Math in Employment Tests A Special Supplement to … in Employment Tests A Special Supplement to...

Math in Employment Tests

A Special Supplement to

Business Mathematics for Colleges

SIXTEENTH EDITION

James E. Deitz, Ed.D.Past President of Heald Colleges

James L. Southam, Ph.D.San Francisco State University

A Special Supplement to

Business Math for Colleges

Taking employment tests is difficult and stressful for many new applicants gradu-ating into the world of work. This stress can be reduced by familiarity and confi-dence, which can be built and developed through practice with the special kindsof mathematical problems that often appear on employment tests. This SpecialSupplement to Business Mathematics for Colleges reviews the types of problemscommonly found in employment tests. While some chapters in the book intro-duced some of these types of problems, this supplement is designed to build abil-ity and confidence in solving most of the mathematical and math-related questionsfound in current employment tests.

The types of problems have been placed into six basic categories: (1) Rate, Time,and Distance Problems; (2) Proportion Problems; (3) Time and Work Problems;(4) Weight and Measure Problems; (5) Percentage Problems, and (6) RelationshipProblems. By studying and learning how to solve problems in these six basic cate-gories, you will be able to feel comfortable and do well in taking many businessand government employment tests.

Three typical employment tests are provided at the end of this supplement.Correct answers are provided to all questions. You should practice and reviewthese tests until you are familiar with and confident about all of these questions.

Category 1: Rate, Time, and Distance Problems

In all rate, time, and distance problems, the formula is simple:

Rate (or speed) × Time = Distance

If you know any two factors, you can easily find the third:

Rate × Time = Distance

Distance ÷ Time = Rate

Distance ÷ Rate = Time

A train leaves a station traveling at 40 mph. How far has the train traveled 6 hourslater?


40 mph × 6hr = 240 mi

2 Math in Employment Tests

EXAMPLE A

A train traveled 550 miles in 11 hours. How fast was the train going?

Distance ÷ Time = Rate

550 mi ÷ 11 hr = 50 mph

A train traveled 300 miles at 60 mph. How many hours did the journey require?


300 mi ÷ 60 mph = 5 hr

Train X leaves station X traveling 40 mph on a 400-mile trip to station Y. Train Yleaves station Y traveling 60 mph over the same 400 miles toward station X. Howmany hours will the trains have traveled when the pass each other?

Distance = 400 mi

Total rate = 40 mph (X) + 60 mph (Y) = 100 mph


400 mi ÷ 100 mph = 4 hr

How far will train X in example D have traveled when the two trains pass eachother?


40 mph × 4 hr = 160 mi

Ellen Ross walks 4 miles per hour. Her brother walks 6 miles per hour. He leaveshome an hour after Ellen, going in the same direction. How far ahead of Ellenwill her brother be when Ellen has walked 32 miles?

Determine the time required for Ellen to walk 32 miles:


32 mi ÷ 4 mph = 8 hr

Determine the distance her brother walks:


6 mph × (8 – 1 = 7 hr) = 42 mi

Subtract:

42 mi – 32 mi = 10 mi ahead

Math in Employment Tests 3

EXAMPLE B

EXAMPLE C

EXAMPLE D

EXAMPLE E

EXAMPLE F

Margie Conklin types 50 words per minute. Sharon Levi types 75 words perminute. They each typed a page with 300 words. Margie started 1 minute beforeSharon. Who finished first?

Margie’s time: (300 words ÷ 50 wpm) – 1 min head start = 5 min

Sharon’s time: 300 words ÷ 75 wpm = 4 min

Sharon finished first: 4 min vs. 5 min


EXAMPLE G

C AT E G O R Y 1C O N C E P T C H E C K

a. Sam Jones and Mary McDonnell start traveling toward each other from360 miles apart. Sam is traveling at 40 miles per hour, Mary at 50miles per hour. How much time will elapse before they meet?

Distance = 360 miTotal rate = 40 mph + 50 mph = 90 mph

360 mi ÷ 90 mph = 4 hr

b. Julie Smith types 50 words per minute. Brad Faxon types 75 words perminute. They each typed a page with 400 words. Julie started 2 min-utes before Brad. Who finished first?

Julie’s time: (400 words ÷ 50 wpm) – 2 min head start = 6 min

Brad’s time: 400 words ÷ 75 wpm = 5 1—3

min

Brad finished first: 5 1—3

min vs. 6 min

Category 2: Proportion Problems

Virtually all employment tests include proportion problems. The unit method is asimple and fast way to solve proportion problems. To use this method, you firstfind a single basic unit of ONE (1) in the problem and then proceed to the answer.These problems may also be solved by proportionate shares (see example J).

To sort 360 letters, three clerks require 4 hours. How many letters can sevenclerks sort in 2 hours?

3 × 4 = 12 clerk hours to sort 360 letters

360 ÷ 12 = 30 letters per clerk hour (1 unit)

7 clerks × 2 hours = 14 clerk hours

14 × 30 = 420 letters

EXAMPLE H

The number of pennies in a cash box was twice the number of nickels. There werefive times as many nickels as there were dimes. All the coins totaled $36. Howmany pennies were there?

Group the coins:

10 pennies + 5 nickels + 1 dime = 45 cents

Determine the number of single units:

$36 ÷ $0.45 = 80 units

There are 10 pennies in each of the 80 units; therefore, multiply to find theanswer:

80 units × 10 pennies = 800 pennies

X, Y, and Z invest in a business as follows: X, $150; Y, $250; Z, $400. Later, thethree divide $1,200 profit in proportion to their investments. How much does eachreceive?

