Set 3

1. 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?

150 soldiers can be supplied by one truck.

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.

250 soldiers can be supplied by one truck.

100 soldiers can be supplied by one truck.

The correct calculation is as follows: 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 = 30 ounces per soldier per day. So 96,000 ounces / 30 ounces = 3,200 soldier-days worth of rations. Since the trip is 10 days, 3,200 soldier-days worth of rations / 10 days = 320 soldiers can be supplied. However, since each soldier gets three meals per day, 320 soldiers / 3 meals per day = 200 soldiers can be supplied by one truck.

Explanation

The correct calculation is as follows: 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 = 30 ounces per soldier per day. So 96,000 ounces / 30 ounces = 3,200 soldier-days worth of rations. Since the trip is 10 days, 3,200 soldier-days worth of rations / 10 days = 320 soldiers can be supplied. However, since each soldier gets three meals per day, 320 soldiers / 3 meals per day = 200 soldiers can be supplied by one truck.

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

C. 135

D. 140

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

B. 130

To estimate the weight of a person who is 5'5" tall, we can infer that the weight would be closer to the weight provided for 5' (110 lbs) than the weight provided for 6' (170 lbs), so the estimated weight would be around 125 lbs.

Explanation

To estimate the weight of a person who is 5'5" tall, we can infer that the weight would be closer to the weight provided for 5' (110 lbs) than the weight provided for 6' (170 lbs), so the estimated weight would be around 125 lbs.

3. 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. 350,000

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. 450,000

A. 550,000

To find the estimate, we first set up the equation 600,000 = (1.20)(E), and then solve for E by dividing by 1.2. The correct answer is E = 500,000. Therefore, options A, B, and C are incorrect.

Explanation

To find the estimate, we first set up the equation 600,000 = (1.20)(E), and then solve for E by dividing by 1.2. The correct answer is E = 500,000. Therefore, options A, B, and C are incorrect.

4. 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?

A. 30 mph

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. 40 mph

C. 50 mph

The man needs to travel faster than the woman in order to catch up to her, considering the time and distance covered by the woman before he starts.

Explanation

The man needs to travel faster than the woman in order to catch up to her, considering the time and distance covered by the woman before he starts.

5. 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?

C. 240 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. 365 square feet.

A. 282 square feet.

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.

Explanation

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.

6. 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. The nurse would pay $63.37

D. The nurse would pay $70.25

C. The nurse would pay $67.78

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.

Explanation: 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

Explanation: 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.

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

B

D

A

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.

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.

8. An automobile gasoline gauge reads 1/8 full. After the gas tank is filled with 15 gallons, the gauge reads 7/8 full. What is the capacity of the tank?

25 gallons

§ Subtract the amount of gas already in the tank from the amount filled. 7/8 – 1/8 = 6/8 or ¾.
§ ¾ of the capacity is equal to 15 gallons. 3/4 x = 15.
§ Solving for x… x = 20.

12 gallons

16 gallons

Subtract the amount of gas already in the tank from the amount filled. 7/8 – 1/8 = 6/8 or 3/4. 3/4 of the capacity is equal to 15 gallons. Solving for x… x = 20.

Explanation

Subtract the amount of gas already in the tank from the amount filled. 7/8 – 1/8 = 6/8 or 3/4. 3/4 of the capacity is equal to 15 gallons. Solving for x… x = 20.

9. An automobile gasoline gauge reads 1/8 full. After the gas tank is filled with 15 gallons, the gauge reads 7/8 full. What is the capacity of the tank?

25 gallons

18 gallons

16 gallons

§ Subtract the amount of gas already in the tank from the amount filled. 7/8 – 1/8 = 6/8 or ¾.
§ ¾ of the capacity is equal to 15 gallons. 3/4 x = 15.
§ Solving for x… x = 20.

To determine the capacity of the tank, subtract the initial amount from the filled amount to get the fraction filled. The fraction filled can then be converted to gallons to find the total capacity of the tank.

Explanation

To determine the capacity of the tank, subtract the initial amount from the filled amount to get the fraction filled. The fraction filled can then be converted to gallons to find the total capacity of the tank.

10. A family budgets 1/3 of its income for rent, 1/4 for food and 1/6 for clothing. If the family has $420 left, what is their monthly income?

2100

· 1/3 + ¼ + 1/6 = ¾
· 1 – ¾ = ¼.
· ¼ x = 420. Solving for x… x = 1680.

840

1260

The correct monthly income is $1680. The total budgeted amount for rent, food, and clothing is 1/3 + 1/4 + 1/6 = 3/4 of the total income. Therefore, the remaining amount is 1 - 3/4 = 1/4 of the total income, which equals $420. Solving for x, we get x = $1680.

