Math Word Problems Exam: Quiz!

1. A company has 450 employees at the beginning of the year. During the year it hires 35 employees, but 12 retires and 15 resign. What is the number of employees at the end of the year?

415

427

442

435

458

At the beginning of the year, the company has 450 employees. Throughout the year, they hire 35 new employees, increasing the total to 485. However, 12 employees retire and 15 resign, resulting in a decrease of 27 employees. Therefore, the number of employees at the end of the year is 458.

Explanation

At the beginning of the year, the company has 450 employees. Throughout the year, they hire 35 new employees, increasing the total to 485. However, 12 employees retire and 15 resign, resulting in a decrease of 27 employees. Therefore, the number of employees at the end of the year is 458.

2. If a file clerk can process 35 letters in half an hour, how many letters can she process in a seven (7) hour day?

245

350

700

590

490

If a file clerk can process 35 letters in half an hour, it means she can process 70 letters in an hour (since half an hour is half of an hour). Therefore, in a 7-hour day, she can process a total of 490 letters (70 letters per hour multiplied by 7 hours).

Explanation

If a file clerk can process 35 letters in half an hour, it means she can process 70 letters in an hour (since half an hour is half of an hour). Therefore, in a 7-hour day, she can process a total of 490 letters (70 letters per hour multiplied by 7 hours).

3. If 16 file cabinets require 24 feet of wall space, 40 cabinets will require how many feet of wall space?

50

55

60

65

70

If 16 file cabinets require 24 feet of wall space, it means that each cabinet requires 24/16 = 1.5 feet of wall space. To find out how many feet of wall space 40 cabinets will require, we can multiply the number of cabinets (40) by the amount of wall space required per cabinet (1.5 feet). Therefore, 40 cabinets will require 40 * 1.5 = 60 feet of wall space.

Explanation

If 16 file cabinets require 24 feet of wall space, it means that each cabinet requires 24/16 = 1.5 feet of wall space. To find out how many feet of wall space 40 cabinets will require, we can multiply the number of cabinets (40) by the amount of wall space required per cabinet (1.5 feet). Therefore, 40 cabinets will require 40 * 1.5 = 60 feet of wall space.

4. An 18 story office building has 15,000 square feet on each floor. Company "A" rents 9 floors and Company "B" rents 4 floors. What is the number of square feet of unrented floor space?

135,000

195,000

210,000

75,000

60,000

Company A rents 9 floors, which means they occupy a total of 9 * 15,000 = 135,000 square feet. Company B rents 4 floors, which means they occupy a total of 4 * 15,000 = 60,000 square feet. The total square footage occupied by both companies is 135,000 + 60,000 = 195,000 square feet. Since the building has a total of 18 floors, the remaining unrented floor space is 18 * 15,000 - 195,000 = 75,000 square feet. Therefore, the correct answer is 75,000.

Explanation

Company A rents 9 floors, which means they occupy a total of 9 * 15,000 = 135,000 square feet. Company B rents 4 floors, which means they occupy a total of 4 * 15,000 = 60,000 square feet. The total square footage occupied by both companies is 135,000 + 60,000 = 195,000 square feet. Since the building has a total of 18 floors, the remaining unrented floor space is 18 * 15,000 - 195,000 = 75,000 square feet. Therefore, the correct answer is 75,000.

5. A machine room has five rows of equipment, with three pieces in each row. A second machine room has eight rows of equipment, with four pieces in each row. How many more pieces of equipment are there in the second machine room?

20

32

15

17

47

The first machine room has a total of 5 rows * 3 pieces per row = 15 pieces of equipment. The second machine room has a total of 8 rows * 4 pieces per row = 32 pieces of equipment. Therefore, there are 32 - 15 = 17 more pieces of equipment in the second machine room.

Explanation

The first machine room has a total of 5 rows * 3 pieces per row = 15 pieces of equipment. The second machine room has a total of 8 rows * 4 pieces per row = 32 pieces of equipment. Therefore, there are 32 - 15 = 17 more pieces of equipment in the second machine room.

6. An employee receives overtime at the rate of 1-1/2 times his regular rate for work over 40 hours performed on weekdays. For any time worked on Sundays or holidays he is paid double his usual rate. John Jones worked his regular 40 hours, and he also incurred 4 hours extra on Friday and 5 hours extra on Sunday, for a total of 49 hours for the week. His regular rate of pay is $15.00 per hour. What should his gross pay be for the week?