Total investment = $150 + $250 + $400 = $800

X s share:

Y s share:

Z s s

’ $ , $

’ $ , $

’

150800

1 200 225

250800

1 200 375

× =

× =

hhare:400800

1 200 600× =$ , $


EXAMPLE I

EXAMPLE J


a. To wash 36 cars, three men require 6 hours. How many cars can ninemen wash in 4 hours?

3 × 6 = 18 man hours to wash 36 cars36 ÷ 18 = 2 cars per man hour (1 unit)

9 men × 4 hours = 36 man hours36 × 2 = 72 cars

b. A, B, C, and D invest in a building together, as follows: A, $4,000; B,$6,000; C, $10,000; D, $12,000. Later, they sell the building for a profitof $8,000. They divide the profit in proportion to their investments. Howmuch profit does each receive?

Total investment = $4,000 + $6,000 + $10,000 + $12,000 = $32,000

A s share’ :,,

$ , $ , ’,,

$ ,4 00032 000

8 000 1 0006 00032 000

8× = ×B s share: 0000 1 500

10 00032 000

8 000 2 50012

=

× =

$ ,

’,,

$ , $ , ’,

C s share: D s share:0000

32 0008 000 3 000

,$ , $ ,× =

Category 3: Time and Work Problems

Time and work problems are another form of problem frequently included inemployment tests. The first and most important step in solving time and workproblems is to find the fraction of the job that can be completed in one unit oftime (for example a day, an hour, or a minute). Once you have found this amount,divide the denominator by the numerator to get your answer.

X can do a job in 5 days. Y can do the job in 10 days. How long will it take thetwo of them working together to do the job?

X and Y together can do a job in 4 hours. X can do the job alone in 16 hours.How long would it take Y to do the job alone?

X and take 4 hours:1hour

X alone takes 16 hours:1hour

Y of job

o

=

=

14

116

ff job

Y alone can do or of the job in hour

Therefore Y ca

14

116

316

1− , , .

, nn complete the job alone in hours513

16 3 513

÷ =⎛

⎝⎜

⎞

⎠⎟.

X takes 5 days:1day

Y takes 10 days:1day

=

=

15

110

of job

of job

X and Y togeether do or of the job in day

Therefore they can finis

15

110

310

1+ , , .

, hh the job in days313

10 3 313

÷ =⎛

⎝⎜

⎞

⎠⎟.


EXAMPLE K

EXAMPLE L


a. A can do a job in 6 minutes. B can do the job in 4 minutes. C can dothe job in 4 minutes. How long will it take for the three of them workingtogether to do the job?

A takes 6 minutes:1minute

B takes 4 minutes:1minute

=

=

1614

of job

of joob

of job

A B and C together do

C takes 4 minutes:1minute =

+ +

14

16

14

1, ,

4423

1

1

, , min .

,

or of the job in ute

Therefore they can finish the job in112

3 2 112

min .utes ÷ =⎛

⎝⎜

⎞

⎠⎟

Category 4: Weight and Measure Problems

The traditional measures shown below are commonly included in employmenttests. You should memorize them.

Test problems generally involve changing from smaller units to larger ones and

vice versa; adding, subtracting, multiplying, and dividing measures; and reasoning to logically apply units of measure. We used conversion rates as shown in the table below in working the following examples and tests.

Weight Capacity

16 ounces (oz) = 1 pound (lb) 2 cups = 1 pint (pt)2,000 pounds = 1 ton 2 pints = 1 quart (qt)

4 quarts = 1 gallon (gal)Length 16 ounces (1 lb) = 1 pint12 inches (in) = 1 foot (ft)3 feet = 1 yard (yd) Area5,280 feet = 1 mile (mi) 144 square inches = 1 square foot (sq ft)1,760 yards = 1 mile 9 square feet = 1 square yard (sq yd)

43,560 square feet = 1 acre (a)Time 640 acres = 1 square mile (sq mi)60 seconds (sec) = 1 minute (min)60 minutes = 1 hour (hr) Volume24 hours = 1 day (da) 1,728 cubic inches = 1 cubic foot (cu ft)7 days = 1 week (wk) 27 cubic feet = 1 cubic yard (cu yd)

4 1—3

weeks = 1 month (mo) 1 cubic foot = 7 1—2

gallons of water52 weeks = 1 year (yr)12 months = 1 year


b. Carl Samuelson and Ron Delaney together can paint a house in 6 days.Carl can paint the house alone in 10 days. How long would it take Ronto do the job alone?

Carl and Ron take 6 days:

Carl alone takes 10 days:1day

116

day of job=

=11

1016

110

115

1

of job

Ron alone can do or of the job in day

Therefor

− , , .

ee Ron can complete the job in days, ( ).15 15 1 15÷ =

TRADITIONAL MEASURES

How many hours equal 9,000 seconds?

How many inches are there in 6 yards?

6 yd × 3 ft = 18 ft

18 ft × 12 in = 216 in

Add 2 yards, 1 foot, 9 inches and 3 yards, 2 feet, 6 inches.

Yards Feet Inches

2 1 93 2 61 15 3 15

–3 –126 1 3

In the final step, smaller units are changed to the next larger units, where possible.

Subtract 3 yards 10 inches from 15 years, 2 feet, 7 inches.

Yards Feet Inches

1 1915 2 7–3 _ –1012 1 9

Because 10 inches cannot be subtracted from 7 inches, 1 foot (12 inches) is takenfrom the Feet column and added to the 7 to make 19 inches, from which 10inches can be subtracted.

How many square yards of linoleum are used for a floor 18 feet wide and 27 feetlong?

