart will they be at the end of 9 days?

6) Angle E is 40° smaller than its complement. The number of degrees in angle E is

7) If a driver completes a trip of 240 miles at the rate of 30 mph, at what rate would the driver have to travel on the return trip in order to average 40 mph for the round trip?

8) A class of 216 recruits consists of three racial and ethnic groups. If 72 are black, 54 are Hispanic, and the remaining recruits are white, how many of the recruits in the class are white?

9) A tank that holds 500 gallons of water can be filled by one pipe in 25 minutes and emptied by another in 50 minutes. How long would it take to fill the tank if both pipes are open?

10) An island is defended by a battery of coastal guns with a maximum range of 5 miles. A ship sailing due north at 24 mph will be within 4 miles of these guns on a straight course. How long will the ship be within range of the coastal guns?

11) If x^2 varies directly as y and if x=2 when y=10, what is the value of y when x=8?

12) A closed rectangular box with a square base is 3 inches high. If the volume of the box is 48 cubic inches, what is the surface area of the box in square inches?

13) A CD system originally priced at $1000 is first discounted by 20%, then later by another 10%. If a 5% tax is added to the purchase price, how would a customer buying the system at its lowest price pay for it to the nearest dollar, including tax?

14) A cash box contains a certain number of coins, of which 63 are dimes and 33 are nickels. The rest of the coins in the box are quarters. If the probability of selecting a quarter from this bank is one in five, how many quarters does the bank contain?

15) Two trains running in the same direction on the same track travel at the rate of 40 and 45 mph. If the slower train starts out an hour earlier, how long will it take the faster one to catch up with it?

16) In a 4-hour exam of 420 questions, there are 60 math problems. If twice as much time should be allowed for each math problem as for each of the other questions, how many minutes should be spent on the math problems?

17) A family drove from New York to San Francisco, a distance of 3000 miles. They drove 1/8 of the distance the first day and 1/7 of the remaining distance the second day. How many miles were left to be driven?

18) Jane's grades on three tests were: 93, 82, and 72. What must she get on her next test so her average for the four tests is 85?

19) If (x - y)^2 = 60 and x^2 + y^2 = 40, then xy = ?

20) A farmer who is 6 feet tall wants to determine the height of his barn, he notices that his shadow is 14 feet long and that his barn casts a shadow of 70 feet long. How high is the barn?

21) How much pure acid must be added to 10 ounces of a 55% acid solution in order to produce a 75% acid solution?

22) What is the perimeter of a right triangle whose legs are 3 and 4 feet?

23) If the sum of the edges of a cube is 36 inches, what is the volume of the cube?

24) If 3^ (n-2)= 27, what does n equal?

25) What is the square root of 4 raised to the 5th power?

26) If a field can be plowed by 12 machines in 7 hours, but 4 machines are broken and cannot be used, how many hours will it take to plow the field with the remaining machines?

27) A naval detachment has enough rations to feed 15 people for 8 days. If 5 more people join, how many fewer days will the rations last?

28) Which of the following represents 1,000,000?

29) What is the measure of angle x?

30) If x is less than 0 and y is greater than 0, then