$730.50

$840.00

$810.00

$800.25

$600.00

John Jones worked 40 regular hours at a rate of $15.00 per hour, which amounts to $600.00. He worked 4 extra hours on Friday, which should be paid at 1-1/2 times his regular rate. So, 4 hours * $15.00 * 1.5 = $90.00. He also worked 5 extra hours on Sunday, which should be paid at double his regular rate. So, 5 hours * $15.00 * 2 = $150.00. Adding all the amounts together, his gross pay for the week should be $600.00 + $90.00 + $150.00 = $840.00.

Explanation

John Jones worked 40 regular hours at a rate of $15.00 per hour, which amounts to $600.00. He worked 4 extra hours on Friday, which should be paid at 1-1/2 times his regular rate. So, 4 hours * $15.00 * 1.5 = $90.00. He also worked 5 extra hours on Sunday, which should be paid at double his regular rate. So, 5 hours * $15.00 * 2 = $150.00. Adding all the amounts together, his gross pay for the week should be $600.00 + $90.00 + $150.00 = $840.00.

7. To calculate the number of hours required to perform a data entry job it is necessary to multiply the number of cards by the number of columns to be entered for each card and divide by the keystrokes per hour. If there are 50 columns to be entered on each card, 10,000 keystrokes per hour, and 1,500 cards, how long will it take?

7 hrs/50 min

7 hrs/30 min

33 hrs/20 min

3 hrs

7 hrs/15 min

To calculate the time required to perform the data entry job, we need to multiply the number of cards (1,500) by the number of columns per card (50), and then divide by the keystrokes per hour (10,000). This will give us the total number of hours needed. The answer "7 hrs/30 min" indicates that it will take 7 hours and 30 minutes to complete the job.

Explanation

To calculate the time required to perform the data entry job, we need to multiply the number of cards (1,500) by the number of columns per card (50), and then divide by the keystrokes per hour (10,000). This will give us the total number of hours needed. The answer "7 hrs/30 min" indicates that it will take 7 hours and 30 minutes to complete the job.

8. What is the total cost of five thousand brick at $0.35 each and a 12 dozen lintels at $100.00 per dozen?

$1201.75

$2950

$1375

$4250

$1350

The total cost of the brick can be calculated by multiplying the number of brick (5000) by the cost per brick ($0.35), which equals $1750.
The total cost of the lintels can be calculated by multiplying the number of dozen (12) by the cost per dozen ($100.00), which equals $1200.
Adding these two costs together, $1750 + $1200 = $2950. Therefore, the correct answer is $2950.

Explanation

The total cost of the brick can be calculated by multiplying the number of brick (5000) by the cost per brick ($0.35), which equals $1750.
The total cost of the lintels can be calculated by multiplying the number of dozen (12) by the cost per dozen ($100.00), which equals $1200.
Adding these two costs together, $1750 + $1200 = $2950. Therefore, the correct answer is $2950.

9. The average salary of the three clerks is $450 per week. If one clerk earns $550, a second earns $300, how much is the salary of the third clerk?

$450

$850

$500

$750

$550

Based on the given information, the average salary of the three clerks is $450 per week. If one clerk earns $550 and a second clerk earns $300, we can calculate the total salary of the three clerks by multiplying the average salary by the number of clerks. Therefore, the total salary of the three clerks is $450 x 3 = $1350. To find the salary of the third clerk, we subtract the salaries of the first two clerks from the total salary. $1350 - $550 - $300 = $500. Therefore, the salary of the third clerk is $500.

Explanation

Based on the given information, the average salary of the three clerks is $450 per week. If one clerk earns $550 and a second clerk earns $300, we can calculate the total salary of the three clerks by multiplying the average salary by the number of clerks. Therefore, the total salary of the three clerks is $450 x 3 = $1350. To find the salary of the third clerk, we subtract the salaries of the first two clerks from the total salary. $1350 - $550 - $300 = $500. Therefore, the salary of the third clerk is $500.

10. A secretary spends 1/4 of her time each week filing, 3/8 of her time typing, and the rest of the time entering data. During a normal 40 hour week, how many hours would be spent entering data?

15 Hours

10 Hours

5 Hours

20 Hours

25 Hours

The secretary spends 1/4 of her time filing and 3/8 of her time typing. To find the time spent entering data, we need to subtract the time spent filing and typing from the total time. Since 1/4 + 3/8 = 5/8, the secretary spends 5/8 of her time filing and typing. Therefore, the remaining time for entering data is 1 - 5/8 = 3/8. Since the total time is 40 hours, the time spent entering data is (3/8) * 40 = 15 hours.