18 ft × 27 ft = 486 sq ft

486 sq ft ÷ 9 = 54 sq yd

9 000 60 1 150 60 1 60 1150 60, (sec min) min sec min; min

(min÷ = = =

÷in hr

in 11 2 30 60 60 3 600 1

2 30 23060

212

hr hr sec hr

hr

) min min , sec

min

= × = =

= =

or

hhr hr9 000 3 600 212

, sec , sec÷ =


EXAMPLE M

EXAMPLE N

EXAMPLE O

EXAMPLE P

EXAMPLE Q

a. Subtract 1 yard, 2 feet, 11 inches from 4 yards, 2 feet, 6 inches.

Yards Feet Inches4

3 1 184 2 6

–1 –2 –112 2 7

b. A contractor dug a swimming pool 36 feet long and 20 feet wide andfilled it to a depth of 6 feet. What was the volume of water in the pool?(Answer in gallons.)

Find the cubic feet of water:

36 ft × 20 ft × 6 ft = 4,320 cu ft of water

Find the volume of 4,230 cu ft of water:

4,320 cu ft × 7 1—2

gal per cu ft = 32,400 gal

c. How many minutes are there in 24 hours?

24 hr × 60 min per hr = 1,440

d. How many square yards of carpet does it take to carpet a room 24 feetlong and 18 feet wide?

24 ft × 18 ft = 432 sq ft432 sq ft ÷ 9 sq ft per sq yd = 48 sq yd

e. A carpenter saws a board 20 feet 10 inches long into two equalpieces. How long is each piece?

20 ft ÷ 2 = 10 ft10 in ÷ 2 = 5 inEach piece is 10 ft 5 in long.

If a 14 foot 9 inch rod were cut into 3 equal pieces, how long would each piece be?

14 ft × 12 in = 168 in

168 in + 9 in = 177 in

177 in ÷ 3 = 59 in

59 in ÷ 12 in = 4 ft 11 in

Find the gallons in a tank 18 feet long by 6 feet wide with 4 feet of water.

Length × Width × Height = Volume

18 ft × 6 ft × 4 ft = 432 cu ft

432 cu ft × 7 1—2

gal per cu ft = 3,240 gallons


EXAMPLE R


EXAMPLE S

Category 5: Percentage Problems

A percent is a fractional expression whose denominator is 100. Percent may beexpressed by using a percent sign (%) or a decimal point (.). Fifteen percent, forexample, is 15% or 0.15.

A worker earning $400 a week saves 12% of her earnings. How much does shesave each week?

Base × Rate = Percentage

$400 × 12% = $48 saved each week

If a customer’s 15% discount on a purchase amounted to $30, what was the totalamount of the sale?

Percentage ÷ Rate = Base

$30 ÷ 0.15 = $200 total sale

Of 120 employees in an organization, 90 attended the company picnic. What per-cent of the employees attended the picnic?

Percentage ÷ Base = Rate

90 ÷ 120 = 75% attended

A company earned a profit of $8,000 in 1997 and $6,000 in 1998. What was therate of decrease?

Find the dollar amount of decrease:

$8,000 – $6,000 = $2,000 decrease

Apply the formula:

Amount of decrease ÷ Original amount = Rate of decrease

$2,000 decrease ÷ $8,000 original amount = 25% rate of decrease

A company had a profit of $9,000 in 1997 and $10,500 in 1998. What was therate of increase?

Find the dollar amount of increase:

$10,500 (1998) – $9,000 (1997) = $1,500 increase

Apply the formula:

Amount of increase ÷ Original amount = Rate of increase

$1,500 increase ÷ $9,000 original amount = 16.67% rate of increase.


EXAMPLE T

EXAMPLE U

EXAMPLE V

EXAMPLE W

EXAMPLE X



a. A customer was given a 15% discount on furniture costing $180. Whatwas the amount of discount?

Base × Rate = Percentage$180 × 15% = $27

b. Another customer was given a 10% discount of $25 on a dining roomset. What was the original cost of the dining room set?

Percentage ÷ Rate = Base$25 ÷ 10% = $250

c. A third customer was given $30 off on a $200 couch. What was therate of discount?

Percentage ÷ Base = Rate$30 ÷ $200 = 15%

d. Three hundred customers purchased season tickets to ball games lastyear; 250 purchased them this year. What is the rate of decrease?

Find the amount of decrease:

300 – 250 = 50

Apply the formula:

50 decrease ÷ 300 original amount = 16.67% rate of decrease

e. A salesman sold 14 cars last year and 16 this year. What is the rate ofincrease?

Find the amount of increase:

16 – 14 = 2

Apply the formula:

2 ÷ 14 = 14.29% rate of increase

Category 6: Relationship Problems

Relationships in a series of numbers may be found by comparing the first three orfour terms in the series.

Complete the series: 3, 6, 9, 12, 15, _____, _____Add 3 to the preceding number. The last two terms are 18 and 21.

A series might combine two or more steps.

Complete the series: 4, 8, 6, 10, 8, 12, _____, _____Alternately add 4 and subtract 2. The last two terms are 10 and 14.

EXAMPLE Y

A series might be progressive.

Complete the series: 1, 3, 6, 10, _____, _____The difference between successive numbers increases by 1. The last two terms are15 and 21.

Complete the series: 1, 2, 6, 24, _____, _____Multiply consecutively times 2, times 3, times 4, and so on. The last two terms are120 and 720.

Complete the series: 1, 4, 2, 8, 4, 16, _____, _____Alternately multiply by 4 and divide by 2. The last two terms are 8 and 32.

Number relationships may also be visualized from a verbal description.

A person walked 2 miles south, then 3 miles east, then 2 miles north, then 4 mileswest. How far was he from his starting point?