Explanation

The correct monthly income is $1680. The total budgeted amount for rent, food, and clothing is 1/3 + 1/4 + 1/6 = 3/4 of the total income. Therefore, the remaining amount is 1 - 3/4 = 1/4 of the total income, which equals $420. Solving for x, we get x = $1680.

11. Travis makes a 255-mile trip by car. He drives the first 2 hours at 45 miles per hour. At what speed must he travel for the remainder of the trip in order to arrive at his destination 5 hours after he started the trip?

50 miles per hour

60 miles per hour

· First begin by finding the total distance he already traveled: 45 x 2 = 90 miles already traveled.
· Subtract to 90 from 255 to find total distance needed to travel: 255 – 90 = 165 miles.
· He already traveled 2 hours, and the question asks how long it will take him to travel the remaining distance 5 hours AFTER he started, so subtract 2 from 5 to get 3 hours.
· D = R x T, 165 = 3r. 165 / 3 = 55 miles per hour.

40 miles per hour

First, find the total distance he already traveled: 45 x 2 = 90 miles. Subtract 90 from 255 to find the total distance needed to travel = 165 miles. Deduct the 2 hours already traveled from the 5 hours to find the remaining time = 3 hours. By using the formula D = R x T, 165 = 3r, solving for r gives 55 miles per hour.

Explanation

First, find the total distance he already traveled: 45 x 2 = 90 miles. Subtract 90 from 255 to find the total distance needed to travel = 165 miles. Deduct the 2 hours already traveled from the 5 hours to find the remaining time = 3 hours. By using the formula D = R x T, 165 = 3r, solving for r gives 55 miles per hour.

12. Three pipes, working together, can fill a tank in 4 minutes. If one pipe can fill a tank in 8 minutes, another in 12, and another in 24 minutes, how long would it take all 3 pipes working together to fill the tank?

6 minutes

§ H/8 + H/12 + H/24 = 1
§ Solving for H…H =4 minutes.

10 minutes

8 minutes

The correct method to solve this problem is to add the rates of all three pipes together to find the combined rate of filling the tank.

Explanation

The correct method to solve this problem is to add the rates of all three pipes together to find the combined rate of filling the tank.

13. Working alone, Allen can build a fence in 8 hours, and Danny can build the same fence in 16 hours. If after working alone for 2 hours, Allen is joined by Danny, how many more hours will it take the two of them to complete the fence?

6 hours

2 hours

§ Allen has worked two hours, so he has completed 2/8 of the job.
§ Danny joins him, so we will get: 2/8 + x/8 + x/16 = 1
§ Solving for x… x = 4 hours.

8 hours

Allen has worked 2 hours, so he has completed 2/8 of the job. When Danny joins, the combined rate is 1/8 + 1/16 = 1/5. Therefore, the remaining time to complete 3/4 of the fence is 4 hours.

Explanation

Allen has worked 2 hours, so he has completed 2/8 of the job. When Danny joins, the combined rate is 1/8 + 1/16 = 1/5. Therefore, the remaining time to complete 3/4 of the fence is 4 hours.

14. A lawn is 21 feet wide and 39 feet long. How much will it cost to weed and feed it if a gardening service charges $0.40 per square yard for this treatment?

$34.60

$42.80

§ First convert feet to yards. 3ft = 1yd. 21/3 = 7, 39/3 = 13.
§ Area of a rectangle is l x w. 13 x 7 = 91. 91 x 0.4 = $36.40.

$39.20

First convert feet to yards. 3ft = 1yd. 21/3 = 7, 39/3 = 13. Area of a rectangle is l x w. 13 x 7 = 91. 91 x 0.4 = $36.40.

Explanation

First convert feet to yards. 3ft = 1yd. 21/3 = 7, 39/3 = 13. Area of a rectangle is l x w. 13 x 7 = 91. 91 x 0.4 = $36.40.

15. In a clothing factory, 5 workers finish production of 6 garments each per day, 3 others turn out 4 garments each per day, and one worker turns out 12 per day. What is the average number of garments produced per worker per day?

5

7

8

§ The key word in this problem here is EACH. First find the total number of garments: 5 x 6 = 30, 3 x 4 = 12, 1 x 12 = 12. Add these together to get 54 total garments. Now divide this by the total number of workers. 54 / 9 = 6.

The key word in this problem here is EACH. First find the total number of garments: 5 x 6 = 30, 3 x 4 = 12, 1 x 12 = 12. Add these together to get 54 total garments. Now divide this by the total number of workers. 54 / 9 = 6.

Explanation

The key word in this problem here is EACH. First find the total number of garments: 5 x 6 = 30, 3 x 4 = 12, 1 x 12 = 12. Add these together to get 54 total garments. Now divide this by the total number of workers. 54 / 9 = 6.

