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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?
Rate × Time = Distance
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?
Distance ÷ Rate = Time
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
Distance ÷ Rate = Time
400 mi ÷ 100 mph = 4 hr
How far will train X in example D have traveled when the two trains pass eachother?
Rate × Time = Distance
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:
Distance ÷ Rate = Time
32 mi ÷ 4 mph = 8 hr
Determine the distance her brother walks:
Rate × Time = Distance
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
4 Math in Employment Tests
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× =$ , $
Math in Employment Tests 5
EXAMPLE I
EXAMPLE J
C AT E G O R Y 2C O N C E P T C H E C K
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
÷ =⎛
⎝⎜
⎞
⎠⎟.
6 Math in Employment Tests
EXAMPLE K
EXAMPLE L
C AT E G O R Y 3C O N C E P T C H E C K
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
Math in Employment Tests 7
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÷ =
8 Math in Employment Tests
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
Math in Employment Tests 9
EXAMPLE R
C AT E G O R Y 4C O N C E P T C H E C K
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.
10 Math in Employment Tests
EXAMPLE T
EXAMPLE U
EXAMPLE V
EXAMPLE W
EXAMPLE X
Math in Employment Tests 11
C AT E G O R Y 5C O N C E P T C H E C K
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
12 Math in Employment Tests
EXAMPLE Z
C AT E G O R Y 6C O N C E P T C H E C K
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 _______________
Math in Employment Tests 13
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 _______________
14 Math in Employment Tests
Sample Test 1 (continued)
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 _______________
Math in Employment Tests 15
Sample Test 1 (continued)
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 ______________
16 Math in Employment Tests
Math in Employment Tests 17
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 _______________
18 Math in Employment Tests
Sample Test 2 (continued)
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 _______________
Math in Employment Tests 19
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
20 Math in Employment Tests
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
Math in Employment Tests 21
Sample Test 3 (continued)
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
22 Math in Employment Tests
Answers
21. _____
22. _____
23. _____
24. _____
25. _____
26. _____
27. _____
28. _____
29. _____
30. _____
Sample Test 3 (continued)
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% % % %
Math in Employment Tests 23
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
+ = ÷ =
24 Math in Employment Tests
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
Math in Employment Tests 25
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.
Answers and Solutions to Sample Test 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
26 Math in Employment Tests
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.
Answers and Solutions to Sample Test 3
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
Math in Employment Tests 27
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
28 Math in Employment Tests
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=
Math in Employment Tests 29
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