1 mile


EXAMPLE Z


a. Complete the series: 4, 8, 12, 16, _____, _____Add 4; the last two terms are 20 and 24.

b. Complete the series: 50, 47, 44, 41, _____, _____Subtract 3; the last two terms are 38 and 35.

c. Complete the series: 5, 10, 7, 12, 9, 14, _____, _____Alternately add 5 and subtract 3; the last two terms are 11 and 16.

d. Complete the series: 2, 4, 8, 16, _____, _____Multiply by 2; the last two terms are 32 and 64.

e. Complete the series: 2, 8, 4, 16, 8, 32, _____, _____Alternately multiply by 4 and divide by 2; the last two terms are 16and 64.

f. A person drove 4 miles east, then back 3 miles west, then back 2miles east, then back 1 mile west. How far was she from her startingpoint?

2 miles

Sample Test 1

1. George Davis can plant 2 acres of corn per day. Henry Davis can plant 3 acres of corn per day.Working together, how many acres can they plant in 6 days?

Answer _______________

2. Jane can do a job in 8 hours. Martha takes 12 hours to do the same job. How long willit take Jane and Martha working together to do the job?

Answer _______________

3. Team A can do a project in 10 days. Team B requires 15 days to complete the sameproject. How long will it take both teams working together to finish the project?

Answer _______________

4. Betty Kusack and Theresa Peña together can do a job in 20 hours. Working alone,Betty can do the job in 60 hours. How long would it take Theresa, working alone, todo the job?

Answer _______________

5. One donut machine makes 330 donuts per hour. Another donut machine makes 310 donuts perhour. With both machines working, how long would it take to make 4,800 donuts?

Answer _______________

6. If Chantall Jefferson can do a job in 3 days, Colleen O’Hara in 3 days, and ClaireMost in 4 days, how long would the job take if Chantall, Colleen, and Claire workedtogether?

Answer _______________


Sample Test 1 (continued)

7. A plane leaves Los Angeles for New York and travels at 600 mph. At the same instant, aplane leaves New York for Los Angeles and travels 480 mph. If the total distancebetween the two cities is 3,600 miles, how much time will elapse before the planes meet?

Answer _______________

8. Refer to problem 7. If the Los Angeles to New York plane departed at 8:30 A.M., howmany miles would it have traveled by 2:30 P.M.? (Ignore time zones.)

Answer _______________

9. Refer to problem 7. Suppose that both planes landed in Chicago, which is 1,200 milesfrom New York and on a straight line between the two cities. What time would theLos Angeles to New York plane arrive in Chicago if it departed from Los Angeles at12 noon? (Ignore time zones.)

Answer _______________

10. Faye Dunston and Franco Girelli start toward each other from 240 miles apart. Fayeleaves 1 hour before Franco. Faye travels at 30 mile per hour, Franco at 40 miles perhour. How many miles will Franco have traveled when they meet?

Answer _______________

11. Sandra Wallace walks at 5 miles per hour; Michael Sanders walks at 3 miles per hour. IfMichael starts to walk in a certain direction 2 hours before Sandra, how far behind Sandrawill he be when Sandra has walked 20 miles?

Answer _______________

12. Two cars started toward each other from 375 miles apart. The speed of one car was 40 mph. It met the other car after 5 hours. What was the speed of the other car?

Answer _______________



13. If four postal clerks require 60 minutes to sort 1,200 letters, how many letters can tenclerks sort in 8 hours?

Answer _______________

14. Three different bakers produce the following numbers of loaves of bread per hour;baker A, 250; baker B, 300; baker C, 350. If they all work the same number of hoursand produce a combined total of 12,600 loaves, how many of these loaves does bakerB produce?

Answer _______________

15. Refer to problem 14. How many hours does each baker work?Answer _______________

16. Paul Eisner, Dylan Connor, and Martina Ybarria invest $25,000, $50,000, and$75,000, respectively, in a business. Later, they sell the business for $96,000 anddivide the proceeds in proportion to their original investment. How much doesMartina get?

Answer _______________

17. A cash box had an equal number of dimes and quarters. It had twice as many penniesand three times as many nickels, The total cash was $416. How many nickels werethere?

Answer _______________

18. Subtract 3 hours, 15 minutes, 10 seconds from 11 hours, 27 minutes, 34 seconds.Answer _______________



19. Add 5 yards, 2 feet, 9 inches; 4 yards, 1 foot, 7 inches; and 1 yard, 6 inches.Answer _______________

20. A room is 24 feet long and 15 feet wide. How much will it cost to cover the floorwith carpet costing $36 a square yard if an extra 4 square yards must be purchased for matching?

Answer _______________

21. A swimming pool is 60 feet long and 30 feet wide. It is 3 feet deep at one end andslopes evenly to a depth of 9 feet at the other end. How many gallons of water will berequired to fill it to 1 foot from the top? (Hint: (3 + 9) ÷ 2 = 6 ft average depth of pool.)

Answer _______________

22. Mary purchased a throw rug priced at $150 and marked 10% off, a coffee table priced at$80 and marked 15% off, and a lamp priced at $65. She had a coupon good for an additional

20% off the entire purchase. How much did Mary pay for the three items? Answer _______________

23. At a company employing 140 people, 40% of the employees took the bus to work, and 5 % lived close enough to walk. The others drove cars. How many employees drive cars to work?

Answer _______________

24. Complete the following series: 4, 12, 8, 16, 12, _____, _____ Answer _______________

25. Complete the following series: 2, 8, 4, 16, 8, _____, _____ Answer ______________



Sample Test 2

1. United Airlines flight A flies 2,000 miles from Minneapolis to New York in 5 hours.United Airlines flight B flies 2,000 miles from Minneapolis to New York in 4 hours. IfUnited flight A starts 1 hour before United flight B, how far ahead of flight B will itbe when flight B has flown 1,500 miles?

Answer _______________

2. A car leaves Cleveland for Albuquerque and travels at 55 mph. Simultaneously, a sec-ond car leaves Albuquerque for Cleveland and travels at 50 mph. If the total distanceis 1,575 miles, how much time will go by before the two cars meet?