Explanation

The secretary spends 1/4 of her time filing and 3/8 of her time typing. To find the time spent entering data, we need to subtract the time spent filing and typing from the total time. Since 1/4 + 3/8 = 5/8, the secretary spends 5/8 of her time filing and typing. Therefore, the remaining time for entering data is 1 - 5/8 = 3/8. Since the total time is 40 hours, the time spent entering data is (3/8) * 40 = 15 hours.

11. If a gear makes 12 turns in 1/8 of a second, how many turns will it make in 20 seconds?

1920 turns

192 turns

30 turns

240 turns

96 turns

The gear makes 12 turns in 1/8 of a second. To find out how many turns it will make in 20 seconds, we can set up a proportion. Since 1/8 of a second is equal to 12 turns, we can set up the proportion: (1/8) second = 12 turns and 20 seconds = x turns. Cross multiplying, we get 1 * x = (1/8) * 20 * 12. Simplifying this equation, we find that x = 1920 turns. Therefore, the gear will make 1920 turns in 20 seconds.

Explanation

The gear makes 12 turns in 1/8 of a second. To find out how many turns it will make in 20 seconds, we can set up a proportion. Since 1/8 of a second is equal to 12 turns, we can set up the proportion: (1/8) second = 12 turns and 20 seconds = x turns. Cross multiplying, we get 1 * x = (1/8) * 20 * 12. Simplifying this equation, we find that x = 1920 turns. Therefore, the gear will make 1920 turns in 20 seconds.

12. A storage shelf measures 2 feet by 3 feet by 5 feet. How many boxes 2 feet by 1 foot by 1 foot could be put on the shelf?

15 boxes

30 boxes

3 boxes

7 boxes

12 boxes

The storage shelf measures 2 feet by 3 feet by 5 feet, which means it has a volume of 2 x 3 x 5 = 30 cubic feet. Each box measures 2 feet by 1 foot by 1 foot, which means it has a volume of 2 x 1 x 1 = 2 cubic feet. To find out how many boxes can fit on the shelf, we divide the volume of the shelf by the volume of each box: 30 / 2 = 15. Therefore, 15 boxes can be put on the shelf.

Explanation

The storage shelf measures 2 feet by 3 feet by 5 feet, which means it has a volume of 2 x 3 x 5 = 30 cubic feet. Each box measures 2 feet by 1 foot by 1 foot, which means it has a volume of 2 x 1 x 1 = 2 cubic feet. To find out how many boxes can fit on the shelf, we divide the volume of the shelf by the volume of each box: 30 / 2 = 15. Therefore, 15 boxes can be put on the shelf.

13. A business with an income of $1,100,000 budgets 1/10 of its income to advertising. If the income of the company is budgeted to decrease by 20%, what would be the amount budgeted for advertising?

$22,000

$880,000

$220,000

$88,000

$110,000

The business budgets 1/10 of its income for advertising, which is equal to $1,100,000/10 = $110,000. If the income of the company is budgeted to decrease by 20%, the new income would be $1,100,000 - ($1,100,000 * 20%) = $1,100,000 - $220,000 = $880,000. Therefore, the amount budgeted for advertising would also decrease by 20% to 1/10 of the new income, which is equal to $880,000/10 = $88,000.

Explanation

The business budgets 1/10 of its income for advertising, which is equal to $1,100,000/10 = $110,000. If the income of the company is budgeted to decrease by 20%, the new income would be $1,100,000 - ($1,100,000 * 20%) = $1,100,000 - $220,000 = $880,000. Therefore, the amount budgeted for advertising would also decrease by 20% to 1/10 of the new income, which is equal to $880,000/10 = $88,000.

14. A storage cabinet contains 60 reams of paper. After 40 reams have been removed, what percent is left?

33-1/3%

40%

66-2/3%

60%

20%

After 40 reams of paper have been removed from the storage cabinet, there are 20 reams left. To find the percentage, we divide the number of reams left (20) by the initial number of reams (60) and multiply by 100. Therefore, the percentage of paper left is 33-1/3%.

Explanation

After 40 reams of paper have been removed from the storage cabinet, there are 20 reams left. To find the percentage, we divide the number of reams left (20) by the initial number of reams (60) and multiply by 100. Therefore, the percentage of paper left is 33-1/3%.