16. Successive discounts of 20 percent and 15 percent are equivalent to a single discount of?

25%

36%

· 100 x 20% = 20.
· 100 – 20 = 80.
· 80 x 15% = 12. 80 – 12 = 68.
· 100 – 68 = 32.

35%

To calculate the equivalent single discount, you first apply the first discount of 20% to get 80. Then you apply the second discount of 15% to 80 to get 68. The single discount would be the difference between 100 and 68, which is 32%.

Explanation

To calculate the equivalent single discount, you first apply the first discount of 20% to get 80. Then you apply the second discount of 15% to 80 to get 68. The single discount would be the difference between 100 and 68, which is 32%.

17. A fugitive drives west at 50 miles per hour. After an hour, the police start to follow her. How fast must the police drive to catch up to her 4 hours after they start?

62 mph

70 mph

The fugitive will have traveled 5 hours at 50 miles per hour for a distance of 250 miles. To reach her in 4 hours, the police must travel at 250 miles per 4 hours, or 62.5 mph.

45 mph

The correct approach involves calculating the distance the fugitive has traveled by multiplying her speed by the total time. The police need to match this distance in a shorter amount of time, hence must travel faster.

Explanation

The correct approach involves calculating the distance the fugitive has traveled by multiplying her speed by the total time. The police need to match this distance in a shorter amount of time, hence must travel faster.

18. If an aircraft is traveling at 630 miles per hour, how many miles does it cover in 1200 seconds?

360 miles

Since 1200 seconds equals 20 minutes and 20 minutes equals hour, so of 630 miles equals 210 miles.

420 miles

525 miles

Since 1200 seconds equals 20 minutes and 20 minutes equals 1/3 hour, so 1/3 of 630 miles equals 210 miles.

Explanation

Since 1200 seconds equals 20 minutes and 20 minutes equals 1/3 hour, so 1/3 of 630 miles equals 210 miles.

19. Assume that it takes an average of 3 man-hours to stack 1 ton of a particular item. In order to stack 36 tons of that item in 6 hours, the number of persons required is?

30 persons

24 persons

10 persons

To stack 36 tons of the item, it takes 108 man-hours (36 x 3). It takes 18 persons to get that much work done in six hours ( = 18).

To stack 36 tons of the item, it takes 108 man-hours (36 x 3). It takes 18 persons to get that much work done in six hours.

Explanation

To stack 36 tons of the item, it takes 108 man-hours (36 x 3). It takes 18 persons to get that much work done in six hours.

20. A room measuring 15 feet wide, 25 feet long, and 12 feet high is scheduled to be painted shortly. If there are two windows in the room, each 7 feet by 5 feet, and a glass door, 6 feet by 4 feet, then the area of wall space to be painted measures:

772 sq. ft.

635 sq. ft.

1045 sq. ft.

We can assume the room is rectangular and has two long walls and two short walls. To answer this question, we must find the total area of the walls, and then subtract the area taken by the windows and door.

First, let's find the area of one of the long walls: 25 ft. × 12 ft. = 300 sq. ft. Since there are two long walls, the total area of the long walls is 300 × 2 = 600 sq. ft.

Now, let's find the area of the shorter walls: 15 ft. × 12 ft. = 180 sq. ft. There are two short walls, so the total area of both short walls is 2 × 180, which is 360 sq. ft. The total wall space, including the windows and door, is 600 sq. ft. + 360 sq. ft., which equals 960 sq. ft.

The windows take up 35 sq. ft. each (7 ft. × 5 ft.), and the door takes up 24 sq. ft. (6 ft. × 4 ft.). So, the total area that does not need to be painted is: 35 + 35 + 24 = 94 sq. ft.

The total area of wall space that does need to be painted is 960 – 94, or 866 sq. ft.

To find the correct answer, calculate the total wall space including windows and door as 960 sq. ft. Then subtract the area taken up by windows and door to get the correct answer of 866 sq. ft.

Explanation

To find the correct answer, calculate the total wall space including windows and door as 960 sq. ft. Then subtract the area taken up by windows and door to get the correct answer of 866 sq. ft.

21. A certain governmental agency had a budget last year of $1,100,500. Its budget this year was 7% higher than that of last year. The budget for next year is 8% higher than this year's budget. What is the agency's approximate budget next year?

$1,300,000

$1,200,000

$1,100,500 × 0.07 = $77,035, and $1,100,500 + $77,035 = $1,177,535, this year's budget. For next year: $1,177,535 × 0.08 = $94,203, and $1,177,535 + $94,203 = $1,271,738

$1,150,000

To calculate the budget for next year, we first find this year's budget by adding 7% to last year's budget. Then, we add 8% to this year's budget to get the approximate budget for next year.

Explanation

To calculate the budget for next year, we first find this year's budget by adding 7% to last year's budget. Then, we add 8% to this year's budget to get the approximate budget for next year.