Answer _______________

3. If the Cleveland to Albuquerque car (from problem 2) left at 9 A.M., how far fromAlbuquerque would it be at 6 P.M.?

Answer ______________

4. Bus A travels 600 miles from Portland to San Franciso at an average rate of 50 mph. Bus B makes the same trip traveling at an average rate of 60 mph and makes a two hour stop along the way. If both busses leave Portland at the same time, which one will be first to arrive in San Francisco? Answer ______________ 5. Mozelle Williams and Melvin Kast start toward each other from 150 miles apart.

Mozelle leaves 1 hour before Melvin. Mozelle travels at 30 mph, Melvin at 20 mph.How many miles will Melvin have traveled when they meet?

Answer _______________

6. The Swenson nursery plants 14 trees per hour. The Johnson nursery plants 12 treesper hour. Working as a team, how many trees can the two nurseries plant in 22 hours?

Answer _______________

7. One manufacturer can produce 800 VCRs per day; another can produce 960 per day.Working together, how many days would it take the two manufacturers to produce39,600 VCRs?

Answer _______________

Sample Test 2 (continued) 8. One computer printer prints 1,060 words per minute. A second brand prints 510 words per

minute. A third unit prints 1,430 words per minute. How many words do the three produce in 1 hour?

Answer _______________ 9. Alberta Emery can sew a dress in 3 days. Allison Taylor requires only 2 days. If they

combine efforts to fill one order to sew 30 dresses, how long will they take to fill the order? Answer _______________ 10. Refer to problem 9. If each woman filled the order for 30 dresses by herself, how many

more days would it take Alberta Emery? Answer _______________ 11. If Warren Stevens can do a job in 4 days, Ted Burnsted in 6 days, Sam Chang in 2 days,

and Jane Reilly in 5 days, how long would it take to complete the job if all four worked together?

Answer _______________ 12. Refer to problem 11. How long would it take Warren and Ted to do the job? Answer _______________ 13. Refer to problems 11 and 12. How much less time would it take Sam and Jane than Warren

and Ted to complete the job? Answer _______________ 14. How many ounces are there in 1 ton? Answer _______________

15. How many minutes are there in 121

days?

Answer _______________ 16. How many inches are there in 32 yards? Answer _______________



17. How many gallons of water would it take to fill a swimming pool that was 10 feetwide, 30 feet long, and 5 feet deep?

Answer _______________

18. Refer to problem 17. If water costs $0.07 per gallon, how much would it cost to fill thepool?

Answer _______________

19. Subtract 1 yard, 2 feet, 9 inches from 3 yards, 2 feet, 2 inches.Answer _______________

20. A room measures 21 feet long and 15 feet wide. How much will it cost to carpet theroom with carpet that costs $18.50 per square yard?

Answer _______________

21. If a Jacuzzi that is 5 feet long, 4 feet wide, and 3 feet deep is filled with water, howmany gallons of water does it contain?

Answer _______________

22. Complete the following series: 2, 8, 4, 16, 8, _____Answer _______________

23. Complete the following series: 5, 15, 10, 20, 15, _____Answer _______________


Sample Test 3

1. Kay Moser typed 50 letters per day for 7 days; Joe Plante typed 50 letter perday for 5 days. What is the total number of letters typed by both?a. 350 b. 600 c. 100 d. 550

2. An automobile traveled for 4 hours 15 minutes at an average speed of 40 mph. How many miles did it travel?a. 170 b. 155 c. 175 d. 200

3. A sales representative received commissions of $39.50 in March, $49.20 inApril, $18.00 in May, and $97.70 in June. What was the average monthlycommission?a. $49.20 b. $51.10 c. $204.40 d. $40.00

4. If a person receives a 30% discount on a purchase of $96.80, how much willthat person pay?a. $29.04 b. $93.90 c. $32.27 d. $67.76

5. Of 465 students in school, 93 went to a ball game. What percent of the stu-dents did not go to the game?a. 20% b. 40% c. 60% d. 80%

6. Two cars are traveling in the same direction, one at 50 mph, one at 55 mph.If the slower car started an hour earlier, how many hours will it take thefaster car to catch up to it?a. 11 b. 9 c. 10 d. 5.5

7. Refer to problem 6. How far will each car have traveled when the slowercar catches up to the faster car?a. 550 mi b. 500 mi c. 600 mi d. 495 mi

8. Julio Martinez saves twice as much as Ken Shaw. Ken saves twice as muchas Phyllis Catchings. If Julio saves a total of $1,500, how much does Phyllissave?a. $1,500 b. $600 c. $375 d. $500

9. If $15,300 is divided among Ibn Rashid, Harold Pierce, and Monica Sneadin the proportions 3, 5, and 9, respectively, how much will Ibn receive?a. $2,700 b. $5,900 c. $5,100 d. $900

10. Two trains were 780 miles apart. They were headed directly toward eachother. One traveled at 30 mph. The other traveled at 35 mph. How manyhours did it take for the trains to meet?a. 26 b. 13 c. 18 d. 12

11. At $14.25 per sq yd, how much would it cost to carpet a room 18 ft by 27 ft?a. $2,308.50 b. $692.55 c. $769.50 d. $6,925.50


Answers

1. _____

2. _____

3. _____

4. _____

5. _____

6. _____

7. _____

8. _____

9. _____

10. _____

11. _____

Sample Test 3 (continued) Answers

12. Two partners, Joseph Alcara and Merriam Trask, own a restaurant. They sell 12._____

a one-third interest to Shelley Cantrell. If the part of the restaurant that Joseph and Merriam still own is worth a total of $15,000, how much was the original value?