15. At 5 a.m. the temperature was 62.5 degrees and at 8 a.m. the temperature was 67.0 degrees. Assuming a constant rate of increase, what time was it when the temperature was 65.5 degrees?

7:45 am

7:00 am

6:30 am

6:45 am

6:00 am

The temperature increased by 4.5 degrees in a span of 3 hours (from 5 a.m. to 8 a.m.). Therefore, the rate of increase is 4.5 degrees per 3 hours, which is equivalent to 1.5 degrees per hour. To find the time when the temperature was 65.5 degrees, we need to calculate how many hours it took for the temperature to increase by 3 degrees (67.0 - 65.5). Since the rate of increase is 1.5 degrees per hour, it took 2 hours (3 degrees / 1.5 degrees per hour). Adding this to the initial time of 5 a.m., we get 7 a.m. as the time when the temperature was 65.5 degrees.

Explanation

The temperature increased by 4.5 degrees in a span of 3 hours (from 5 a.m. to 8 a.m.). Therefore, the rate of increase is 4.5 degrees per 3 hours, which is equivalent to 1.5 degrees per hour. To find the time when the temperature was 65.5 degrees, we need to calculate how many hours it took for the temperature to increase by 3 degrees (67.0 - 65.5). Since the rate of increase is 1.5 degrees per hour, it took 2 hours (3 degrees / 1.5 degrees per hour). Adding this to the initial time of 5 a.m., we get 7 a.m. as the time when the temperature was 65.5 degrees.

16. A company's total expenses were $225,000 during its first year of operation, of which $18,450 was sales expense. What percentage was sales expense to the total expenses?

10.2%

7.3%

8.2%

12.0%

12.2%

The sales expense of $18,450 is a part of the total expenses of $225,000. To find the percentage, we divide the sales expense by the total expenses and multiply by 100. So, ($18,450 / $225,000) * 100 = 8.2%. Therefore, the sales expense was 8.2% of the total expenses.

Explanation

The sales expense of $18,450 is a part of the total expenses of $225,000. To find the percentage, we divide the sales expense by the total expenses and multiply by 100. So, ($18,450 / $225,000) * 100 = 8.2%. Therefore, the sales expense was 8.2% of the total expenses.

17. A certain factory employs 2000 women, 1,500 single men, and 6,500 married men. If each group is expanded proportionally until there are 11,500 employees, what will the number of the additional women be?

150

230

300

500

975

The total number of employees in the factory is 2000 + 1500 + 6500 = 10000. To find the proportion of women in the total number of employees, we divide the number of women by the total number of employees: 2000 / 10000 = 0.2.
If we expand the total number of employees to 11500, we can find the number of additional women by multiplying the expanded total by the proportion of women: 11500 * 0.2 = 2300.
Therefore, the number of additional women will be 2300 - 2000 = 300.

Explanation

The total number of employees in the factory is 2000 + 1500 + 6500 = 10000. To find the proportion of women in the total number of employees, we divide the number of women by the total number of employees: 2000 / 10000 = 0.2.
If we expand the total number of employees to 11500, we can find the number of additional women by multiplying the expanded total by the proportion of women: 11500 * 0.2 = 2300.
Therefore, the number of additional women will be 2300 - 2000 = 300.

18. A machine operates at the rate of 650 operations per minute; however, 20% must be deducted to allow for machine handling time by the operator. There are 13,000 operations to be put through the machine six times to complete the job. How long will it take?

1 hr/20 min

2 hrs/50 min

2 hrs/30 min

3 hrs/2 min

2 hours

The machine operates at a rate of 650 operations per minute, but 20% must be deducted for machine handling time. This means that the machine can actually process 80% of the operations per minute. To find out how long it will take to complete the job, we need to calculate the total number of operations and divide it by the number of operations the machine can process per minute.

The total number of operations is 13,000 multiplied by 6 (since the job needs to be completed six times). This equals 78,000 operations.

To find out how long it will take, we divide 78,000 by 650 operations per minute (80% of the machine's rate).

78,000 / (650 * 0.8) = 2 hours and 30 minutes.

Therefore, the correct answer is 2 hrs/30 min.

Explanation

The machine operates at a rate of 650 operations per minute, but 20% must be deducted for machine handling time. This means that the machine can actually process 80% of the operations per minute. To find out how long it will take to complete the job, we need to calculate the total number of operations and divide it by the number of operations the machine can process per minute.

