Astb Can You Solve These Basic Navy Exams Math Problem

1. Ron is half as old as Sam, who is three times as old as Ted. The sum of their ages is 55. How old is Ron?

D. Ron is 25 years old.

B. Ron is 20 years old.

A. Ron is 10 years old.

The correct answer is C. Let T = Ted's age; S = Sam's age = 3T; R = Ron's age = , or . The sum of the ages is 55, which means T + 3T + = 55. To find the common denominator (2), you can add to the left side of the equation: T = 10. If Ted is 10, then Sam is 30, and Ron is , which is 15 years old.

Let T = Ted's age; S = Sam's age = 3T; R = Ron's age = T/2. The sum of the ages is 55, which means T + 3T + T/2 = 55. Solving the equation leads to T = 10. If Ted is 10, then Sam is 30, and Ron is 15 years old.

Explanation

Let T = Ted's age; S = Sam's age = 3T; R = Ron's age = T/2. The sum of the ages is 55, which means T + 3T + T/2 = 55. Solving the equation leads to T = 10. If Ted is 10, then Sam is 30, and Ron is 15 years old.

2. An Army food supply truck can carry three tons. A breakfast ration weighs 12 ounces, and the other two daily meals weigh 18 ounces each. Assuming each soldier gets three meals per day, on a 10-day trip, how many soldiers can be supplied by one truck?

D. 225 soldiers

B. 175 soldiers

The correct answer is C. Three tons = 6,000 pounds. At 16 ounces per pound, 6,000 pounds = 96,000 ounces that can be carried by the truck. The total weight of each daily ration is 12 ounces + 18 ounces = 18 ounces = 48 ounces per soldier per day, and = 2,000. So days = 200 soldiers supplied.

A. 150 soldiers

The correct answer is C. Three tons = 6,000 pounds. At 16 ounces per pound, 6,000 pounds = 96,000 ounces that can be carried by the truck. The total weight of each daily ration is 12 ounces + 18 ounces = 18 ounces = 48 ounces per soldier per day, and 48 * 10 = 480 ounces per soldier for the entire trip. 96,000 ounces / 480 ounces per soldier = 200 soldiers supplied.

Explanation

The correct answer is C. Three tons = 6,000 pounds. At 16 ounces per pound, 6,000 pounds = 96,000 ounces that can be carried by the truck. The total weight of each daily ration is 12 ounces + 18 ounces = 18 ounces = 48 ounces per soldier per day, and 48 * 10 = 480 ounces per soldier for the entire trip. 96,000 ounces / 480 ounces per soldier = 200 soldiers supplied.

3. Based on the following information, estimate the weight of a person who is 5'5" tall.

A. 125

A. 125 B. 130 C. 135 D. 140 E. 145

C. 135

D. 140

The estimate of 130 lbs. for a person who is 5'5" tall falls between the provided weights of 110 lbs. for 5' and 170 lbs. for 6'. It is reasonable to assume that a person who is 5'5" would weigh around 130 lbs based on this information.

Explanation

The estimate of 130 lbs. for a person who is 5'5" tall falls between the provided weights of 110 lbs. for 5' and 170 lbs. for 6'. It is reasonable to assume that a person who is 5'5" would weigh around 130 lbs based on this information.

4. A study shows that 600,000 women die each year in pregnancy and childbirth, one-fifth more than scientists previously estimated. How many such deaths did the scientists previously estimate?

C. 600,000

A. 450,000

The correct answer is E. Let E = the estimate. One-fifth more than the estimate would be , or 120%, of E, so 600,000 = (1.20)(E). Dividing both sides by 1.2 leaves E = 500,000.

B. 550,000

The correct answer is E. Let E = the estimate. One-fifth more than the estimate would be 120%, or 600,000 = (1.20)(E). Dividing both sides by 1.2 leaves E = 500,000.

Explanation

The correct answer is E. Let E = the estimate. One-fifth more than the estimate would be 120%, or 600,000 = (1.20)(E). Dividing both sides by 1.2 leaves E = 500,000.