a. $22,500 b. $30,000 c. $45,000 d. $7,50013. 13. A bus left San Diego at 1:30 and traveled 50 mph. A train left San Diego at 13._____

3:30 traveling in the same direction at 70 mph. At what time will the train catch up with the bus?

a. 6:30 b. 9:00 c. 11:18 d. 8:30 14. If plane X averages 800 mph and plane Y averages 400 mph, how many 14._____

hours will plane X travel before it overtakes plane Y if plane Y has a 2 hour and 30 minute head start?

a. 141 b. 2

21 c. 5 d. 7

21

15. Two cars, 1200 miles apart, start traveling toward each other. Both cars travel at 15._____

an average rate of 50 mph. How many hours will it take the two cars to meet? a. 10 b. 12 c. 14 d. 24

16. Two teenagers who were 60 miles apart walked toward each other. They met 16._____

in 4 hours. One teenager averaged 7 mph. How fast did the other travel?

a. 7 mph b. 874 mph c. 6

73 mph d. 8 mph

17. Two cars started toward each other from 400 miles apart. They met in 17._____

5 hours. Car X averaged 45 mph. How many mph did car Y average? a. 45 b. 55 c. 35 d. 37

18. A bus averaging 45 mph leaves New York at 9:30 A.M. How many miles will 18._____

it have traveled at 4:45 P.M.? a. 281.25 b. 326.25 c. 236.25 d. 282.5 19. A submarine travels at a rate of 12 mph under water and 24 mph on top. In a 19._____

100-mile trip, it travels 20 miles below and the rest on top. How many hours does the 100-mile trip take?

a. 461 b. 8

21 c. 5 d. 7

241

20. How long will it take a train averaging 70 mph to cover its entire route of 20._____

385 miles if it loses 45 minutes of travel time in stops? a. 5 hr 30 min b. 6 hr 150 min c. 7 hr d. 4 hr 45 min



21. If a hiker travels 18 miles in 4 hours, how many miles will be covered in 7.5days walking 8 hours per day?a. 240 b. 262.5 c. 320 d. 270

22. Thai Le can do a job in 3 days. Anh Huynh can do the same job in 2 days.How many days would it take them to do the job together?a. 1.8 b. 1.5 c. 1 d. 1.2

23. Aren Chomski, Warner Howe, and Brown Ledbetter invested $1,000, $1,500,and $3,500, respectively, in a business partnership. If the annual profit of$1,500 is divided among them in proportion to their investments, how muchwill Aren receive?a. $300 b. $250 c. $1,000 d. $375

24. Three salespeople, Melissa Lever, Tom Borders, and Rose Tanaka sold acombined total of $8,400. Melissa sold $3,360; Tom and Rose split thereminder. If a $300 bonus was divided among the three in proportion to theirsales, how much did Rose receive?a. $90 b. $180 c. $50.40 d. $75.60

25. From Los Angeles to Dallas, a plane takes 3 hours, 5 minutes. A train takes11 hours, 10 minutes. How many hours are saved by taking the plane?

26. How many pint jars can be filled with 4 gallons, 3 quarts or 16 ouncesof liquid?a. 37 b. 42 c. 35 d. 39

27. Boat Y and boat Z start traveling toward each other from 600 mile apart. Y istraveling at 35 mph, Z at 40 mph. How many hours will pass before theymeet?a. 7 b. 8 c. 9 d. 10

28. Refer to problem 27. Y and Z start traveling toward each other from 600miles apart. Y is traveling at 35 mph, Z at 40 mph. How many miles will Ytravel before they meet?a. 400 b. 320 c. 350 d. 280

29. Departments X, Y, and Z had sales of $1,100, $1,900, and $2,500, respec-tively. A $700 advertising charge was allocated proportionately. How muchis Department X’s share of the advertising charge?a. $140 b. $350 c. $110 d. $116.67

30. Refer to problem 29. How much would Department Z's expense be if the advertising charge was increased to $1,500?a. $750 b. $681.82 c. $654.37 d. $690

a. b. c. d.73

417

1

431

3

419

3

4


Answers

21. _____

22. _____

23. _____

24. _____

25. _____

26. _____

27. _____

28. _____

29. _____

30. _____


31. If Alain Junev and Parc Lafontaine together to do a job in 6 hours and Alainalone does the job in 10 hours, how long does it take Parc alone to do thejob?a. 12 hr b. 20 hr c. 15 hr d. 9 hr

32. A company had expenses of $15,500 in 1994 and $18,600 in 1995. Whatwas the percent increase?

33. Last year, the Jordan Company had expenses of $1,200,000. This year theycut expenses by 18%. If 30% of the Jordan Company expenses were charged to rent, what was the amount of rent paid this year?a. $360,000 b. $177,120 c. $295,200 d. $315,000

34. If an agent’s 8% commission for selling a product amounted to $1,200, whatwas the total amount of the sale?a. $12,000 b. $9,600 c. $8,600 d. $15,000

35. How many days will be required for 5 people to build 5 machines if 5 peo-ple can build 20 machines in 8 days?a. 5 b. 4 c. 2 d. 1.6

36. Mae Miles drove 231 miles in 1 day. If this distance is 40% more than shedrove the day before, how many miles did she drive the day before?a. 165 b. 162.7 c. 323.4 d. 57.75

37. How many square feet does one wall of a 24 ft by 24 ft room with a 12 fthigh ceiling contain?a. 48 b. 6,912 c. 288 d. 64

38. Solve the equation: 17 + (16 ÷ 4) + 3.5 = ______a. 11.75 b. 24.5 c. 9.125 d. 25.4

39. A secretary earns $1,400 per month, spends 90% of what is left after deduc-tions of 22%, and saves the rest. How many months will it take the secretaryto save $1,528.80?a. 11 b. 12 c. 13 d. 14

40. A $300 lamp is sold at a 40% discount; 15% of the sales price goes foradvertising. What is the advertising cost?a. $180 b. $60 c. $27 d. $18

a. b. c. d.15 162

325 20% % % %


Answers

31. _____

32. _____

33. _____

34. _____

35. _____

36. _____

37. _____

38. _____

39. _____

40. _____

Answers and Solutions to Sample Test 1

1. 2 acres by George + 3 acres by Henry = 5 acres per day;6 days × 5 acres = 30 acres.