The total number of operations is 13,000 multiplied by 6 (since the job needs to be completed six times). This equals 78,000 operations.

To find out how long it will take, we divide 78,000 by 650 operations per minute (80% of the machine's rate).

78,000 / (650 * 0.8) = 2 hours and 30 minutes.

Therefore, the correct answer is 2 hrs/30 min.

19. An employee worked Monday through Friday from 9:15 to 5:15, with 45 minutes for lunch and Saturday from 9:00 to 12:00. How many hours and minutes did he work that week?

10 hrs/15 min

36 hrs/15 min

43 hrs

39 hrs/15 min

38 hrs/45 min

The employee worked from 9:15 to 5:15 Monday through Friday, which is 8 hours each day. With 45 minutes for lunch, the total time worked each day is 7 hours and 15 minutes. Therefore, the total time worked from Monday to Friday is 36 hours and 15 minutes. Additionally, the employee worked from 9:00 to 12:00 on Saturday, which is 3 hours. Adding this to the previous total, the employee worked a total of 39 hours and 15 minutes that week.

Explanation

The employee worked from 9:15 to 5:15 Monday through Friday, which is 8 hours each day. With 45 minutes for lunch, the total time worked each day is 7 hours and 15 minutes. Therefore, the total time worked from Monday to Friday is 36 hours and 15 minutes. Additionally, the employee worked from 9:00 to 12:00 on Saturday, which is 3 hours. Adding this to the previous total, the employee worked a total of 39 hours and 15 minutes that week.

20. A rectangular computer is 42 inches longer than it is wide and has a perimeter of 204 inches. What is the width of the machine?

30 inches

9 inches

72 inches

45 inches

40 inches

The rectangular computer is 42 inches longer than it is wide. Let's assume the width of the machine is x inches. Therefore, the length of the machine would be x + 42 inches. The perimeter of a rectangle is calculated by adding all four sides together, so we can set up the equation: 2(x + x + 42) = 204. Simplifying this equation, we get 4x + 84 = 204. By solving for x, we find that the width of the machine is 30 inches.

Explanation

The rectangular computer is 42 inches longer than it is wide. Let's assume the width of the machine is x inches. Therefore, the length of the machine would be x + 42 inches. The perimeter of a rectangle is calculated by adding all four sides together, so we can set up the equation: 2(x + x + 42) = 204. Simplifying this equation, we get 4x + 84 = 204. By solving for x, we find that the width of the machine is 30 inches.

21. An IBM sorting machine operates at a rate of 450 cards per minute. 18,000 cards have to be put through the machine five times to complete a job. How long will it take to complete the job?

2 hours

3 hrs/30 min

3hrs/20 min

4 hours

3 hrs/33 min

The sorting machine operates at a rate of 450 cards per minute. To complete the job, 18,000 cards have to be put through the machine five times. Therefore, the total number of cards to be processed is 18,000 * 5 = 90,000 cards.

If the machine can process 450 cards per minute, then it will take 90,000 cards / 450 cards per minute = 200 minutes to process all the cards.

Since there are 60 minutes in an hour, 200 minutes is equal to 200/60 = 3 hours and 20 minutes. Therefore, it will take 3 hours and 20 minutes to complete the job.

Explanation

The sorting machine operates at a rate of 450 cards per minute. To complete the job, 18,000 cards have to be put through the machine five times. Therefore, the total number of cards to be processed is 18,000 * 5 = 90,000 cards.

If the machine can process 450 cards per minute, then it will take 90,000 cards / 450 cards per minute = 200 minutes to process all the cards.

Since there are 60 minutes in an hour, 200 minutes is equal to 200/60 = 3 hours and 20 minutes. Therefore, it will take 3 hours and 20 minutes to complete the job.

22. If paper costs $0.70 per ream, or $7.80 per dozen reams, how much is saved on each ream by purchasing by the dozen?

$0.05

$0.06

$0.50

$0.60

$0.80

By purchasing by the dozen, the cost per ream is reduced from $0.70 to $0.65. Therefore, the amount saved on each ream by purchasing by the dozen is $0.70 - $0.65 = $0.05.

Explanation

By purchasing by the dozen, the cost per ream is reduced from $0.70 to $0.65. Therefore, the amount saved on each ream by purchasing by the dozen is $0.70 - $0.65 = $0.05.