5. A woman drives west at 45 miles per hour. After half an hour, a man starts to follow her. How fast must he drive to catch up to her three hours after he starts?

D. The man must drive at 50 miles per hour.

The correct answer is A. The woman will have traveled 3.5 hours at 45 miles per hour for a distance of 157.5 miles. To reach her in 3 hours, the man must travel at 157.5 miles per 3 hours, or 52.5 mph.

B. The man must drive at 45 miles per hour.

C. The man must drive at 40 miles per hour.

The correct answer can be calculated by determining the distance the woman has traveled after 3 hours and then dividing that distance by the remaining time the man has to reach her.

Explanation

The correct answer can be calculated by determining the distance the woman has traveled after 3 hours and then dividing that distance by the remaining time the man has to reach her.

6. All of the rooms in a building are rectangular, with eight-foot ceilings. One room is nine feet wide by 11 feet long. What is the combined area of the four walls, including doors and windows?

D. 400 square feet

A. 128 square feet

C. 352 square feet

The correct answer is E. Each 9-foot wall has an area of 9(8), or 72 square feet. There are two such walls, so those two walls combined have an area of 144 square feet. Each 11-foot wall has an area of 11(8), or 88 square feet, and again there are two such walls: 88(2) = 176. Finally, add 144 and 176 to get 320 square feet.

B. 260 square feet

7. How much water must be added to one liter of a 5% saline solution to get a 2% saline solution?

0.5 liters

3 liters

The correct answer is C. Use the equation .05(1) = .02(x), where x is the total amount of water in the resulting 2% solution. Solving for x, you get 2.5. Subtracting the 1 liter of water already present in the 5% solution, you will find that 1.5 liters need to be added.

2 liters

The correct answer is found by using the equation .05(1) = .02(x), where x is the total amount of water in the resulting 2% solution. Solving for x, you get 2.5. Subtracting the 1 liter of water already present in the 5% solution, you will find that 1.5 liters need to be added.

Explanation

The correct answer is found by using the equation .05(1) = .02(x), where x is the total amount of water in the resulting 2% solution. Solving for x, you get 2.5. Subtracting the 1 liter of water already present in the 5% solution, you will find that 1.5 liters need to be added.

8. Newly hired nurses have to buy duty shoes at the full price of $84.50, but nurses who have served at least a year get a 15% discount. Nurses who have served at least three years get an additional 10% off the discounted price. How much does a nurse who has served at least three years have to pay for shoes?

A. $63.35

C. $62.75

D. $65.20

The correct answer is B. You can't just take 25% off the original price, because the 10% discount after three years of service is taken off the price that has already been reduced by 15%. Figure the problem in two steps: After the 15% discount, the price is $71.83. 90% of that—subtracting 10%—is $64.65.

You can't just take 25% off the original price, because the 10% discount after three years of service is taken off the price that has already been reduced by 15%. Figure the problem in two steps: After the 15% discount, the price is $71.83. 90% of that—subtracting 10%—is $64.65.

Explanation

You can't just take 25% off the original price, because the 10% discount after three years of service is taken off the price that has already been reduced by 15%. Figure the problem in two steps: After the 15% discount, the price is $71.83. 90% of that—subtracting 10%—is $64.65.

9. Jason is six times as old as Kate. In two years, Jason will be twice as old as Kate is then. How old is Jason now?

A. Jason is 3 years old.

C. Kate is 5 years old.

The correct answer is A. J = 6K. J + 2 = 2(K + 2), so 6K + 2 = 2K + 4, which means K equals . J equals 6K, or 3.

B. Jason is older than Kate by 6 years.

The correct calculation is based on setting up the equations using the given information and solving for the age of Jason.

Explanation

The correct calculation is based on setting up the equations using the given information and solving for the age of Jason.

10. A patient's hospice stay cost one-fourth as much as his visit to the emergency room. His home nursing cost twice as much as his hospice stay. If his total healthcare bill was $140,000, how much did his home nursing cost?