2.

3.

4.

5. 330 + 310 = 640 donuts per hour; 4,800 ÷ 640 = 7 1/2 hours

6.

7.

8. 600 × 6 hr = 3,600 mi

9. 3,600 mi – 1,200 = 2,400 mi traveled; 2,400 mi ÷ 600 mph = 4 hr, or 4 P.M.

10. Faye: 1 hr at 30 mph = 30 mi head start

Distance left = 240 mi – 30 mi = 210 mi

Total rate = 30 mph + 40 mph = 70 mph

Time = 210 miles ÷ 70 mph = 3 hr when Faye and Franco meet

Franco travels 3 hr × 40 mph = 120 mi

11. Sandra: 20 miles ÷ 5 mph = 4 hrsMichael: 3 mph × (2 + 4) hrs = 18 milesSandra's 20 miles – Michael's 18 miles = 2 miles behind

600 480 1 080 3 600 1 080 313

mph mph mph miles mph hr+ = ÷ =, ; , ,

113

13

14

13

13

14

1112

day for Chantall for Colleen for Claire p= + + =, , ; eer day together

days working together

;

12 11 11

12÷ =

Betty and Theresa do of the job each hour Betty does of the job e1

201

60; aach hour

hr

;

;1

201

603

601

602

601

3030 1 30− = − = = ÷ =

Team A does or of a project each day team B does or of1

103

301

152

30( ) ; ( ) tthe project

each day days for both; ;3

302

305

3030 5 6+ = ÷ =

Jane can do or of the job each hour Martha can do or of18

324

112

224

( ) ; ( ) tthe job

each hour hours for both; ;3

242

245

2424 5 4

45

+ = ÷ =


12. 40 mph × 5 hr = 200 mi; 375 mi – 200 mi = 175 mi; 175 mi ÷ 5 hr = 35 mph

13. 4 × 1 hr = 4 clerk hours per 1,200 letters; 1,200 letters ÷ 4 = 300 letters per clerk

hour; (10 × 8) × 300 = 24,000 letters

14.

15. 12,600 total loaves produced ÷ 900 per hr of combined work = 14 hr each baker

worked

16.

17. 1 dime + 1 quarter + 2 pennies + 3 nickels = $0.52; $416 ÷ $0.52 = 800 units;

800 units × 3 nickels per unit = 2,400 nickels

18. 11 hr 27 min 34 sec – 3 hr 15 min 10 sec = 8 hr 12 min 24 sec

19. 5 yd 2 ft 9 in4 1 71 6

410 3 22+1 –3 –1211 yd 1 ft 10 in

20. (24 ft × 15 ft) ÷ 9 = 40 sq yd

(40 sq yd + 4 sq yd) × $36 = $1,584

21.

22. $150 × 10% discount = $15; $150 – $15 = $135 discounted price of rug;

$80 × 15% discount = $12; $80 – $12 = $68 discounted price of coffee table $135 + $68 + $65 = $268 cost before 20% coupon $268 × 20% = $53.60; $268 – 53.60 = $214.40 paid by Mary

6 1 5

60 30 5 712

ft ft from top ft average depth of water

ft ft ft ga

− =

× × ×( ) ll per cu ft gallons= 67 500,

$ , $ , $ , $ ,

$ ,$

25 000 50 000 75 000 150 000

75 00015

+ + =

Martina’s share:00 000

96 000 48 000,

$ , $ ,× =

250 300 350 900

300900

13

13

12 600

+ + =

=

×

loaves

Baker B’s proportion:

, lloaves = 4 200, loaves for baker B


23. 40% + 5% = 45%; 100% – 45% = 55% drove; 140 × 55% = 77 drove 24. 20, 16. Alternately add 8 and subtract 4. 25. 32, 16. Alternately multiply by 4 and divide by 2.


1. A: 2,000 mi ÷ 5 hr = 400 mph B: 2,000 mi ÷ 4 hr = 500 mph B: 1,500 mi ÷ 500 mph = 3 hr A: 400 mph × (1 + 3) hr = 1,600 mi A’s 1,600 mi – B’s 1,500 mi = 100 mi ahead 2. 55 mph + 50 mph = 105 mph; 1,575 mi ÷ 105 mph = 15 hr 3. 9 A.M. to 6 A.M. = 9 hr; 9 × 55 mph = 495 mi; 1,575 mi – 495 mi = 1,080 mi 4. Bus A: 600 miles ÷ 60 mph = 10 hours + 2 hours = 12 hours Bus B: 600 miles ÷ 50 mph = 12 hours The two busses arrive at the same time. 5. Mozelle: 1hr × 30 mph = 30 mi head start Distance left: 150 mi – 30 mi = 120 mi Rate: 30 mph + 20 mph = 50 mph

Time: 120 mi ÷ 150 mph = 522 hr, or 2.4 hr, when Mozelle and Melvin will meet

Melvin’s distance = 522 hr × 20 mph = 48 mi

6. 14 trees + 12 trees = 26 trees per hr; 22 hr × 26 trees = 572 trees

7. 800 + 960 = 1,760 VCRs per day; 39,600 VCRs ÷ 1,760 per day = 2122 days

8. 1,060 + 510 + 1,430 = 3,000 words per min; 3,000 × 60 = 180,000 words per hr

9. Alberta: 1 day = 31 of dress; Allison: 1 day =

21 of dress;