B

D

A

The correct answer is C. Let E = emergency room cost; H = hospice cost, which is E; N = home nursing cost, which is 2H, or 2( )E. The total bill is E + H + N, which is E + E + E = 140,000. Add the left side of the equation to get E = 140,000. To solve for E, multiply both sides of the equation by . E = 140,000( ), or 80,000. H = E, or 20,000, and N = 2H, or 40,000

Let E = emergency room cost; H = hospice cost, which is E; N = home nursing cost, which is 2H, or 2(E). The total bill is E + H + N, which is E + E + E = 140,000. Add the left side of the equation to get E = 140,000. To solve for E, multiply both sides of the equation by 1. E = 140,000 * 1, or 80,000. H = E, or 20,000, and N = 2H, or 40,000.

Explanation

Let E = emergency room cost; H = hospice cost, which is E; N = home nursing cost, which is 2H, or 2(E). The total bill is E + H + N, which is E + E + E = 140,000. Add the left side of the equation to get E = 140,000. To solve for E, multiply both sides of the equation by 1. E = 140,000 * 1, or 80,000. H = E, or 20,000, and N = 2H, or 40,000.

11. The first digit of the square root of 112,092 is?

The correct answer is C. When a number is marked off in groups of two digits each, starting at the decimal point, the square root of the largest square in the left hand group, whether one or two digits, is the first digit of the square root of the number. In this case (11-20-92), 9 is the largest square in 11, and 3 is the square root of 9.

A

D

B

When a number is marked off in groups of two digits each, starting at the decimal point, the square root of the largest square in the left hand group, whether one or two digits, is the first digit of the square root of the number. In this case (11-20-92), 9 is the largest square in 11, and 3 is the square root of 9.

Explanation

When a number is marked off in groups of two digits each, starting at the decimal point, the square root of the largest square in the left hand group, whether one or two digits, is the first digit of the square root of the number. In this case (11-20-92), 9 is the largest square in 11, and 3 is the square root of 9.

12. Roberta draws two similar pentagons. The perimeter of the larger pentagon is 93 feet; one of its sides measures 24 feet. If the perimeter of the smaller pentagon equals 31 feet, then the corresponding side of the smaller pentagon measures.

A. Finding the corresponding side of the smaller pentagon requires calculating the area of the larger pentagon.

C. The corresponding side of the smaller pentagon can be determined by dividing 93 by 31.

D. Similarity of pentagon shapes does not allow for the calculation of corresponding side lengths.

The correct answer is B. A proportion can find an unknown side of a figure using known sides of a similar figure; a proportion can also find an unknown side using known perimeters. = . Cross-multiply: 93s = (31)(24).

In this problem, the principle of proportions and the relationship between similar polygons are key to finding the corresponding side length of the smaller pentagon given the information about the larger pentagon's perimeter and side length.

Explanation

In this problem, the principle of proportions and the relationship between similar polygons are key to finding the corresponding side length of the smaller pentagon given the information about the larger pentagon's perimeter and side length.

13. A certain water pollutant is unsafe at a level of 20 ppm (parts per million). A city's water supply now contains 50 ppm of this pollutant. What percentage of improvement will make the water safe?

A. An amount equaling 10 ppm of the pollutant would have to be removed to bring the 50 ppm down to 20 ppm (10 ppm is 20% of 50 ppm).

C. An amount equaling 15 ppm of the pollutant would have to be removed to bring the 50 ppm down to 20 ppm (15 ppm is 30% of 50 ppm).

The correct answer is E. An amount equaling 30 ppm of the pollutant would have to be removed to bring the 50 ppm down to 20 ppm (30 ppm is 60% of 50 ppm).

B. An amount equaling 40 ppm of the pollutant would have to be removed to bring the 50 ppm down to 20 ppm (40 ppm is 80% of 50 ppm).

Each incorrect answer provides a different calculation based on changing the amount of the pollutant that needs to be removed to make the water safe, showing the correct calculation in answer E.

Explanation

Each incorrect answer provides a different calculation based on changing the amount of the pollutant that needs to be removed to make the water safe, showing the correct calculation in answer E.