Combined: 1 day = 31 +

21 =

65 of dress; 30 ÷

65 = 36 days

10. Alberta Emery: 30 dresses × 3 days = 90 days Allison Taylor: 30 dresses × 2 days = 60 days 90 days – 60 days = 30 days longer for Alberta Emery

11. 1 day = 41 +

61 +

21 +

51 =

12030 +

12020 +

12060 +

12024 =

120134 ;

134120 =

6760 day


12. Warren and Ted: 1 day = 41 +

61 =

51 of job; 12 ÷ 5 = 2.4 days

13. Sam and Jane: 1 day = 21 +

51 =

107

2.4 days – .7 days = 1.7 days less 14. 16 (ounces in a pound) × 2,000 (pounds in a ton) = 32,000

15. 121 days × 24 hr = 36 hr; 36 hr × 60 min = 2,160 min

16 32 yd × 3 ft = 96 ft; 96 ft × 12 in = 1,152 in

17. 10 ft × 30 ft × 5 ft = 1,500 cu ft; 1,500 cu ft × 721 gal per cu ft = 11,250 gal

18. $0.07 × 11,250 gal = $787.50 4 2 1 14 19. 3 yd 2 ft 2 in –1 –2 –9 1 yd 2 ft 5 in 20. 21 ft × 15 ft = 315 sq ft; 315 sq ft ÷ 9 = 35 sq yd 35 sq yd × $18.50 = $647.50

21. 5 ft × 4 ft × 3 ft = 60 cu ft; 60 cu ft × 7 21 gal = 450 gal

22. Alternately multiply by 4 and divide by 2. Next value is 32. 23. Alternately add 10 and subtract 5. Next value is 25.


1. 50 × 7 = 350; 50 × 5 = 250; 350 + 250 = 600

2. 15 min = 41 hr; 4

41 × 40 = 170

3. ($39.50 + $49.20 + $18.00 + $97.70) ÷ 4 = $51.10 4. 0.30 × $96.80 = $29.04; $96.80 – $29.04 = $67.76


5. (465 – 93) ÷ 465 = 0.80, or 80%

6. 50 × (T + 1) = 55 × T; T = 10

7. 10 hours × 55 mph = 550 miles or 11 hours × 50 mph = 550 miles

8. $1,500 ÷ 2 = $750 (Y); $750 ÷ 2 = $375

9.

10. 30 + 35 = 65; 780 ÷ 65 = 12

11. (18 × 27) ÷ 9 = 54; 54 × $14.25 = $769.50

12.

13. 50 × (T + 2) = 70 × T; T = 5; 3:30 + 5 = 8:30

14.

15. 1,200 ÷ 100 (average rate of two cars combined) = 12 hours

16. (7 + R) × 4 = 60; R = 8

17 (45 + R) × 5 = 400; R = 35

18.

19.

20. 385 ÷ 70 = 5 1/2 hr or 5 hr 30 min; 5 hr 30 min + 45 min = 6 hr 15 min

21. 18 ÷ 4 = 4.5 mph; 7.5 × 8 = 60 hr; 60 × 4.5 = 270

22.

23. $ , $ , $ , $ , ;$ ,$ ,

; $ , $1 000 1 500 3 500 6 0001 0006 000

16

16

1 500 250+ + = = × =

1day:13

12

13

12

56

6 5 1 2job for Thai and job for Anh job days; ; .+ = ÷ =

100 20 80 20 12 123

80 24 313

123

313

5− = ÷ = ÷ = + =; ; ;hr hr

9:30 . . to 4:45 . . is 7 hr 15 min;A M P M 714

45 326 25× = .

400 212

800 212

× +⎛

⎝⎜

⎞

⎠⎟= × =T T T;

$ , $ ,15 00023

22 500÷ =

3 5 9 173

173

1715 300 2 700+ + = × =; ; $ , $ ,Ibn gets


24.

25.

26. 4 gal × 8 pt = 32 pt; 3 qt × 2 pt = 6 pt; 16 oz = 1 pt; 32 + 6 + 1 = 39 pt

27. (35 + 40) × T = 600; T = 8

28. 600 ÷ 75 = 8; 8 × 35 = 280

29.

30. ($2,500 ÷ $5,500) × $1,500 = $681.82

31.

32. ($18,600 – $15,500) ÷ $15,500 = 0.20 = 20%

33. 1,200,000 × 82% (100% – 18%) = 984,000; 984,000 × 30% = $295,200

34. $1,200 ÷ 0.08 = $15,000

35. 5 people can build 2.5 machines in one day (20 ÷ 8); 5 machines ÷ 2.5 = 2 days

36. 231 = 140%; 231 ÷ 1.4 = 165

37. 24 wide × 12 high = 288

38. 17 + 4 + 3.5 = 24.5

39. 100% – 22% = 78%; 1,400 × 78% = $1,092; 100% – 90% = 10%;

$1,092 × 10% = $109.20; $1,528.80 ÷ $109.20 = 14 months

40. 100% – 40% = 60%; $300 × 60% = $180; 180% × 15% = $27

1hour:1

1016

16

110

115

1of job for Alain and of job for Alain Parc+ − =; ; 55 1 15÷ =

$ , $ , $ , $ , ;$ ,$ ,

$ $1 000 1 900 2 500 5 50011005 500

700 140+ + =⎛

⎝⎜

⎞

⎠⎟× =

111060

32560

74560

734

− = =;

$ , $ , $ , ; $ , $ , ;$ ,$ ,

;8 400 3 600 5 040 5 040 2 2 5202 5208 400

310

310

− = ÷ = = ×$$ $300 90=


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